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EDITED BYJ. H. MUIRIIEAD, LL.D.
KANT'S METAPHYSIC
OF EXPERIENCE
By the Same Author
THE GOOD WILL
A STUDY IN THE COHERENCE THFORY
OF GOODNESS
(Library of Philosophy)
"An extremely valuable and suggestive contribution
to ethical philosophy " — Iltbbe rt Journal
"A philosophical work of outstanding strength and
wide thinking ... A remarkable piece of thinking and
of expression " — Birmingham Post
KANT'S METAPHYSIC
OF
EXPERIENCE
A COMMENTARY ON THE FIRST HALF OF THE
KRITIK DER REINEN VERNUNFT
By
H. J. PATOM,M.A.,D.LiTT.(OxoN)
Professor of Logic and Rhetoric in the I 'nnemlv of Gla^mn,
sonttinic Felloe of 7 fit Qucm'* Collet, ,nthe I'nnenity of 0\ford
IN Two VOLUMES
VOLUME TWO
LONDON
GEORGE ALLEN & UNWIN LTD
MUSEUM STREET
FIRST PUBLISHED IN 1936
All rights reserved
PRINTED IN GREAT BRITAIN BY
UNWIN BROTHERS LID, WOKING
CONTENTS
VOLUME TWO
BOOK VII
THE SCHEMATISM OF THE
CHAPTER
XXXII
XXXIII
XXXIV
CATEGORIES
. \ *
3.
4.
5.
CATEGORY AND SCHEMA
1. A summary of Kant's argument 17
2. Importance of the chapter on Schematism 20
The transcendental Doctrine of Judgement 21
Subsumption under the categories 24
The difficulty of subsumption under the
categories 25
6. The transcendental schema 28
7. The restriction of the category through the
schema 3 1
8. The schema in general 32
9. Special characteristics of the transcendental
schema 37
10. Summary of conclusions 39
THE TRANSCENDENTAL SCHEMATA
1. Category and schema 42
2. The schema of quantity 44
3. The schema of quality 48
4 . The schemata of relation 52
5. The schemata of modality 56
6. Kant's summary 60
7. The number of the schemata 63
THE SIGNIFICANCE OF THE SCHEMA
i. Subsumption and syllogism 66
Category and schema 68
The transcendental synthesis of imagination 71
The schematism of the understanding 73
Value of Kant's doctrine 75
6. The possibility of reconstruction 77
2.
3.
4.
5.
CHAPTER
XXXV
CONTENTS
BOOK VIII
THE PRINCIPLES OF THE
UNDERSTANDING
PAGE
THE SUPREME PRINCIPLE OF SYNTHETIC
JUDGEMENTS
1. The nature of Kant's argument 81
2. The principle of analytic judgements 83
3. Different kinds of synthetic judgement 84
4. The * third thing' 86
5. The possibility of experience 90
6. The principle of all synthetic judgements 94
XXXVI THE PRINCIPLES OF THE UNDER-
STANDING
1. Different kinds of principle 97
2. The Principles of the Understanding 98
3. Intuitive and discursive certainty 100
4. The proof of the Principles 103
5. Modern science and the Principles of the
Understanding 106
BOOK IX
THE MATHEMATICAL PRINCIPLES
XXXVII THE AXIOMS OF INTUITION
1 . The Principle of the Axioms 1 1 1
2. The proof in the first edition 112
3. The proof in the second edition 1 14
4. Successiveness of synthesis 117
5. Intuition and object 119
6. The doctrine of the Aesthetic 12 1
7. The axioms of geometry 124
8. Quantitas and quantum 125
9. The formulae of arithmetic 129
10. The application of mathematics to objects
of experience 131
CONTENTS 9
CHAPTER PAGE
XXXVIII THE ANTICIPATIONS OF SENSE-PERCEP-
TION
1. The Principle of the Anticipations 134
2. The proof in the first edition 139
3. The proof in the second edition 141
4. Intensive quantity 144
5. The synthesis of quality 147
6. The causality of the object 150
7. The doctrine of continuity 152
8. Empty space and time 154
9. Kant's conclusion 155
BOOK X
THE ANALOGIES OF EXPERIENCE
XXXIX THE PRINCIPLE OF THE ANALOGIES
1. The formulation of the Principle 159
2. The argument in the first edition 161
3. The modes of time 163
4. The argument in the second edition 167
5. The assumptions of the argument 170
6. The conclusion of the argument 173
7. The general character of the proof 175
XL THE SPECIAL CHARACTER OF THE
ANALOGIES
1. The Analogies are regulative 178
2. The first meaning of * Analogy* 179
3. The second meaning of * Analogy' 180
XLI THE FIRST ANALOGY
1. The Principle of permanence 184
2. The argument of the first edition 186
3. The argument of the second edition 190
XLI I SUBSTANCE
1. In what sense is apprehension successive? 192
2. The permanent and time-determination 195
3. The permanence of time 199
VOL. II A*
io CONTENTS
CHAPTER PAGE
XLII SUBSTANCE— continued
4. Substratum and substance 201
5. Can substance be perceived? 204.
6. The quantum of substance » 207
7. Material substance 209
8. The conservation of matter 213
9. The empirical criterion of substance 215
10. The concept of change 217
1 1 . Science and experience 218
XLIII THE SECOND ANALOGY
1 . The Principle of causality 22 1
2. The six proofs of causality 224
3. The first proof 225
4. The object and its temporal relations 230
5. The second proof 238
XLIV THE SECOND ANALOGY (CONTINUED)
1. The third proof 245
2. Origin of the concept of causality 248
3. The fourth proof 249
4. The fifth proof 253
5. The sixth proof 257
XLV THE ARGUMENT FOR CAUSALITY
1. Kant's presuppositions 262
2. Kant's argument 263
3. Objective and subjective succession 265
4. The conditions of experience 268
5. The process to experience 271
6. Causality and time 273
7. Particular causal laws 275
8. The transcendental synthesis of imagination 278
XLVI CAUSALITY AND CONTINUITY
1. Kant's concept of causality 281
2. The successiveness of cause and effect 283
3. The continuity of change 284
4. The law of continuity 288
5. Continuity as the formal condition of appre-
hension 289
CHAPTER
XLVII
XLVIII
THE
CONTENTS ii
PAGE
THE THIRD ANALOGY
1. The Principle of interaction 294
2. The meaning of coexistence 297
3. The proof in the second edition 298
THE THIRD ANALOGY (CONTINUED)
1. The proof in the first edition 310
2. Interaction and sense-perception 316
3. Interaction and the unity of apperception 319
4. Interaction and coexistence 324
5. Kant's proof of interaction 329
BOOK XI
POSTULATES OF EMPIRICAL
THOUGHT
XLIX POSSIBILITY
1. The Principles of possibility, actuality, and
necessity
2. The interdependence of the categories of
modality
3. Thought and its object
4. The First Postulate
5. Possibility in relation to different types of
concept
6. The possibility of experience
L ACTUALITY AND NECESSITY
1. The Second Postulate
2. The Third Postulate
3. Some traditional conceptions
4. Leibnizian possibility
5. The meaning of the word 'Postulate*
6. The competence of Kant's exposition
BOOK XII
TRANSCENDENTAL IDEALISM
LI EMPIRICAL REALISM
1. Problems of the Critical Philosophy
2. Descartes and Berkeley
3. The Refutation of Idealism
335
339
342
345
354
357
362
364
366
368
370
375
376
377
12 CONTENTS
CHAPTER PAGE
LI EMPIRICAL REALISM— continued
4. Turning the tables on idealism 381
5. Empirical realism and transcendental idealism 384
6. Sense and imagination ' 385
LIT INNER SENSE AND SELF-KNOWLEDGE
1. The paradox of inner sense 387
2. Understanding, imagination, and inner sense 390
3. Illustrations of Kant's doctrine 393
4. Inner sense and the phenomenal self 398
5. Apperception and self-knowledge 401
LIII SELF-KNOWLEDGE AND KNOWLEDGE
OBJECTS
1. The existence of the self 404
2. The existence of the object 406
3. Reality of inner and outer sense 410
4. Ideality of inner and outer sense 411
5. Time and inner sense 413
6. Inner sense and the phenomenal self 415
7. Appearance and illusion 416
8. Difficulties of inner sense 418
9. A rough analogy 424
LIV THE TRANSCENDENTAL USE OF CON-
CEPTS
1. Empirical realism and transcendental idealism 426
2. The empirical use of concepts 427
3. The transcendental use of concepts 429
4. Mathematical concepts 431
5. The categories 432
6. Kant's conclusion 435
LV NOUMENON AND TRANSCENDENTAL
OBJECT
1. Phenomena and noumcna 439
2. Alleged knowledge of noumena 440
3. The transcendental object 442
4. Origin of belief in noumcna 445
5. Kant's conclusion in the first edition 447
CONTENTS 13
CHAPTER PAGE
LVI PHENOMENA AND NOUMENA
1. Categories and knowledge of noumena 450
2. The positive and negative meaning of
'noumcnon' 452
3. Can we know the thmg-m-itself ? 453
4. Thought and intuition 455
5. The concept of 'noumenon' as a limiting
concept 456
6. Understanding not limited by sensibility 458
7. The union of understanding and sensibility 459
8. The limits of knowledge 460
EPILOGUE 463
GENERAL INDEX 465
•INDEX OF ANNOTATED PASSAGES 505
BOOK VII
THE SCHEMATISM
OF THE CATEGORIES
CHAPTER XXXII
CATEGORY AND SCHEMA
§ i. A Summary Account of Kant's Argument
Kant believes himself to have proved generally that all
objects of experience must conform to the pure categories;
that is to say, the given manifold must be combined in accor-
dance with the principles of synthesis present in judgement as
such. He believes himself to have shown also, though still in
the most general way, that the required combination is imposed
upon the given manifold by the transcendental synthesis of
imagination through the medium of the pure manifold of time.
We should now expect him to show that the transcendental
•synthesis of imagination, if it is to hold together the given
manifold in one time, must combine the manifold in certain
definite ways, and that each of these ways conforms to, or is
an example of, the principle of synthesis conceived in one of
the pure categories. Until this is done, we have had no account
of the details which alone can make his general doctrine fully
intelligible.
In a sense this task is performed in the Analytic of Principles,
with which we have now to deal. Kant, however, treats the
whole question primarily from the side of the object, and tells
us what are the characteristics which objects must have if the
manifold is combined in one time : his references to the subjec-
tive machinery of cognition, and especially to the transcendental
synthesis of imagination, are only incidental.1 His complicated
explanation is certainly careless in terminology, and possibly
1 He assumes that the unity of time is imposed by the transcendental
synthesis of imagination, and simply asks what characteristics objects
in time must have, if time is to have unity. In the Aesthetic Kant
already argued that time must be one, but the unity of time is possible
only through synthesis, as is indeed implied in the Aesthetic itself,
though not made explicit; compare B 160 n. I take it that apart from
the unity of the time in which all objects are, the unity of apperception,
and consequently experience itself, would be impossible.
1 8 THE SCHEMATISM [XXXII § i
confused in thought. The difficulties in following it are very
great; and it may perhaps help the reader, if I try to give
first of all, with special reference to one particular category,
a summary and very rough account of what he is doing. ,
We are supposed to know that every object of experience
must conform to the pure category of ground and consequent ;
that is to say, the given manifold must be combined as grounds
and consequents. We manifestly do not apprehend grounds
and consequents by sense; but Kant believes we can find
something corresponding to ground and consequent in the
objects of our experience, if we consider that all objects must
be combined in one time. What he finds is 'necessary succes-
sion'; that is, invariable succession in accordance with a rule
— such that if A is given in time, B must follow.
The difficulties of this view and the question of its truth
or error do not at the moment concern us. 'Necessary succes-
sion' is supposed to be the characteristic, or way of combination,
which must be found in all objects so far as their qualities
change in one objective time. This characteristic is called the
'transcendental schema',1 and it is imposed upon the manifold
by the transcendental synthesis of imagination.2 In virtue
of the transcendental schema we can apply the pure category
of ground and consequent to objects of experience; for if A
must always be followed by B, we can regard A as the ground
and B as the consequent.
If this is so, we can understand how the pure category
must have objects to which it applies ; for all objects must be
in one time. The pure category of ground and consequent
1 It should be noted that Aristotle also spoke of rd a ^r\ /tat a ra>v
KaTiyyoptcov, and this may possibly have suggested Kant's employment
of the word; but I do not think that Aristotle's usage throws any
light on that of Kant.
2 See A 142 = B 81 : * The transcendental schema is a transcendental
product of the imagination*. In this preliminary statement I ignore
the difficulty that Kant sometimes speaks as if a schema were a rule
of imagination rather than a characteristic imposed by imagination.
What I describe as 'characteristics' imposed by the transcendental
synthesis are characteristics belonging to the manifold as combined
in certain ways which are necessary if time is to possess unity.
XXXII § x] CATEGORY AND SCHEMA 19
is by itself empty: we cannot understand by mere examination
of the category whether there are any objects given to which
it must apply. Only when we consider it in the light of the fact
that all objects must be in one time, can we understand that
it must apply to objects so far as the qualities of these objects
change in time. In so doing we find that the category as applied
to objects in time has a more limited and also a more precise
significance ; for it then becomes the concept of a ground which
always precedes its consequent in time. In other words it
becomes the schematised category of cause and effect.1
Kant will argue in the Second Analogy that all change in
objects is necessary change, or necessary succession, and so
must fall under the category of cause and effect.2 In the chapter
entitled 'The Schematism of the Pure Concepts of the Under-
standing' he is not concerned with showing that necessary
succession, or any other transcendental schema, is a necessary
" characteristic of objects. His aim is merely to tell us what
is the transcendental schema corresponding to each pure
category ; and he expects us to recognise that the transcendental
schema described does fall under the pure category. Such
recognition is a matter of judgement.
Thus for Kant the transcendental schemata3 are universal
characteristics which, he hopes to show later, must belong to
all objects as objects in time. These universal characteristics
belong to objects, not as given to sensation, but as combined1
1 1 discuss later whether it is necessary to distinguish the schematised
category — a phrase which Kant himself never uses — from the transcen-
dental schema. See Chapter XXXIV § 2,.
2 If so, it must fall also under the pure category of ground and
consequent — the genus of which cause and effect is a species.
3 The schemata are transcendental (i) as imposed by the mind,
and (2) as universal and necessary conditions of all objects in time.
It should be understood, as always, that such a condition is not any-
thing temporally prior to the object: it is rather an element in, or
characteristic of, the object, and without it the object would not be
an object for us.
4 This combination is not only a combination of the manifold of
each object: it is also a combination of different objects with one
another m the system of nature.
20 THE SCHEMATISM [XXXII § 2
by the transcendental synthesis of imagination in one time.
What we have to do at present is to learn what these tran-
scendental schemata are, and to see, if we can, whether
each transcendental schema falls under its corresponding
category.
§ 2. Importance of the Chapter on Schematism
In considering Kant's account of the transcendental sche-
mata we must not allow ourselves to be put off by the obscurity
of his exposition. However artificial his view may appear to
be, it is an essential part of his argument.1 If we assume pro-
visionally that the pure categories really are derived from the
form of thought, it is absolutely vital to discover whether
objects, as combined by imagination under the form of time,
must possess characteristics which fall under the categories.
If we reject ab initio such derivation of the pure categories,
we must still discover what plausibility there is in his view
of the relation between the necessary characteristics of objects
in time and the pure categories ; otherwise we shall fail to under-
stand why Kant thought as he did, not merely in this particular
chapter, but throughout the Kritik.
Even at the worst the chapter on Schematism has more
than the value of throwing light on Kant's errors. If we reject
his derivation of the categories, this chapter acquires a new
and special importance: it suggests the possibility of making a
fresh start, and of justifying the categories from the nature
of time without any reference to the forms of judgement.
The Kantian doctrine might perhaps be reformed and re-
established, if we could show that the categories are implicit
in our knowledge of time, and are principles of synthesis
without which no object could be known to be an object in
time.
Whatever be our view of the derivation of the categories,
1 Kant himself says with justice that it is an important, and indeed
absolutely indispensable, though extremely dry, investigation; and
he connects it, as I do in Chapter XXXIII, with the account of
Phenomena and Noumena in the Kritik. See Prol. § 34 (IV 316).
XXXII §3] CATEGORY AND SCHEMA 21
the chapter on Schematism is essential to an understanding
of the Critical Philosophy.1
§3. The Transcendental Doctrine of Judgement
Formal Logic in dealing with concepts, judgements, and
inferences considers only their form, and is concerned with
the conditions of formal validity. It does not, and it cannot,
give us instructions about how we can make true judgements,
and still less does it tell us what true judgements we can make.2
If by the power of judgement3 we mean the power of deciding
whether or not particular objects fall under the concepts we
possess, this power is a special gift which cannot be taught,
though it can be improved by exercise and helped by examples.4
Transcendental Logic is in a different position. The concepts
or categories with which it deals are a priori, and therefore
the objective validity, not only of the categories in general,
but of each separate category, must be established a priori.
We must be able to show not only what are the pure categories,
but also what is the 'case'6 to which each applies. This means
1 As it is far from easy to follow Kant's general account of the
transcendental schema, the reader who wishes to get on with the
argument in detail may find it advantageous to omit the rest of this
chapter on a first reading.
2 If concepts are supposed to be given, Formal Logic can tell us
how to make analytic judgements, but these are true only if there
is an object corresponding to the given concepts.
3 It is unfortunate that in English we have only one word for
'Urteir (judgement) and ' Urteilskraft* (the power of judging).
4 Kemp Smith, Commentary, p. 333, asserts that Kant is taking
advantage of the popular meaning of judgement. However popular
this meaning may be, it has a philosophical history going back, I
believe, to the Aristotelian doctrine of opoi (ev rfj alaOrjaei r\ Kplaig.
Eth. NIC. noQb.). It is in any case one of the most widespread and
essential doctrines of the Critical Philosophy. Compare, for example,
Anthr. §§ 40-4 (VII 196-^01); K.d.U. Ill, IV, § 35, § 77, etc. (V 177,
1 79, 2 86-7, 407, etc.) ; K.d.p. V. (V 67) ; Met. d. Sitten, Tugendlehre § 1 3
(VI 438) ; Log. § 81 (IX 131) ; Letter to Prince von Belozelsky (XI 331).
6Ai35 — 1*174. The word 'case1 (Fall) seems to imply a reference
to individual objects ; but since the case is to be shown a priori, it
must be shown, not by an appeal to empirical sense-perception, but
by an appeal to the conditions under which objects must be given.
22 THE SCHEMATISM [XXXII § 3
that we must be able to exhibit in universal but adequate
marks1 the conditions under which objects can be given2
in conformity with the categories.
These 'conditions' may be described as universal charac-
teristics3 which must belong to all objects known by means
of our senses. These characteristics are supposed to be found
in objects as given to sense, and for this reason they are called
'sensuous conditions'4 or 'conditions of sensibility'.5 Strictly
speaking, these characteristics are not to be found in the
manifold merely as given to sense under the form of time.
They belong to the manifold as given to sense under the form
of time and as combined in one time by the transcendental
synthesis of imagination.6 In his statement of the problem
Kant insists only that certain necessary characteristics must
belong to objects as sensed, if the pure categories are to apply
a priori to sensible objects.
These universal and necessary characteristics of sensible
objects are the transcendental schemata. Apart from these
1 ' Kennzcichen1 ; see A 136 — B 175. I do not think that the 'marks'
are to be regarded as separate from the Conditions' exhibited m the
marks.
2 A 136 — B 175. This is a relative use of the word 'given'. Objects
are given absolutely under the form or condition of time. They are
given relatively to the understanding so far as the given manifold
is combined in one time through the transcendental synthesis of
imagination. Compare Chapter XXVIII § n.
3 Compare A 147 = B 186 where the 'sensuous determination of
permanence* is given as an example of such a 'sensuous condition*.
These necessary and universal characteristics of objects are also
conditions of objects, for without them there could be for us no
objects at all.
4 A 136 = B 175.
6 A 139 = B 179 ; compare also A 140 = B 179 and A 146 = B 186.
They are conditions of sensibility because they are necessary to the
unity of time (and space), time (and space) being the more ultimate
conditions of sensibility.
6 Kant is contrasting the object as thought abstractly in the pure
category with the concrete individual object which is given; and at
the moment he postpones all reference to the transcendental synthesis
of imagination, and concentrates on the fact that the object must
be sensed.
XXXII § 3] CATEGORY AND SCHEMA 23
the pure categories would be without content1 or meaning;2
that is to say, they would not refer to any assignable object.
Transcendental Logic must therefore be able to give us
what Kant calls a Transcendental Doctrine3 of Judgement.
It must tell us what are the transcendental schemata, the neces-
sary and universal characteristics of sensible objects in virtue
of which the pure categories can be applied.4 It must also
tell us what are the synthetic a priori judgements which arise
when we apply the pure categories to sensible objects in virtue
of the transcendental schemata. These synthetic a priori
judgements are called the 'Principles of the Pure Understand-
ing'— and they are the conditions of all other a priori knowledge.
In order to justify these judgements we must show that the
transcendental schemata really are universal and necessary
characteristics of all objects given to our senses.
" *A 136 = B 175.
2 A 147 = B 1 86. The content or meaning of concepts involves
for Kant a reference to actual, or at least possible, objects, and in
the case of a priori concepts a necessary reference to such objects.
Apart from this the pure category is merely a logical form, a concept
of the form of judgement or of the unity of ideas in j'udgement. If we
regarded the pure category as somehow applying to objects, we could
not indicate the determinations of the thing to which the category
was supposed to apply. Compare A 88 — B 120, A 247 = B 304,
and many other places.
3 'Doktrin'; see A 136 = B 175. It might also be called a 'canon*
(A 132 = B 171) or a 'Kritik* (A 135 --=-- B 174) of Judgement. A
* doctrine' seems to aim at the extension (Erweiterung) of our cognitions,
a Kntik at their correction (Benchtigung)\ see A 12 — - B 26 and
A 135 — B 174. I suppose Kant uses the word 'doctrine' here because
we can point out, not merely the conditions of our synthetic a priori
judgements, but the actual synthetic a priori judgements which we
can make: he does not mean that we can extend the use of under-
standing beyond the limits of possible experience. Perhaps the word
is used more loosely for 'a demonstrated theory* in which everything
is certain a priori; see Log. Einl. I (IX 14-15) and A 54 = B 78. In
A 796 = B 824 a 'canon* is defined as 'the sum total of the a priori
principles of the correct employment of certain powers of knowledge* ;
compare Log. Einl. I (IX 13).
4 Kant says 'the sensuous condition* under which alone the cate-
gories can be used. The following clause shows that he has in mind
all such conditions.
24 THE SCHEMATISM [XXXII § 4
The whole Transcendental Doctrine of Judgement may also
be called the Analytic of Principles, since the judgements
with which it is primarily concerned are the Principles of the
Pure Understanding. It is divided into two parts. The first
part is concerned with the transcendental schemata, and is
entitled 'The Schematism of the Pure Concepts of the Under-
standing*. The second part gives us the proof of the Principles,
and is entitled 'The System1 of all Principles of Pure Under-
standing'.2
§ 4. Subsumption under the Categories
The power of judgement is a power to subsume under
rules, that is, to decide whether anything stands under a given
rule or not.3 All concepts, according to Kant, serve as rules,4
and we can say that in subsumption we decide whether anything
stands under a given concept or not ; indeed this is the ordinary
meaning of subsumption.5 Formal Logic manifestly cannot
1 The word 'system* implies an organic whole, not a mere aggregate ;
compare A 832 = B 860.
2 The proof of the Principles is in the main directed to show that
the transcendental schemata must be characteristics of all objects
which are known to be in one time.
3A 132 = B 171 and A 133 = B 172. Kant's reference in brackets
— 'casus datae legis* — suggests that he has in mind the procedure of
the law-courts. 4 A 106.
5 Kant, in his Formal Logic, extends the meaning of the word
subsumption to cover the minor premise of hypothetical and disjunc-
tive, as well as of categorical, syllogisms. The minor premise is said
to subsume a cognition under the condition of the universal rule
asserted in the major premise; see Log. § 58 (IX 120-1) and A 304
= B 360. Kemp Smith, Commentary, p. 336, seems to base on this
the view that Kant is really concerned with subsuming under rules as
opposed to concepts. I do not think this is so. In the categorical
syllogism, All men are mortal, Caius is a man, therefore Cams is
mortal, we subsume in the minor premise our cognition Caius under
the concept of man, which is the condition of mortality. Compare
A 322 = B 378, which is, however, obscure. Kemp Smith translates
as if we subsumed the predicate (mortal) under its condition (man).
This seems to me impossible; and I agree with Erdmann that we
subsume Caius under the condition 'man* which is taken in its whole
extension in the judgement 'All men are mortal'. Further remarks
on the syllogism will be found below; see Chapter XXXIV § i.
XXXII § 5] CATEGORY AND SCHEMA 25
teach us how to do this, since it ignores the matter given to
thought. Transcendental Logic can, however, show that objects
must fall under the categories, since it takes into account the
pure ijianifold of time and the transcendental synthesis of
imagination whereby the given manifold must be combined
in one time.1
Granted Kant's pre-suppositions, it seems to me correct
to speak either of applying the categories to objects or of sub-
suming objects under the categories. The main objection to
this usage seems to rest on the view that a category cannot be
used as a predicate and cannot have instances.2 But if the cate-
gories could not be predicates of possible judgements, and
could not apply to instances,3 they would not be concepts at
all. Such a view seems to me remote from the Kantian
doctrine.
I need hardly add that if Kant had used the word 'sub-
sumption' for the activity of the transcendental imagination in
combining the given manifold in accordance with the prin-
ciples of synthesis conceived in the pure categories, he would
indeed be guilty of misusing a technical term. I see no trace
of such a usage in the chapter on Schematism. Kant is here
concerned with sensible objects as described in the Transcen-
dental Deduction, that is, as combined in one time (and space).4
§ 5. The Difficulty of Subsumption under the Categories
Whenever we subsume an object under a concept, that is,
whenever we judge the object to be an instance of a universal,
there must be a certain homogeneity between the object
1 Compare A 55 -« B 79-80 and A 76-7 = B 102.
2 See Chapter XV § 3, and compare Kemp Smith, Commentary,
P- 335, etc.
3 The concepts of the forms of judgement have of course instances
in the judgements which manifest these forms ; compare A 239 — B 298.
But the pure categories are concepts whose instances must be objects
— objects whose manifold is combined in accordance with the principles
of synthesis present in the forms of judgement; compare B 128.
4 Further difficulties in regard to subsumption will be dealt with
later. See Chapter XXXIV § i.
a6 THE SCHEMATISM [XXXII § 5
and the concept. This is obvious enough in the case of empirical
concepts, which are due to abstraction from given intuitions;
in them we conceive or think common marks belonging to this
and other objects given in intuition. It is also obvious even in
the pure concepts of mathematics : the mathematical concept of
circle, for instance, can have an example constructed in pure
intuition; and since this pure intuition is homogeneous (as
regards its circularity) with the empirical intuitions from which
we abstract the concept of plate, there is no difficulty in saying
that a plate is an imperfect instance of a mathematical
circle.1
There may be some doubt as to the exact interpretation of
this example ; but Kant's main point is that whether a particular
concept is empirical or pure — whether it is derived by abstrac-
tion from empirical intuition, or whether pure intuitions are
constructed in accordance with it — there is always a corre-
sponding intuition which entitles us to apply the concept to
objects of sensuous experience. In the case of the categories
there is no corresponding intuition, whether empirical or pure.2
Hence the categories appear not to be homogeneous with the
sensible objects subsumed under them, inasmuch as none of
1 A 137 = B 176. I have here expanded — in the light of what
follows — a statement which is too brief to be clear. Kant says that the
circularity which is thought m the empirical concept of plate can
be intuited in the pure concept of circle, and gives this as his reason
for the homogeneity of the two concepts. His statement is obscurely
expressed, and he seems to make no difference between 'an object'
and 'the idea (or even the concept) of an object'; but I take his point
to be that even a pure mathematical concept has a corresponding
intuition', the category, as he goes on to show, has none. Hence the
pure mathematical concept can have a certain homogeneity with
objects given to empirical intuition, and with the empirical concepts
of these objects; see A 138 = B 177.
Vaihmger emends Kant's statement about circularity, by transposing
'thought' and 'intuited*. This does not remove the obscurity, and it
makes the distinction between the empirical concept of plate and the
pure mathematical concept of circle here irrelevant; but in any case
Kant's main point is that there must be homogeneity between the
concept and the object (or concept of the object) which is subsumed
under it. 2 Compare Chapter XVI §§ 8-9.
XXXII § 5] CATEGORY AND SCHEMA 27
the intuitions through which objects are given corresponds in
any way to the categories.1
In spite of the objections2 raised to this doctrine Kant's
contention seems to me to be sound. It is obviously so, if we
remember that for him the pure categories are the forms of
judgement as applied to intuitions ; but even if we ignore this,
and consider the categories only as schematised, it is hardly
less obvious, at any rate as regards the categories of relation
and modality. We can see plates in empirical intuition, and we
can construct circles a priori in pure intuition, but we cannot
see causes as causes,3 nor can we construct them a priori.41
This is a real difference which it seems to me idle to deny.
Nor is the problem solved by saying that the category is the
form and the intuition the matter, and that these have no
existence apart from one another. The forms of intuition are
.space and time, and the categories are forms, not of intuition,
but of thought. No doubt it is absurd to suggest that we are
first of all aware of unrelated sensations, and then subsume
them under the categories; but to interpret Kant's doctrine
as asserting such a temporal succession seems to me unjusti-
fiable. The categories are present whenever we are aware of
an object (as opposed to a mere sensation) ; but this fact does
not do away with Kant's problem. Indeed it is just this fact
which raises the problem how the categories as forms of thought
can, and must, determine all objects given to sensuous intuition.
1 In order to avoid misconceptions it may be said at once that
although the intuitions, considered as given intuitions, are not homo-
geneous with the category, yet the intuitions as combined to form
objects in one time are homogeneous with the category.
2 Some of these objections rest on the view that Kant supposed
us to be aware of the pure categories and the sensuous intuitions in
separation before we are aware of them in conjunction. Supported
though this is by many even of the best commentators — for example
by Caird and even at times by Riehl — I do not believe that Kant
entertained such an idea for a moment. 3 Compare A 137 = B 176.
4 The difference is not so sharp in the case of the categories of
extensive and intensive quantity, where Kant himself insists we have
'intuitive evidence'; see A 160-1 = B 200, A 162 — B 201, A 180
= B 223.
*8 THE SCHEMATISM [XXXII § 6
If we are to understand Kant we must allow him to state
his problem in his own way, and we must try to see what the
problem is. We must also remember that Kant tends to state
his problems sharply without giving any indication /)f his
proposed solution.1 In this case we already know the general
lines which his solution must take; for we know, from the
Transcendental Deduction, that the categories must apply
to all objects because the transcendental synthesis of imagina-
tion combines the manifold in one time. This does not mean
that the chapter on Schematism is superfluous. We have still
to show — the argument cries out for it — that the combination
of the manifold in one time imposes on all objects certain
universal characteristics corresponding to the separate categories.
§ 6. The Transcendental Schema
Kant puts forward the suggestion that there must be a third'
thing to connect the category and the intuition. This mediating
idea must be pure, for otherwise the connexion would be
empirical ; and it must be homogeneous both with the category
and with the intuition. To be homogeneous with the category,
it must be intellectual; that is, it must be a product of spon-
taneity or synthesis (which is the general characteristic of the
understanding).2 To be homogeneous with the intuition, it
must be sensuous; and to be both sensuous and yet pure, it
must be connected with the form of intuition. This mediating
idea is the transcendental schema.3
In his search for the transcendental schema Kant turns,
as we should expect, to time as the form of intuition.4 The
1 Compare Chapter XVII § i.
2 Kant's phrase is obscure, and the meaning seems to me uncertain.
What he says in the following paragraph suggests that to be homo-
geneous with the category, it must be universal and must rest on
an a priori rule. It can be this only if it is the product of the trans-
cendental synthesis of the imagination.
3 A 138 = B 177. This description connects it with the transcen-
dental synthesis of imagination. Compare especially 6151 and B 162 n.
4 The reason why Kant neglects space m this chapter is no doubt
that for him space is only the form of outer intuition, while time,
though it is the immediate condition (or form) of inner intuition,
XXXII § 6] CATEGORY AND SCHEMA 29
pure category is a concept of the pure synthetic unity of a
manifold in general]1 and consequently the pure synthetic
unity of the manifold of time must fall under it,2 as the species
must fall under the concept of the genus.3 Time, however,
not only contains in itself a manifold of pure intuition; it is
also the form of inner sense, and so is the formal condition of
the combination of all ideas whatsoever.4 I take Kant to mean
that the empirical manifold, whatever else it is, must be temporal
and must have the general characteristic of being combined
in such a way that it accords with the unity of time.5
This doctrine Kant develops with reference to what he calls
a 'transcendental time-determination'.6 Unfortunately he does
not explain this phrase ; it must, I think, mean, not a deter-
mination or characteristic of time itself, but a characteristic
which must belong to objects so far as they are temporal and
are combined in one time.
A transcendental time-determination is said to be homo-
geneous with the category inasmuch as it is universal and
rests on an a priori rule. Its universality is presumably the
complete universality of the categories inasmuch as it must
belong to all objects ; for all objects of human experience are
is also the mediate condition of outer intuition, and so can be described
as 'the formal a priori condition of all appearances in general'; see
A 34 = B 50 and compare Chapter VII § a. But space as well as
time must have its part in the schematisation of the categories, and
Kant has to take space into account when he deals with the Principles.
1 A 138 = B 177. In itself it has no reference to the manifold of
human intuition as such, nor even to the pure manifold of space and
time, but the synthetic unity of space and time must be a particular
case of the synthetic unity of intuition in general ; compare B 144-5.
2 Kant says in A 138 = B 177 that the category 'constitutes*
(ausmacht) the unity of time (or the unity of the transcendental
time-determination — which, I take it, amounts to pretty much the
same thing). In B 144 the unity is said to come into the intuition
by means of the category through understanding — intuition here
being intuition in general. See also B 160-1.
3 Compare Chapter XIII § 6. 4 Compare A 99.
5 The most obvious example of this is that if time has extensive
quantity the manifold in time must also have extensive quantity.
6 ' Zeitbestimmung* \ A 138 = B 177.
30 THE SCHEMATISM [XXXII § 6
in time.1 A transcendental time-determination is also homo-
geneous with appearances, or empirical intuitions of objects,2
inasmuch as every empirical intuition occurs in time and lasts
through time.3
Hence the transcendental time-determination is the mediating
idea which enables us to subsume4 appearances (or objects)
under the category. As such it is identified with the transcen-
dental schema which we have been seeking.
All this is difficult and is hardly intelligible apart from the
examples which follow ; but I think we can understand that if
time — and I would add space — is to be known as a unity,
certain ways of combination must be found in objects the
manifold of which is combined in one time (and space).5
We can also understand that such a way of combination might
be an example of a more general way of combination, or
principle of synthesis, thought in the pure category. We may
be able to find something homogeneous with the categories,*
not in intuitions themselves, but in the ways in which intuitions
must be combined so as to form objects in one time (and space),
or in the characteristics which objects must have if intuitions
are combined in these ways.
1 The sense in which it rests on an a priori rule is more difficult ;
perhaps Kant means that it is a product of the transcendental synthesis
of imagination, such synthesis being governed by an a priori rule.
The categories themselves, it should be noted, cannot be said to rest
on a priori rules: on the contrary they may be described as the a
priori rules in accordance with which the transcendental synthesis
of imagination works.
2 Kant, I think, has in mind, not the isolated appearance such as
'this red', but the whole appearance or intuition of, for example,
a house.
3 Kant says time is 'con tamed* in every empirical idea.
4 This suggests that it is the middle term in the categorical syllogism ;
but see Chapter XXXIV § i.
5 We may put it m this way : that the empirical synthesis of appre-
hension must be subjected to a transcendental unity — the unity of
time — and ultimately to the unity of apperception ; compare A 108.
XXXII § 7] CATEGORY AND SCHEMA 31
§ 7. The Restriction of the Category through the Schema
The transcendental schemata enable us to apply the cate-
gories to sensible objects given under the form of time, but
they also restrict the application of the categories to such
objects. The Transcendental Deduction has already shown
us that the categories admit only of an empirical, and not of
a transcendental, use;1 that is to say, they apply only to objects
of possible experience, not to things as they are in themselves.
Kant reminds us2 that concepts can have no meaning3 unless
an object is given for them, or at any rate for the elements
of which they are composed; hence we cannot legitimately
apply concepts to things as they are in themselves without
considering whether such things are given to us and how they
are given. For human beings things are given only as they
modify or affect our sensibility and so appear to us under
the forms of sensibility, that is to say, as temporal and spatial.
The categories, if they are to apply to given objects, must con-
tain within themselves more than the principles of synthesis
present in the form of thought as such ; for the form of thought
has in itself nothing to do with the way in which objects are
given. The categories must also contain in themselves formal
conditions of sensibility, which Kant identifies with the formal
conditions of inner sense. Only so can they contain the universal
condition under which alone the categories can be applied to
objects. Such is the general teaching of the Transcendental
Deduction ; and we have now only to indicate what are these a
priori or formal conditions of sensibility, to which Kant has
given the name of transcendental schemata.
These conditions, as I have already pointed out,4 are ways in
which the given manifold is combined in one time by the tran-
1 Compare Chapter XI § 4 and Chapter LIV.
2 A I39-B 178.
3 'Meaning*, as usual, may be equated with 'objective reference*.
The remark about the 'elements' — compare also A 96 — suggests that
a fictitious concept, such as the concept of 'chimaera', may have a
kind of meaning, since the elements of which it is composed have
objective reference. 4 Compare § 3 above and the end of § 6.
32 THE SCHEMATISM [XXXII § 8
scendental synthesis of imagination, or characteristics which
objects must have in virtue of the given manifold being so
combined. The main difficulty is to know the sense in which
the category 'contains* these conditions. Every pure category
contains a principle of synthesis derived from the form of
judgement; and the way in which the manifold is combined
in one time is, on Kant's view, a species which falls under the
genus conceived in the pure category. If the category contains
the condition of sensibility in a more intimate sense, if it
is the specific concept of this particular way of combining
the manifold in one time, then Kant has in mind, not the pure
category, but the schematised category.1 The schematised
category does contain in itself the transcendental schema,
in the sense that it is the concept of that schema. Thus — to take
the example given already2 — the schematised category of cause
and effect may be described as the concept of the necessary
succession of grounds which precede their consequents in time.'3
This, however, raises difficult questions as to the relation
between the schematised category and the transcendental
schema which can be better examined when we have studied
the details of Kant's doctrine.
§ 8. The Schema in General
The schema, Kant goes on to say, is a product of imagination.4
It must not, however, be confused with a picture or image,
which is also a product of the imagination. A picture or image
1 Compare Chapters XII § 7 and XIII § 6. 2 See § i above.
8 It is possible that Kant is referring to the way in which the category
contains the schema, when he says — in A 132 = B 171 — that the
category contains the condition of a priori rules, and again — in
A 135 = B 174 — that the universal condition of rules is given in
the category. Compare also the statement — in A 159 — 6 198 — that
the Principles alone supply the concept (presumably the category)
which contains the condition, and as it were the 'exponent*, of a rule
in general. I feel too doubtful of Kant's precise meaning in these
passages to commit myself to any interpretation.
4 A 140 = B 179. Kant says 'the schema in itself* in opposition,
I think, to the schema as brought under the pure category by the
procedure (or schematism) of the understanding.
XXXII § 8] CATEGORY AND SCHEMA 33
is an individual intuition. The schema is to be distinguished
from an individual intuition inasmuch as the synthesis of
imagination, in producing the schema, aims only 'at unity
in the, determination of sensibility'.1 This accords with the
view that the schema is a way of combination or a characteristic
resulting from combination.2
So far Kant is presumably concerned with the transcendental
schema, but he proceeds to illustrate the difference between
a schema and an image with reference, not to the categories,
but to particular concepts. There is here a difficulty; for the
transcendental schema was introduced as an idea mediating
between the category and intuitions, and there was said to be
no necessity for such a mediating idea between particular
concepts and intuitions.3 Nevertheless all concepts might have
schemata which were necessary for other purposes than such
mediation. If so, a description of what may be called the
schema in general might throw additional light on the nature
of the transcendental schema: it might show us what the
transcendental schema has in common with other schemata.4
Unfortunately, Kant's account of the schema in general,
while it is interesting in itself, raises difficulties rather than
removes them. He deals, as usual, firstly with the pure concepts
of mathematics, and secondly with ordinary empirical concepts.
If we take 'triangularity* as our example of a mathematical
concept, we must, according to Kant, distinguish carefully
three things: (i) the concept of triangularity itself, (2) the
image of an individual triangle, and (3) the schema. The
concept of triangularity is a concept of the marks common to
all triangles: the schema is a rule for constructing the image
1 Compare also A 118, A 123.
2 One might perhaps call it a characteristic of combination. It
might also be called a kind of synthetic unity.
3 Compare K.d.U. § 59 (V 351), where examples are for empirical
concepts what schemata are for categories.
4 Unless it has something in common with these schemata, the
only reason for introducing these schemata must be by way of contrast.
But Kant's account hardly bears this out, though he does make a
contrast later. In any case unless there really is something in common,
it is unfortunate that the two things should have the same name.
VOL. II B
34 THE SCHEMATISM [XXXII § 8
a priori in intuition, or in other words a rule of imaginative
synthesis. The schema, therefore, does in a way mediate
between the concept and the individual image. We know
what triangularity is when we know how to construct a tyiangle
a priori in imagination. We know that this figure drawn on
paper is an imperfect instance of triangularity, when our
imagination, in apprehending the given appearances as a triangle,
performs, and is known1 to perform, the same synthesis as
is necessary to construct a triangle a priori in imagination.2
In the case of simple objects like triangles, we might suppose
that we recognise them merely from their common marks,
that is, from their observed resemblance to one another. Even
in this case we do not know that the objects seen are triangles,
unless we know the principle upon which they can be con-
structed ; but Kant's doctrine is more obvious when we consider
objects of a greater complexity. We have, for example, no
image of the number a thousand, but we know what a thousand
is, if we know how to construct such an image. And we know
that we have a thousand dots before us, if in counting the
given dots we have performed the same synthesis as would be
necessary to construct a thousand a priori?
The same principle holds of empirical concepts, although
in this case our power of constructing an image in imagination
depends upon previous experience of the object. We know
what a dog is, when we know from experience how to construct
an image of dog in imagination. The schema, or rule of con-
struction, admits of great variety in detail and so is adequate
to the concept, while any individual image that we construct,
or any actual dog that we see,4 falls far short of the universality
1 Such knowledge may have different degrees of 'clarity*.
2 Compare A 224 = B 271 : 'The figurative synthesis by which we
construct a triangle in imagination is wholly identical with that
which we exercise in the apprehension of an appearance in order to
make for ourselves an empirical concept of it*. See also Chapter VI § 8.
3 For example, we combine ten sets of ten ten times over.
4 Kant, I believe, is here distinguishing images from objects, not
as Pnchard suggests, treating them as if they might be mentioned
indifferently; see Kant's Theory of Knowledge, p. 251 n. 4,
XXXII § 8] CATEGORY AND SCHEMA 35
of the concept. This is true even in the case of a simple mathe-
matical concept. The concept of triangularity (and the rule
for constructing triangles) involves the possibility of being
equilateral or isosceles or scalene, but any individual image of a
triangle realises only one of these possibilities.
All this is sound enough, and it is in accordance with what
we have already learned about concepts.1 But the question
inevitably arises whether we can really distinguish the concept
from the schema along these lines. Kant always regards a
concept, not merely as a concept of the marks common to a
number of objects, but as a concept of the synthesis of these
marks,2 and this means that every concept is the concept of
a rule of synthesis. We might indeed regard the schema as the
rule of synthesis unreflectively at work in imagination, and the
concept as the concept of the rule, when the synthesis is, in
Kant's phrase, brought to concepts.3 This seems to me a possible
distinction, and one which may have been at the back of Kant's
mind. His language, however, prevents us from taking this as
his express theory ; for he says that the schema can exist only in
thought* and he speaks of it as the idea (or representation) of a
method and of a universal procedure of imagination.5 If this is to
be taken literally, it destroys the distinction I have suggested.
Another interpretation is possible — that the schema, in spite
of what Kant has said, is really regarded by him as a kind of
schematic image. This is suggested by his statement that the
schema of sensuous concepts6 (as of figures in space) is a
product, and as it were a monogram, of pure a priori imagination,
1 Compare Chapters XIII § 5 and XX §§ 4-6.
2 I pass over difficulties in regard to simple concepts like 'redness',
though I imagine that Kant regards the concept of redness as involving
the concept of its synthesis with possible red objects; see B 133-4 n.
3A 78 — B 103. The rule or schema is then what is contained or
conceived in the concept. 4A 141 = B 180.
6 A 140 = B 179. An 'idea' here is presumably a concept.
8 He must mean 'pure sensuous concepts', unless the schema of
an empirical concept is confined to the mathematical properties
thought in the concept. A 'sensuous concept' is one which has a
corresponding intuition. If it is empirical, the concept is derived
from the intuition by analysis and abstraction. If it is pure, the
36 THE SCHEMATISM [XXXII § 8
through which, and in accordance with which, images them-
selves first become possible.1 A monogram is now commonly
regarded as a series of letters so interwoven as to constitute
a whole: sometimes, though not always, it is composed of the
initial letters of a name, and as such it may suggest the plan
or rule of a procedure in spelling out a name. But there is an
older usage in which 'monogram* meant a sketch or outline,
and Kant himself seems to use it in this sense.2 There is an
interesting passage where Kant compares certain creations
of the imagination to monograms in this respect — that they
offer us only individual strokes,3 determined by no assignable
rule, and constitute as it were a wavering sketch or a shadowy
outline4 rather than a determinate picture.5 Some of the
points made here may be due to the context, but the passage
suggests that if the schema is like a monogram, it is some sort
of wavering and schematic image. Such a wavering image
.might be the imaginative embodiment of the rule in, accordance
with which the synthesis of imagination works.
These considerations, inconclusive as they are in themselves,
throw, I fear, little light on the nature of the transcendental
schemata. They tend to suggest that the transcendental
schemata may share with the schema in general the common
characteristic of being a rule, rather than a product, of the
imagination.6 In his detailed account of the transcendental
intuition is constructed a priori in accordance with the concept.
A category, on the other hand, is a purely intellectual concept derived
from the nature of thought.
1 A 141-2 = B 181. Kant adds that these images are connected
with the concept through the schema — which means that the schema
in general, like the transcendental schema, is a mediating idea. The
necessity for mediation arises here because no image can be fully
congruent with the concept. 2 See A 833 = B 86 1.
8 'Zuge.' This may mean 'features', but I think it is at any rate
more precise than 'qualities', which is Kemp Smith's translation.
4 ' Schattenbild.' This may mean a silhouette, unless it is intended
to suggest something uncertain and changing. 5 A 570 — B 598.
6 I do not deny that a rule may be regarded as a product of the
imagination, if the imagination works in accordance with that rule;
but it is a different kind of product from a picture on the one hand
and a combination on the other.
XXXII § 9] CATEGORY AND SCHEMA 37
schemata Kant speaks in places as if the transcendental sche-
mata were rules, and even as if they were syntheses; but I
think he can be most satisfactorily interpreted if we take the
transcendental schema to be a way of combination, or a charac-
teristic of combination, which is produced by the transcendental
synthesis of imagination.
§ 9. Special Characteristics of the Transcendental Schema
The transcendental schema must in any case differ in certain
respects from other schemata ; and this difference Kant attempts
to make clear in one of those closely packed sentences which
he is apt to produce at the most crucial stage of an argument.
His first point is obvious. Let us suppose that a particular
schema — if this term may be used for the schema of a particular
concept (as opposed to a universal concept or category) — is a
rule of the imagination in constructing an image or an object1
in accordance with a particular concept. Since no intuition or
image can correspond to a category, the transcendental schema
cannot be a rule for constructing an image, or in Kant's phrase
it cannot be brought into an image.2
An image corresponding to the categories would have to be
constructed in pure intuition, and the nearest approach to
such an image would be time itself. Kant himself points out
that the pure image of all objects of the senses in general is
time.3 But it would be artificial to say that time is the image
corresponding to the categories. It is better to say that there is
no corresponding image.
We now come to Kant's second point. Instead of saying —
as we might expect in view of his account of the schema in
general — that the transcendental schema is the rule of the
transcendental synthesis of imagination, he says that it is the
1 The same process is at work whether we are constructing an
image in mere fancy, or whether we start from a given sensation or
sensations and construct an actual object of perception.
2 A 142 = B 181.
3 A 142 = B 182. Time and space are constructed by the transcen-
dental synthesis of imagination. Space is the pure image of all
quantities for outer sense.
38 THE SCHEMATISM [XXXII §9
transcendental synthesis itself. The transcendental schema is
'simply the pure synthesis in conformity with a rule of unity
in accordance with concepts in general,1 which2 the category
expresses'.3
Such a use of terms seems at first sight calculated to reduce
the reader to despair. We may be tempted to affirm — and
perhaps this is the best way to interpret him — that if Kant
means anything, he must mean that the transcendental schema
is the rule of the pure synthesis. Certainly the schema is not
to be regarded as an act of pure synthesis ;4 but I think Kant
may conceivably mean here that the schema is that specific
kind of a priori combination which is produced by the pure
synthesis of imagination and is in conformity with the principle
of synthesis (or rule of unity) conceived in the category. If
this is a possible interpretation, it accords with that hitherto
given.5
Kant's third point is also put obscurely. His statement
is so complicated that it may be divided into three parts. The
transcendental schema is (i) a transcendental product of the
imagination; (2) it is concerned with6 the determination of
inner sense in general as regards conditions of its form (time)
with respect to all ideas; (3) it is so concerned with respect to
1 * Concepts in general' must be opposed to categories. The rule
of unity is a principle of synthesis involved in conception or judge-
ment as such.
2 The reference of 'which* is uncertain. The pure category might
be said to express either the pure synthesis (compare A 78 = B 104)
or the unity of the pure synthesis (compare A 79 — B 105). It might
also, I think, be said to express the rule. Whichever interpretation
we adopt, the general doctrine remains the same.
3 A 142 — B 181.
4 Nevertheless Kant (in A 143 = B 183) speaks of the schema of
reality as 'the continuous and uniform production of reality in time',
where 'production' (Erzeugung) certainly looks like an act.
5 I am assuming here that the a priori combination may be identified
by Kant with the characteristic which results from, or is manifested
in, such combination.
8 'betrifft.' The expression of Kant's doctrine here bears a close
resemblance to his account of the transcendental synthesis of imagina-
tion in B 150 and B 152.
XXXII § ic] CATEGORY AND SCHEMA 39
all ideas so far as these must be connected a priori in one
concept in conformity with the unity of apperception.
The first part is just what we should expect. The third part
is an ejpborate way of saying that the ideas in question must be
ideas of an object.1 The second part, which is the most impor-
tant one, I take to mean, not that the transcendental schema
is itself a determination or characteristic of inner sense or of
time, but that it is a determination or characteristic of all our
ideas of objects — or, more simply, of all objects — so far as they
are known to be combined in one time.2
§ 10. Summary of Conclusions
The obscurity of Kant's exposition places great difficulties
in the way of the interpreter. The main burden of his doctrine
is that the transcendental schema is a product of the transcen-
dental synthesis of imagination ; but the account given of the
schema in general suggests that the transcendental schema
might be a rule of the transcendental synthesis;3 and the
transcendental schema is even described in one place as if it
were the transcendental synthesis itself.
In spite of these difficulties I have little doubt that the
transcendental schema is best regarded as a product of the
transcendental synthesis of imagination. This product is a
necessary characteristic which sensible objects must have
because the given manifold must be combined by the transcen-
dental synthesis in one time.
It is not easy to state Kant's doctrine in a simple way ; and
yet I think that what he is trying to describe is itself compara-
1 The 'concept in conformity with the unity of apperception* must
be a concept of an object, and may be a category. Ideas of objects
may, I think, be identified here with objects themselves so far as
these are known.
a The references to inner sense are, as usual, a source of difficulty,
and I think it unfortunate that Kant ignores space; but we must
not forget that for Kant all ideas are ideas of inner sense and so fall
under the form of time. 'Determination* may mean 'determining'.
3 The rule of the transcendental synthesis may be regarded as in
a sense the product of the transcendental synthesis.
40 THE SCHEMATISM [XXXII § 10
lively simple, if only we can be brought to concentrate upon it
rather than on the words in which it is described.
The transcendental synthesis of imagination is supposed
to combine the pure manifold of time into a unity, ajnd this
unity is supposed to be necessary for, and as it were demanded
by, the unity of apperception, without which knowledge is
impossible. This implies that the empirical manifold must be
combined in one time, and as so combined it must exhibit
certain characteristic ways of combination which all objects,
as temporal, must have.
Such a view is at least intelligible, but if it is to have any
importance, we must make it more definite: we must show
what are the characteristic ways of combination belonging to
all objects as temporal. Kant believes that the unity of apper-
ception is manifested in the forms of judgement, or of thought,
considered as principles of synthesis ; and he believes that the
characteristic ways of combination belonging to all objects
as temporal must correspond to the principles of synthesis
present in the forms of judgement — or in other words they
must fall under the pure categories in the sense that they must
be a species of which the pure category gives the genus. He
claims, as I understand him, to have proved generally in the
Transcendental Deduction that this must be so; but mani-
festly his proof can carry little conviction unless he can show
us in all temporal objects those characteristic ways of combina-
tion which he alleges must fall under the pure categories.
These characteristic ways of combination are the transcendental
schemata and are the product of the transcendental synthesis
of imagination. They may also be described as the necessary
temporal characteristics of objects, characteristics without
which objects would not be sensible objects in time;1 and
they must in some sense be revealed to sense-perception, if
we recognise that imagination is a necessary ingredient in sense-
perception.2
We are not likely to get a clearer view of the transcendental
1 Hence they are described too as 'formal conditions of sensibility.'
2 Compare A 120 n. and B 151.
XXXII § ID] CATEGORY AND SCHEMA 41
schemata until we have examined each of them in detail, but
one further complication must be added. The pure category
as applied and restricted to its corresponding schema becomes
the schematised category: for example the pure category of
ground and consequent as applied and restricted to the transcen-
dental schema of necessary succession becomes the schematised
category of cause and effect. This no doubt raises the question
whether the schematised category is really different from the
transcendental schema. Kant, although he does not use the
term 'schematised category', gives to the schematised categories
names1 which differ from the names given to the transcendental
schemata. Hence it is all-important that at the outset we should
distinguish both the pure category and the schematised category
from the transcendental schema.
1 He generally uses what I have called the name of the schematised
category even when he refers to the pure category, as for example
in the Metaphysical Deduction, where the category derived from the
hypothetical form of judgement is called by anticipation, not the
category of ground and consequent, but the category of cause and
effect.
VOL. II B*
CHAPTER XXXIII
THE TRANSCENDENTAL SCHEMATA
r
§ i. Category and Schema
We must now examine the different transcendental schemata
which correspond to the pure categories. I propose to state
in each case (i) what is the pure category, (2) what is the
schematised category, and (3) what is the transcendental
schema. It will be necessary to supplement Kant's own account
by information derived from other parts of the Kritiky and
also to introduce some measure of tidiness ; for his description
is unfortunately incomplete and careless where we are most
in need of precision.
Every pure category may be described1 as the concept of
the synthesis2 of x, where x serves to indicate the special nature
of the synthesis. The principle of the synthesis is supposed
to be implicit in the form of judgement.3 The manifold syn-
thetised is the manifold of intuition m general, and the pure
category has in itself no reference to space and time. Unless
the given manifold is synthetised in accordance with the
category, there can be no knowledge of objects. These general
considerations are always applicable and need not be repeated
in each case.
The schematised category may be described as the concept
1 Kant says that the pure categories cannot be defined — see A 241
and A 245 and compare B 300 — but this means that their definition
is not a 'real definition'; that is, it does not show that there is any
real object to which the pure categories apply.
2 Or 'the synthetic unity'. So far as the category is the concept
of an object, the synthesis must be regarded, not as the act of combin-
ing, but as the combination made by the act and supposed to be present
in the object. The category might be described as the concept of
an object in general so far as the manifold of the object is combined
in a certain way. Nevertheless all combination is the result of an act
of synthesis, and Kant tends to treat the concept of the act and
the concept of the combination produced by the act as if they were
the same concept. 3 See especially for details Chapter XIV § 4.
XXXIII § i] THE TRANSCENDENTAL SCHEMATA 43
of the synthesis^ of x in time. The principle of synthesis is
the same as that of the pure category, but its application is
restricted to a manifold of intuition given under the form
of time and space.2
The transcendental schema is the product which results
from the synthesis conceived in the schematised category:3
as such it is a necessary characteristic of all temporal objects
and is, I think, revealed to us (at least in part)4 through sensuous
intuition, provided that we understand intuition to involve
imagination as well as sense.
This general framework may be difficult to work out in
all details, and it may not do justice to the subtlety of Kant's
thought ; but it is far better to have even an inadequate frame-
work which may subsequently be corrected than to be faced
with a chaos of unrelated assertions.
I would again insist that we shall understand Kant only
if we interpret him as giving an analysis of what is present
in all instances of knowing an object. Every object6 must
exhibit all the transcendental schemata, and must fall, as
1 Or 'the synthetic unity*. The schematised category may be de-
scribed as the concept of an object in time and space so far as the mani-
fold of the object is combined in a certain way. When Kant deals
with the synthesis in time, his tendency to identify the concept of
the act of synthesis and the concept of the combination produced
by the act of synthesis is particularly noticeable.
2 I think it necessary, in the light of the Principles, to bring in
space as well as time for the understanding of Kant's view. In his
account of the schematism he himself avoids references to space.
8 If so, it is also conceived in the pure category as the 'higher
concept* under which the schematised category falls.
The transcendental schema, it should be noted, is the product of
the act of synthesis, but it may also be regarded as resulting from,
or manifested in, the combination produced by the act. In the definition
of the categories 'synthesis* is taken most naturally as 'the combination
made by the act of synthesis* : in the definition of the schema 'synthesis'
is most naturally taken as 'the act which produces this combination*.
I have not thought it necessary to comment on this in the separate
definitions, and I do not think Kant makes a sharp distinction.
4 The schemata of relation are perhaps confirmed, rather than
revealed, by sensuous intuition.
5 We should, I think, confine our attention to physical objects —
the objects which Kant has primarily in view.
44 THE SCHEMATISM [XXXIII §2
regards its different aspects, under all the categories. We
must not be misled into supposing that Kant describes a
whole series of syntheses which take place at different times.
There is only one synthesis which combines the given manifold,
whatever be its empirical character, in one time and space,
although that synthesis has different aspects and imposes
different characteristics on the objects combined. And similarly
there is only one form of judgement, or one principle of syn-
thesis in judgement, though this too has different aspects,
which Kant treats with an excessive formalism when he finds
them embodied in the different forms of judgement as
described by the traditional logic.
Throughout this chapter I am trying to make Kant's position
clear, rather than to criticise it. Even so, some of the details
must remain obscure till we come to the further exposition
in the Principles.
§ 2. The Schema of Quantity
Under the head of quantity the pure category is derived
from the universal form of judgement 'All S is P'.1 The name
of the category is 'totality9, though it is usually referred to as
'quantity* ; and it may be described as the concept of the synthesis
of the homogeneous? The ground for this description is that
1 The order in which the categories are given in A 80 = B 106
suggests that the category of totality is derived from the singular
judgement. Although the same parallelism holds in the Prolegomena
(IV 302-3), I believe that this is a slip, and is due to the fact that in
the list of the forms of judgement Kant follows the traditional order
(universal, particular, singular), while in the list of the categories
he follows the order by which the third can be compounded of the
first two (unity, plurality, totality), because (B in) totality is plurality
considered as unity. It is only natural to derive unity from the singular
judgement, as Kant himself implies that he does in A 71 — B 96,
in the Prolegomena § 20 (IV 302 n.), and in A 245-6, where he refers
to judicium commune. His argument would be more plausible if he
derived the three categories of unity, plurality, and totality from the
fact that every judgement makes use of common concepts ; compare
Chapter X § 5 and Chapter XIV § 8.
2 It might be described as the concept of 'the unity of the synthesis
of the manifold of a homogeneous intuition in general* ; see A 142-3
= B 182, and compare B 162, B 203, A 242 = B 300, and A 245-6.
XXXIII §2] THE TRANSCENDENTAL SCHEMATA 45
in the universal judgement the objects referred to by the
subject-concept are considered to be homogeneous with
one another.
The 'schematised category is the concept of the synthesis
of the homogeneous in time and space, and may be described
as the category of extensive quantity. The transcendental
schema which is the product of this synthesis is number
(numerus), called also quantity as a phenomenon (quantitas
phaenomenori).1
The synthesis of imagination, starting from given sensations
and attempting to determine an object in time and space,
determines the homogeneous space which the object occupies
and the homogeneous time through which it endures. This
gives the object shape (which seems to include size) and dura-
tion.2 What we are concerned with here is, however, something
more general, something common to size and to duration.
This something Kant describes as number.
We might have expected it to be described rather as extensive
quantity, which appears to be more obviously sensuous than
number.3 Kant, however, asks himself what is the common
characteristic of every synthesis which produces the different
kinds of extensive quantity. His answer is that every synthesis
which produces extensive quantity4 (whether in time or space)
must be a successive synthesis of the homogeneous.5 In holding
this he is assuming that in order to determine any line, however
1 A 146 = B 1 86. The synthesis is here taken as an act of synthesis
and is successive.
2 Compare A 724 = B 752, 'Gestalt' and 'Dauer'.
3 Compare A 162 = B 203 ff. Perhaps Kant's desire to connect the
schema specially with successive synthesis in time is the reason why
he describes the schema as number: sensuous extensive quantity is
indeterminate apart from measurement.
4 I think we must take 'extensive quantity* throughout to be deter-
minate extensive quantity, that is, a quantity which is measured or
specified mathematically. Kant does not deny that we can be aware
of an indeterminate quantity or quantum without successive synthesis ;
see the important footnote to A 426 = B 454.
6 A 163 = B 204 and A 242 — B 300. The successiveness of the
synthesis (in the sense that we must take each unit separately one
after another) is the mark of extensive quantity.
46 THE SCHEMATISM [XXXIII §2
small, we must apprehend its parts one after the other, and add
them together, or synthetise them into a whole j1 and the same,
he maintains, is equally true of even the smallest period of
time.2 To determine the quantity of anything is to determine how
many units it contains, and these units (whatever they may be)
must be successively added, if the thing is to be measured.3
The successive addition of homogeneous units is counting,
and what it produces is number. Since space and time are
homogeneous, and since all objects are in a common space
and time, all objects are known (so far as they are spatial
and temporal) through a transcendental synthesis of imagination
which successively synthetises the homogeneous parts of
space and time. Hence every object must have number, or,
perhaps it would be better to say, must be numerable.
Kant's own account4 is intelligible only in the light of his
Axioms of Intuition, and it is obscured by the fact that he
makes no reference to space. Thus he does not explain that
intuitions must have homogeneity because they are spatial
and temporal. His description of number is misleading; for
he says that number is an idea which comprehends the succes-
sive addition of homogeneous units.5 This would identify
'number* with 'counting' (unless he means that number is
the idea which comprehends in a total the homogeneous
units successively added). He concludes that number is there-
fore the unity of the synthesis of the manifold of a homogeneous
intuition in general in that9 I generate7 time itself in the
1 See A 162-3 — B 203. Every line is made up of parts, not of
points, and mathematical measurement may choose any part it pleases
as the unit of measurement; see K.d.U. § 26 (V 254).
2 A 163 = B 203. 3 A 242 = B 300. 4 A 142-3 = B 182.
6 Compare what he says about number in A 140 = B 179.
6 'dadurch dass.' The first half of this sentence is a definition of
the pure category of quantity, and it is only what is added that makes
it a definition of number — unless indeed 'intuition in general* (as in
A 724 = B 752 and perhaps in B 203) indicates only that the difference
between time and space may be ignored; see Chapter XXXVII § 3.
7 Apart from the transcendental synthesis of imagination there would
be no time and no succession; compare A 99-100, A 101-2, A 107,
B 154-5, and B 1 60 n. It must be remembered that for Kant time
has reality only in relation to the human mind.
XXXIII § 2] THE TRANSCENDENTAL SCHEMATA 47
apprehension of the intuition.1 This is so difficult as almost
to bar comment; and it remains doubtful whether Kant is
regarding number as the act of counting or not.2 Number
may perhaps be a synthetic unity (or combined manifold)
produced by the successive addition of homogeneous units;3
but it cannot be either the act of counting or the unity of the
act of counting.4
If we reinterpret Kant's doctrine by bringing in space,
as I have done and as he himself does later, his account of
the schema appears to be sound. It may seem hardly necessary
to ask whether the schema has also a connexion with the
universal form of judgement ; but there is always a possibility
that more than mere formalism lies behind Kant's seemingly
artificial expressions. The demand of all judgement, and
indeed of all conception, is that a plurality of homogeneous
units should be conceived as a totality: this is not confined
to the form 'All S is P'. Kant's doctrine may be interpreted
as asserting that because sensible objects are in space and time
and so can be measured, there must be objects which have
sufficient homogeneity to be conceived (or to be judged by
the form 'All S is P'), and that even complete homogeneity
1 If this implied that the homogeneity of intuitions is derived from
the fact that the apprehension of them is successive, such an implication
would be mistaken. There is no such implication in the Axioms,
and I do not think we should impute this to Kant here. The homo-
geneity of objects belongs to them in virtue of the time through
which they last and the space which they occupy, not in virtue of
the time which we require to apprehend them. Nevertheless for Kant
there is neither time nor space except in so far as they are (directly
or indirectly) apprehended inasmuch as the objects in time and
space are (directly or indirectly) apprehended. And if we are to
determine any past time or any unperceived space, we can do so
only by taking up successively and combining the units by which
we measure it.
2 Compare A 103 (and also A 78 = B 104 and A 724 = B 752).
3 Compare Kant's own description of number in the Dissertation
— § 15 Cor. (II 406) — as 'multitudo numerando, h.e. in tempore dato
successive unum uni addendo, dtstmcte cognita*.
4 This description of number is perhaps an example of Kant's ten-
dency to identify the concept of an object with the concept of the
synthesis by which the object is constructed.
48 THE SCHEMATISM [XXXIII § 3
would not render these objects indistinguishable from one
another.1 More simply, in knowing sensible objects, and indeed
in knowing any individual sensible object, there must be a
synthesis of the homogeneous. The pure category of quantity
is therefore shown to have objective validity ; and at the same
time it ceases to be a mere empty form of judgement and
acquires 'sense and significance' as the schematised category
of extensive quantity. Even if we cannot accept Kant's deriva-
tion of the category, we need not deny that his view has more
plausibility than is commonly recognised.
§ 3. The Schema of Quality
Every sensible object, since the synthesis through which
it is known is also a synthesis of time and space, must have
extensive quantity; that is, it must have homogeneous parts
external to one another which can be successively countecf.
But every sensible object, if it is to be a real object (and not
merely the form of an object), must involve more than a
synthesis of time and space. Its matter must be synthetised
with the forms of time and space, and only so can it be
real. Hence the next schema is referred to as the schema of
reality.
In spite of this it is clear from Kant's account that the pure
category which has to be schematised would be better called
the category of limitation, that is, of reality combined with
negation? It may be described for our present purpose as
the concept of the synthesis of being and not-being. This category
is connected by Kant with the infinite judgement 'S is non-P'.
The artificiality of the form should not obscure the fact — as I
1 It should be noted that, according to Kant, objects which were
entirely homogeneous could nevertheless be distinguished from one
another, and so could be counted, because as sensible (and not merely
conceivable) they would have different positions in space. See A 263
= B 319; A 272 = B 328; A 281 = B 337-8. So far as I know Kant
does not discuss this problem with reference to time.
2 See B in. It may also be called the category of quality ; see
A 145 = B 184.
XXXIII § 3] THE TRANSCENDENTAL SCHEMATA 49
believe it to be — that every judgement both affirms and denies,1
and in so doing delimits, or determines, reality. It therefore
demands that its object should somehow be characterised
by a combination of being and not-being.
The schematised category is the concept of the synthesis of
being and not-being in time and space, and may be described
as the category of reality (or limitation) in time and space.2
The transcendental schema which is the product of this
synthesis is properly called degree?
Kant's own account4 of this schema is obscure and inaccurate,
and it is intelligible only in the light of the Anticipations of
Sense Perception.5 He believes that the mere forms of time
and space are nothing real, and that if we are to have a real
object of experience, these empty forms must be filled with a
given matter, which is in the first instance sensation.6 Being
in time and space is to be found only in sensation (or the sensum)
and its correlate not-being is empty time and space. The
synthesis of sensation with the forms of time and space, or
1 It may be said that an affirmative judgement implies a negative
judgement and vice versa, but the negative judgement is another and
a different judgement. This is true of the judgement taken abstractly
as a proposition, but I believe that the affirmative judgement, taken
concretely, denies as well as affirms, while the negative judgement,
taken concretely, affirms as well as denies; and this does not mean
that there is no difference between an affirmative and a negative
judgement.
2 It may be described also as the category of quality. If we could
call it the category of intensive quantity we should get a parallel with
extensive quantity (compare B 202) ; but Kant seems to treat intensive
quantity as equivalent to degree. As generally in this chapter, he
ignores space.
3 Kant calls it sensatio or reahtas phaenomcnon (A 146 =• B 186).
This is, I think, misleading. He means, not mere sensation, but degree
of sensation, or sensation as having degree. He means also degree of
what corresponds to sensation as well as degree of sensation itself.
4 Degree* appears to be identified with 'intensive quantity'. Intensive
quantity is given in sensation at a moment: we do not apprehend
each of its parts separately and successively in order to combine
them into a total (see A 168 = B 210).
4 A 143 = B 182-3. 6 B 207 ff.
6 We may for the present ignore 'what corresponds to sensation*.
50 THE SCHEMATISM [XXXIII § 3
of being with not-being, alone gives us a determinate object.
And according to Kant this synthesis, which fills time and
space with sensation, must do so in different degrees.1 Any
sensation that we care to take (for example, the sensation of a
red colour),2 however faint it may be, is never the faintest
possible sensation: there is always possible a still fainter
sensation between any given sensation and complete absence
of sensation. This means that in what fills time and space
there is always a more or less which is to be distinguished
from the more or less of time and space which is filled. A
colour may be brighter than another, though it lasts for a
shorter time and covers a smaller surface. Thus every sensible
object must have a degree of its sensed qualities, and such
degree is a necessary characteristic of reality in time and
space.
This very difficult doctrine will have to be considered in.
detail later.3 Here it need only be observed that the connexion
1 Kant seems to infer from this that when we know an object,
time and space are neither completely filled nor completely empty,
so that an object must always exhibit in itself a determinate combina-
tion of being and not-being. 2 See A 169 = Ban.
3 See Chapter XXXVIII. Kant's own definition of the schema is
'the continuous and uniform production of reality in time, as we
descend in time from the sensation which has a definite degree to its
complete disappearance, or gradually mount from negation to such
a degree*. Here the schema is described as if it were the syn-
thesis itself, though we might expect it to be the product of the
synthesis.
Kant explains that 'what corresponds to a sensation* is that whose
concept indicates being (in time). He asserts that this is what is
thought in the pure concept of the understanding; but the pure
category conceives being without any relation to time, and it is the
schematised category which refers to being in time. For the schema-
tised category being is what fills time, and not-being is empty
time.
He also says, if the reading is correct, that because time is the
form of objects only as appearances, what corresponds to sensation
is the transcendental matter of objects as things-in-themselves ! This
contradicts the statement that it is 'being m time*, unless he uses
the phrase 'things-in-themselves* in its physical, and not in its meta-
physical, sense (see A 45 = B 63) ; but in that case he would hardly
call the matter 'transcendental*. There is here some looseness of
XXXIII §3] THE TRANSCENDENTAL SCHEMATA 51
of this schema with the quality of judgements seems the most
artificial of all Kant's connexions; for it is a pure accident
that the difference of affirmation and negation is said to deter-
mine the quality of judgements. Nevertheless it is only fair
to Kant to recognise that this connexion does not depend
merely on the accidental use of the word 'quality' for two very
different things. Every judgement affirms or denies objective
reality. This has in itself nothing to do with time or space,
but when we translate it — in Caird's phrase1 — into terms of
time, then what it affirms or denies is objective existence
or reality in time and space. What exists in time and space
is the sensible object, whose reality is known, in the first
instance, through sensation. Furthermore, what sensation
gives us is a quality of the object, and this quality (whereby
it fills time and space) always has degree or intensive quantity.
In this case also, if we were convinced that some schema
must correspond to the form of judgement, it would not be
unreasonable to regard the schema in question as the degree
of qualities given in sensation.2 We know that it must be
possible to determine real objects by combined affirmation
and negation, because if there is to be experience at all, some-
expression. The matter of things-in-themselves is unknown; com-
pare A 366. What Corresponds' in the phenomenal object to our
sensations is the matter of the phenomenal object; this matter (whose
inner nature is unknown) we refer to a source beyond the mind;
and it is this same matter which constitutes the phenomenal object
an empirical reality (compare A 720 = B 748).
The emendation of Kant's statement by inserting the word 'not*
(which Kemp Smith accepts from Wille) is not very convincing.
1 Compare Caird, The Philosophy of Kant, p. 407, and also The
Critical Philosophy of Kant , Vol. I, p. 441.
2 It may be objected that extensive quantity is itself a quality of
things. Kant himself recognises extension to be a primary quality
of bodies; see ProL § 13 Anm. II (IV 289). He also describes spatial
quanta as having the quality of shape (A 720 = B 748), and quantity
itself as having the quality of continuity (A 176 — B 218). But in
connexion with the schema he is using the word * quality* in the
sense in which it is opposed to extensive quantity. Quality in this
sense is given in sensation, while extensive quantity is determined
by the time and space which is filled by the given quality.
52 THE SCHEMATISM [XXXIII
thing must be given in sensation1 and synthetised in time and
space.2 Every object must therefore exhibit in itself that
combination of being and not-being which is known as degree,
a combination demanded by all judgement so far as it delimits
objects by affirmation and negation.
§ 4. The Schemata of Relation
An actual object of experience must have more than quantity
and quality. It must have a definite position3 in one common
time and space, and this position is determined by its relation
to other objects. Kant gives us three schemata of relation
corresponding to the three pure categories derived from the
categorical, hypothetical, and disjunctive forms of judgement;
and these schemata are concerned with the necessary relation
of sensible objects to one another in a common time and space.4
Here there is no suggestion that a schema is either a synthesis
or a rule of synthesis. Each schema is defined as the characteristic
which is the product of the synthesis.5
The first pure category is the concept of the synthesis of
subject and predicate. In the categorical form of judgement
subject and predicate are for Formal Logic interchangeable;
but for Transcendental Logic, since the pure category is the
form of judgement as used to determine sensible objects,
1 By affirmation and negation we delimit or determine time and
space as well as what is in time and space. But space and time are
not real things, and we determine real things only when we determine
what is given in time and space. Even time and space are real only
when they are filled.
It is interesting to note that Plato as well as Kant identified space
with TO fit} ov, although for Plato space was matter (vA^), not form.
2 The very difficult question as to the necessity of different degrees
of reality in time and space must be dealt with later; see Chapter
XXXVIII.
8 lDasem\ which is a being there (or then) and is equivalent to
existence, that is, existence in space and time. An imaginary object
may have quantity and quality in a sense, but only an actual
object has existence in our common space and time.
4 Kant, as usual in this chapter, ignores space, but his account
is not intelligible apart from space, and must be supplemented from
the doctrine of the Analogies. 5 A 143-4 = B 183-4.
XXXIII § 4] THE TRANSCENDENTAL SCHEMATA 53
the subject is regarded as a subject which can never be a pre-
dicate.1 Apart from empirical sensation we cannot know
whether anything corresponds to the thought of such a
subjeqj:.2
The schematised category is the concept of the synthesis
of the permanent and the changing in time, where the permanent
is the unchanging subject (or substance) to which the changing
predicates (or accidents) belong: the permanent is, in short,
the unchanging substratum of all change, and the schematised
category is the category of substance and accident (or of
subsistence and inherence). The transcendental schema which
is the product of the synthesis is permanence. Kant ignores
the fact that the category, and presumably the schema, involves
two correlative terms,3 and he is content to refer to the schema
indifferently as 'permanence1 or 'the permanent'.4
The second pure category is the concept of the synthesis
of ground and consequent. Kant habitually describes it as the
category of cause and effect, but it has no reference to time.
He himself says that if we leave out all reference to temporal
succession, the category of cause is merely the concept of
something from which we can make an inference to the existence
of something else.5 This would not enable us to distinguish
*B 129; A 147 = B 1 86; A 242-3 — B 300-1. I suppose Kant
holds that unless this is so, there is no real distinction between subject
and predicate. His argument might be more satisfactory if he merely
insisted that thought demands something to think about by means
of its concepts.
2 B 149; A 243 = B 301.
8 See B no. Kant perhaps ignores change as a correlate of per-
manence, because change is dealt with in connexion with the second
schema of relation, and all three schemata must be considered together.
4 Kant is careless in his account of substance. He says (i) that it
is permanence, the permanence of the real in time, (2) that it is the
idea of the real as a substratum which endures while everything else
changes; and (3) that it is the permanent or unchanging. The Latin
name is constans et perdurabile rerum, or substantia phaenomenon
(A 146 = B 1 86).
6 A 243 = B 301. I think the words 'the existence of should be
omitted from this statement, but even so the definition would be
unsatisfactory.
>4 THE SCHEMATISM [XXXIII §4
between cause and effect,1 nor have we any right to suppose
that there is any object corresponding to the concept.
The schematised category is the concept of the synthesis
of ground and consequent where the consequent succeeds the
ground in time, and it is to be described as the category of
cause and effect. The transcendental schema which is the pro-
duct of the synthesis is necessary succession, or succession
in accordance with a rule.2 This means, not that an event A
must always be succeeded by some other event, but that it
must (other conditions remaining the same) be succeeded
by the event B.3
The third pure category is more difficult. In the disjunctive
judgement we think of a whole whose parts mutually exclude,
and so mutually determine, one another in the whole.4 Hence
the pure category of communion is the concept of the synthesis
of a whole whose parts mutually exclude and determine one
another. It has of course no reference to time.
1 Perhaps Kant has in mind the fact that such an inference can
in special cases work in both directions; for example, we can argue
either from the three sides of a triangle to its three angles or vice
versa. Or perhaps he means that inference is sometimes from effect to
cause — if there is a footprint, a man has passed.
2 Kant says also that the schema of cause is 'the real upon which,
whenever posited, something else always follows.' The word 'posited*
(gesetzt) is always puzzling. Here it seems to mean 'has a position
in time', 'occurs'. The schema of effect would then presumably be
'the real which always follows upon a given event'. Causality applies,
not to the succession of times, but to the succession of appearances
in time.
8 Whether rightly or wrongly, Kant always assumes that causality
implies regular succession; and what I call 'necessary succession' is
to be taken as meaning 'regular succession'. Necessary regularity,
like permanence, is something whose presence can be confirmed by
observation, although it cannot be established by observation.
4 Compare A 73-4 = B 98-9 and B 112-13. We may consider this
to be implied in the form of judgement 'A is either B or C or D.'
In the judgement 'a triangle is either equilateral or isosceles or scalene',
we divide what Kant calls the 'sphere' of triangularity into the mutually
exclusive parts which constitute the whole sphere. It is irrelevant to
object that this bears no analogy to simultaneity because a triangle
cannot be both equilateral and isosceles at the same time; for all
reference to time is excluded from the pure category.
XXXIII §4] THE TRANSCENDENTAL SCHEMATA 55
This statement is, however, too simple for the full under-
standing of Kant's view. He himself gives a description of
what purports to be the pure category, but (as in the case
of causality) he does not distinguish it from the schematised
category. He says that it is 'the reciprocal causality of sub-
stances in relation to one another'.1 It would be more exact
to say that it is 'the reciprocal causality of substances in regard
to their accidents'.2 If we exclude all reference to time and to
terms implying time, we must say that the pure category
of communion3 is the concept of the synthesis of ultimate subjects
such that the predicates of the one subject have their ground
in the other, and vice versa.4
The schematised category is the concept of the synthesis
of permanent substances such that the changing accidents of
the one substance have their cause in the other, and vice versa:5
it may be called the category of interaction. The transcendental
schema which is the product of the synthesis is the necessary
simultaneity of the accidents of one substance with those
of another, or, as Kant says, simultaneity in accordance with
a universal rule.6
It may be added that Kant finds permanent substances
only in space, and he believes that the different spatial parts
of a substance are themselves substances.7
1 See A 244 = B 302. 2 Compare A 144 = B 183.
3 It would be well to use the term 'communion' (Gemetnschaft or
commumo) for the pure category, and 'interaction' (Wechselwirkung
or commercium) for the schematised category. Compare A2I3 = 62 60
(although commumo is there restricted to commumo spatu) and A 2 14
= 6261.
4 Compare B 257-8. This is implied in the form of judgement
'Either A is B or C is D*. This second statement does not contradict
the first, but it adds to it that the parts of the whole are themselves
subjects which determine one another in regard to their predicates.
For the significance of this see n. 7 below.
6 Compare B 257-8.
6 A 144 ~ B 183-4. I propose to use 'necessary simultaneity* as
the parallel to 'necessary succession*.
7 M.A.d.N. (IV 503 and 542). Hence the parts of a whole substance
are themselves substances which determine one another in regard to
their accidents. Compare n. 4 above.
56 THE SCHEMATISM [XXXIII §5
The schemata of relation are (with the exception of the
schema of interaction) more plausibly connected with the
corresponding form of judgement than are the schemata
of quantity and quality. On the other hand it is not so clear
that the characteristics imposed by the synthesis of relation
must be found in all sensible objects. The transcendental
synthesis of imagination manifestly imposes extensive quantity
on objects, and I think we may agree that it involves a synthesis
of quality also, and even that quality must necessarily have
a degree. But it is certainly not obvious why the transcendental
synthesis should impose necessary permanence, necessary
succession, and necessary simultaneity.
This fact is explicitly recognised by Kant. In the Principles
he will attempt to show that sensible objects must have all
the categorial characteristics specified, but in the case of
quantity and quality wre are said to have intuitive certainty
or evidence, while in the other cases we have only discursive
certainty. Nevertheless in all cases we have certainty.1
§ 5. The Schemata of Modality
We have now seen that for Kant the one synthesis of imagina-
tion by which we construct objects in time and space has
three necessary aspects: (i) it is a synthesis of time and space
(the forms of intuition), and so involves extensive quantity
or number ; (2) it is a synthesis of appearances given to sensation
(the matter of intuition) in time and space, and so involves
intensive quantity or degree; (3) it is a synthesis which com-
bines different appearances in one common time and space,
and so (Kant will prove) involves permanence, necessary
succession, and necessary simultaneity, or the reciprocal
causality of permanent substances in regard to their changing
accidents.2
1 See A 161-2 = B 200-1 and A 180 = B 223; and compare
Chapter XXXVI § 3 where this point will be discussed.
2 We may speak of (i) as the synthesis of mere intuition, of (2) as
the synthesis of sense-perception, and of (3) as the synthesis of
experience; see A 180 = B 223. The synthesis of experience, I think,
includes the first two. This should be compared with Kant's summary
XXXIII § 5] THE TRANSCENDENTAL SCHEMATA 57
These syntheses, or aspects of the one synthesis, determine
different categorial features of the object of experience. The
first two determine the object itself, the third determines
the object in its relation to other objects. When we come
to the schemata of modality, we are concerned, not with
features belonging to the object, but rather with its relation
to the mind which knows it.1 Hence we have no longer to
discover new aspects of the one synthesis which determines
objects in time (and space): we have to observe (if we may
simplify matters provisionally) that the first aspect of the
synthesis which we have already described is the condition
of our knowing an object to be possible;2 the second is the
condition of our knowing it to be actual; and the third is
the condition of our knowing it to be necessary. Possibility,
actuality, and necessity add nothing to the content of the
object; but every object may be said to be known as possible,
actual, and necessary, according to the different ways in which
it is related to time.3
Kant connects the pure categories of modality with the
distinction between problematic, assertoric, and apodeictic
judgements. This distinction does not concern the content
of the judgement, that is, does not concern the way in which
different cognitions are united in the judgement. It concerns
only the way in which the judgement (whatever be its content)
is thought.4 If we entertain the judgement as a logical possibility,
it is problematic.5 If we affirm its truth, it is assertoric. If
in A 145 — B 184. There we have (i) the synthesis of time itself or
the production of time, (2) the synthesis of sensation or sense-
perception with the idea of time, or the filling of time, (3) the synthesis
of different sense-perceptions relatively to one another in the whole
of time. 1 Compare A 233-5 = B 286-7.
2 Compare A 180 — B 223. This statement must be taken as
provisional and as simplifying Kant's position unduly. The condition
of the possibility of objects is agreement with the forms of space
and time and also with the categories; see A 218 = B 265. See also
Chapter XLIX § 2.
8 Compare A 145 = B 184. The schema of modality is concerned
with 'whether and how the object belongs to time*.
4 A 74 = B 100. Compare Chapter X § i.
6 We merely conceive or suppose it.
58 THE SCHEMATISM [XXXIII § 5
we must think it because of the laws of thought, then it is
apodeictic.1
The pure categories which are implicit in these forms of
judgement are possibility, actuality or existence, and necessity.2
Kant seems to hold that they, even more than the other pure
categories, can be explained only by a tautology.3 If we omit
all reference to time and space, we are left only with logical
possibility, which means the mere absence of contradiction
in our ideas ; logical actuality or truth,4 which seems to mean
no more than affirmation by the mind; and logical necessity,
which would appear to be present when what we affirm is
inferred from given concepts or judgements in accordance
with the formal laws of thought.5 In all this we are concerned
only with the characteristics of our own thinking, and not
with qualities of objects.
The pure categories of modality are therefore merely corj-
cepts of the synthesis which is present in every judgement.
The pure category of possibility is a concept of that synthesis
as self-consistent in accordance with the formal law of thought.
The pure category of actuality is a concept of the same synthesis
as professing to determine a real object.6 The pure category
1 A 75-6 = B 10 1. Kant finds a parallel to this in understanding
which conceives, judgement which affirms an actual case falling under
the conception, and reason which infers a logical necessity (A 130 =
B 169). Logical necessity, however, would seem to cover, not only
the conclusion of a syllogism, but also immediate inference, and even
analytic judgements. Compare A 304 = B 361.
2 For the sake of simplicity we may ignore their correlates impossi-
bility, non-existence, and contingency. Kant docs not appear to
distinguish between existence (Dasein or Existenz) and actuality
(Wirkhchkeit). We have Dasein in A 80 - - B 106, Existenz in B in,
and Wirkhchkeit in A 145 = B 184. It might be well to use actuality
for the category, and existence (as having a reference to time) for
the schema. 3 A 244 = B 302.
4 It seems to be a claim to truth rather than truth itself. Kant
himself bases the assertonc judgement in the principle of sufficient
reason, while he bases the problematic judgement on the principle
of non-contradiction, and the apodeictic judgement on the principle of
excluded middle; see Log. EmL VII (IX 52-3). I confess that I find
his view here very difficult to understand. 5 A 75-6 = B 101.
6 This seems to be involved in its claim to truth.
XXXIII § 5] THE TRANSCENDENTAL SCHEMATA 59
of necessity is a concept of the same synthesis as following
logically from other concepts or judgements in accordance
with the formal laws of thought.1 Even these pure categories
must, towever, as categories be supposed to determine somehow
all objects in their relation to the mind.
The schematised category of possibility is the concept of
the transcendental synthesis of imagination, so far as that synthesis
involves the forms of intuition. The transcendental schema
which is the product of this synthesis may be said to be the
agreement of the synthesis of different ideas with the conditions
of time in general? An object,3 as opposed to an idea, is possible,
if it is compatible with the nature of time, or can be conceived
as existing at some time or other.4
The schematised category of actuality is the concept of the
transcendental synthesis of imagination, so far as that synthesis
involves the matter of intuition given at a determinate time. The
transcendental schema which is the product of this synthesis
is existence at a determinate time.* An object is actual, if it
is bound up with the material conditions of experience, that
is with sensation.6
The schematised category of necessity is the concept of
1 Compare A 75-6 = B 101.
2 A 144 = B 184. We might add 'and of space in general*. We
have to add also that in A 218 = E 2 65 Kant asserts that agreement
with the formal conditions of thought is also necessary, if an object
is to be possible. This completes what is said here, for the synthesis
of time and space is a synthesis in accordance with the categories
or the forms of thought.
3 The example which Kant gives is the fact that an object may
have contradictory characteristics in succession. The possibility that
the same thing could have contradictory characteristics is unintelligible
to a thought which ignores time.
4 Kant says that the schema is 'the determination of the idea of
a thing at some time or other*. This might be taken to mean that
if we can imagine the thing as existing in time and space, then it is
possible. But this question is complicated and difficult, for Kant
holds that the sphere of the possible is not wider than that of the
actual; see A 230 = B 282 ff.
5 A 145 = B 184. Existence at a determinate time always involves
a connexion with sensation. 6A2i8 = 62 66.
60 THE SCHEMATISM [XXXIII § 6
the transcendental synthesis of imagination as determining the
given manifold with reference to the whole of time. The trans-
cendental schema which is the product of this synthesis is
existence in relation to the whole of time.1 An object is necessary
when the material conditions with which it is bound up are
determined in accordance with the universal laws, or formal
conditions, necessary for the unity of time.2
All this is difficult, and must be taken as a summary and
provisional preparation for the Postulates by reference to
which alone it can be understood.
§ 6. Kant's Summary
Having described the schemata in detail Kant proceeds
to sum up the results which are supposed to flow from this
description. Each schema is said to 'contain and to make
representable'3 certain things. I do not know what Kant
means by 'make representable'.4 I should like it to mean
that the schema is a sensuous characteristic or mark in virtue
of which something can be known.
The schema of the category of quantity contains and makes
1 A 145 = B 184. The schema is said to be aeternitas or necessitas
phaenomenon; see A 146 — B 186. We know the necessity of an
object when we know the chain of causes which produced it.
2 Compare A 218 = B 266.
8 A 145 = B 184, 'enthalte und vorstellig mache.' This phrase should
be repeated each time, and I doubt whether it is satisfactory to
substitute for it the word 'is', as in Kemp Smith's translation. I
also doubt the propriety of adding fnur eine Zeitbestimmung* (only
a time-determination) as is done by Adickes and accepted by Kemp
Smith. The text as it stands is unsatisfactory, but I question whether
it is improved by making Kant say that the schema (which is a
transcendental time-determination) not only contains, but also makes
representable, a time-determination. Kant not uncommonly equates
'is* and 'contains', but it would be strange if the schema made itself
representable.
4 This phrase is also used in A 143 = B 183; but there it is applied
to a 'transition' (Vbergang) from reality to negation which makes
every reality representable as a quantum — so that the sense seems
to be rather different.
XXXIII § 6] THE TRANSCENDENTAL SCHEMATA 61
representable the generation (or synthesis) of time itself in
the successive apprehension of an object.1
The schema of the category of quality contains and makes
representable the synthesis of sensation (or sense-perception)
with the idea of time ; that is, it contains and makes represent-
able the filling of time.2
The schema of the category of relation contains and makes
representable the relation of sense-perceptions to one another
in the whole of time,3 that is, according to a rule of time-
determination.4
The schema of the category of modality contains and makes
representable time itself as the correlate of the determination
of an object? that is, it indicates whether and how the object
belongs to time.6
These statements, it must be recognised, are obscure,
and they repeat rather than clarify what has already been
said. Thus there is, under the heads of quantity and quality,
the same tendency to connect the schema with the synthesis
1 Number (or, perhaps better, extensive quantity) is the product
of such a synthesis of homogeneous times (and spaces) in appre-
hending an object. It may perhaps also be a mark of this synthesis>
if we do not regard the product as separable from the synthesis.
2 Degree of sensation (or of what corresponds to sensation) is
what fills time (and space). It is the product, and perhaps the mark,
of the synthesis which combines sensation with time.
3 (zu alter Zeit.'
4 The permanence, succession, and simultaneity of sense-perceptions
or appearances are, according to Kant, a product (and perhaps a
mark) of the synthesis which combines all sense-perceptions in one
time (and space). They enable us to distinguish the relations of
substance and accident, cause and effect, and interaction.
5 It may be noted that we can know times (and spaces) empirically
only by knowing the objects in these times (and spaces); see A 216
= B 264.
6 The object is possible, if it is compatible with the form of time,
and so can exist at some time or other. It is actual, if its matter is
given at some determinate time. It is necessary, if its existence is
determined in relation to the whole of time in accordance with the
Analogies. These are the ways in which the object can belong to time,
or the ways in which time is the correlate of the determination of
an object.
6a THE SCHEMATISM [XXXIII § 6
of imagination, while under the head of relation (and
perhaps also under the head of modality) the schema is
connected rather with the product of the synthesis.1 Whatever
be the difficulties of Kant's exposition, I cannot see any other
way of understanding his doctrine except on the supposition
already adopted — that the schemata are sensuous characteristics
which must belong to all objects so far as the manifold of
these objects is combined in one time (and space).
This view is, I think, borne out by Kant's conclusion.2
The schemata are a priori time-determinations3 in accordance
with rules ; and these time-determinations (following the order
of the categories) concern (i) the time-series, (2) the time-
content, (3) the time-order (or the order of what is in time),
and (4) the totality of time in its relation to all possible objects.
All objects must have extensive quantity so far as they extend
through a series of homogeneous times. They must have
intensive quantity so far as they fill time. They must be sub'-
stances interacting causally with one another so far as there
is an objective order of events in time. And they must be
possible, actual, and necessary in virtue of their various re-
lations to time as a whole. The first two assertions Kant regards
as intuitively certain; the third requires something that may
be called proof; while the fourth requires only explanation
or elucidation after the first three have been established.
The last paragraphs4 of Kant's discussion explain very
clearly his view that the schemata give 'meaning' or objective
reference to the categories, and at the same time restrict their
application to objects of sense alone.5 We may be tempted
1 This difference may be connected with the fact that under the
first two headings we have intuitive evidence': Kant may therefore
be more inclined to lay emphasis on the synthesis, since the product
is evident to all, but the synthesis is not.
2 A 145 =- B 184-5.
3 It should now be clear that these are not determinations of time
itself, but temporal determinations of objects.
4 A 145-7 = B 185-6. The obscure sentence with which these
paragraphs begin is discussed in Chapter XXXIV § 4.
6 Compare Chapter XXXII § 7 and also Chapter LIV.
XXXIII § 7] THE TRANSCENDENTAL SCHEMATA 63
to suppose that when we abstract from the schemata which
restrict the application of the categories to things as they
appear to our senses, we shall then have pure categories which
will apply to things as they are in themselves.1 Kant does not
deny that we must think things-in-themselves by means of
the pure categories — we have indeed no other way of thinking.
He does deny that such thinking can give us knowledge ; for
knowledge always demands intuition as well as conception.
The pure categories in abstraction from the schemata have
still what he calls a 'logical' meaning: they are concepts of
the unity (or synthesis) of ideas which is implicit in the forms
of judgement. But no object is given for them, and they have
no 'meaning' — in the sense that we cannot indicate the nature
of any object to which they apply; and consequently they are
not a source of knowledge.2
§ 7. The Number of the Schemata
If we hold that the categories cannot be derived from the
forms of judgement, it is clear that a large part of Kant's
doctrine must be arbitrary or artificial, comparable in some
ways to the many attempts which have been made to square
the circle. Nevertheless it is unwise not to recognise the in-
genuity and plausibility of his attempt, concealed though
it is by the untidiness of his expressions. On the whole I
must admit for myself that what surprises me most is the way
in which his efforts approximate to something very like success.
It may be thought that there is one very marked failure,
since we are offered only one schema for the three categories
of quantity and quality, whereas for each of the categories
of relation and modality there is a separate schema. Yet
even here it should be observed that Kant can speak as if
there were only one schema for the three categories of relation,
and one for the three categories of modality.3 He does not
1A 147 = B 186.
2 In the text Kant says that they have no 'meaning* which might
yield a concept of the object. He corrects 'concept* to 'knowledge*
in Nachtrage LXI. 3 A 145 = B 184; compare § 6 above.
64 THE SCHEMATISM [XXXIII § 7
regard the difference between one schema and three schemata
as the sharp distinction which it appears to be at first sight.
How is this to be explained ?
We must remember that every category is involved in Jcnowing
any object. Hence there is only one ultimate synthesis involved
in all knowledge, although this synthesis is complex and has
different aspects concerned with quantity, quality, relation,
and modality. If we treat these aspects separately, and speak
of a synthesis of quantity, a synthesis of quality, and so on,
each of these syntheses in turn may be regarded as having
three different aspects. Where these aspects are of greater
complexity, as in the case of relation and modality, Kant
gives them special treatment ; where they are of less complexity,
as in the case of quantity and quality, he treats them all together.
His carelessness of expression1 should not obscure the presence
of three different aspects in every case.
It should, for example, be clear that in determining the
existence of any object, we must determine it, not only as a
permanent substance with changing accidents, but also as
having the succession of these accidents causally determined,
and as acting and reacting simultaneously with all other sub-
stances. Unless all three relations are present, Kant believes
that we cannot determine the existence of any object in time
and space.
So too in the case of quantity. We are given only one schema,
namely number, but in numbering or measuring any object
all three categories are present. Every number is a plurality
of units taken as a totality, and number is said to belong to
the category of totality only because totality is plurality regarded
as unity.2 The schema of quality in a similar way involves
reality, negation, and limitation. Indeed it is only in this case
that Kant even attempts to show the interconnexion of the
1 For example, the suggestion that quantity is concerned only
with the category of totality, and that quality is concerned only with
the category of reality.
*B in. A plurality, it may be added, is always a plurality of
units.
XXXIII § 7] THE TRANSCENDENTAL SCHEMATA 65
categories, although this becomes a little clearer when we
come to consider the Principles as a whole.
The difference between one schema and three is merely
an indication of the less or greater difficulty of making clear
what is involved in one aspect of synthesis; and we shall
never understand the Analogies and the Postulates, unless
we realise that in them we are dealing with a synthesis which
is essentially one.
VOL. II
CHAPTER XXXIV
THE SIGNIFICANCE OF THE SCHEMA
§ i. Subsumption and Syllogism
In the light of what we have learned about the schemata,
we may be tempted to suppose that Kant's argument in the
Analytic of Principles takes the form of a series of syllogisms
in which the transcendental schema is the middle term. In
the major premise we subsume the schema under its corre-
sponding category; in the minor premise we subsume the
object under the schema; and in the conclusion we subsume
the object under the category.1
Even if this were so, the Analytic of Principles wo
be properly called the Doctrine of Judgement; for it
the two premises which Transcendental Logic has to e
and both of these premises are for Kant matters of ju
in the technical sense.2 The fact that the conclusion
by the ordinary rules of Formal Logic does not n
chapter a treatise on the syllogism.
Nevertheless a syllogism of this kind seems an oc
1 For example, 'All necessary succession exhibits the relation of
ground and consequent.
All objective succession is necessary succession.
.'.All objective succession exhibits the relation of ground and
consequent/
The major premise is given in the chapter on Schematism, and
the minor in the Second Analogy. Both premises are supposed to
be matters of judgement in the technical sense.
2 See Chapter XXXII § 3. Incidentally the view of Adickes— that
Kant arbitrarily invented the whole doctrine of schematism in order
to have a chapter corresponding to the chapter on judgement in
Formal Logic — is the more unnecessary because Kant requires in
any case such a chapter for his Principles. I have great respect for
the later work of Adickes, but this suggestion, like some others
made in his edition of the Kntik, seems to me to require no refutation.
The only excuse for it is the youth of the writer at the time, and I
think it unfortunate that Kemp Smith should have followed him
in exaggerating the influence of Kant's so-called 'architectonic*.
XXXIV § i] THE SIGNIFICANCE OF THE SCHEMA 67
of syllogism to use in the circumstances. It is a syllogism
whose conclusion is known before we begin;1 for we are
supposed to have proved in the Transcendental Deduction
that the categories generally must apply to objects.2 We are
not arriving at a conclusion by the elimination of a middle
term; we are rather making intelligible the conclusion by
discovering the precise nature of the middle term on which
it rests.3
Kant's way of stating his doctrine lends colour to the view
that he is engaged in a syllogistic argument, but I doubt whether
this is the correct interpretation. For one thing the conclusion
of such a syllogism is not really the conclusion at which we
wish to arrive. His real aim is not to show that the object
falls under the pure category, but to show that it falls under
the schematised category ; and we cannot do this by eliminating
the middle term in the syllogism. This view is perhaps con-
firmed by the fact that in this chapter, as indeed elsewhere,
he consistently describes the categories as if they were
schematised categories.
The categories with which Kant is really concerned are
the schematised categories. In the chapter on schematism
he is dealing in detail with that element in the categories
which has hitherto been left vague, namely the condition of
sensibility which each contains. In abstraction from such
a condition or schema the pure categories are without 'sense
1 Compare the statement in A 322 — B 378.
2 Perhaps we are even supposed to have proved generally that
the schema is the middle term by which this conclusion is reached.
Thus Kant says expressly (in A 139 =-- B 178-9) 'we have seen in
the Transcendental Deduction . . . that pure a priori concepts contain
besides the function of understanding (that is, the form of thought)
in the category, also formal conditions of sensibility', or in other words
schemata. He also says that the categories contain the general condition
for rules (see A 135 = B 174 and A 159 = B 198); and this condition
may be the schema.
3 We are also indicating the aspect of the object which falls under
the category. It is one thing to know that an object must somehow
exhibit the relation of ground and consequent, and quite another
thing to know that it is the succession of changes in the object which
exhibits this relation.
68 THE SCHEMATISM [XXXIV § 2
and significance1.1 As restricted to their only legitimate use,
that is, as applied to objects in virtue of the transcendental
schemata, the categories are schematised. The schematised
categories 'contain' the transcendental schemata; and the
transcendental schemata are exhibited in all objects so far
as the manifold of these objects is combined by imagination
in one time and space.
If this is the correct interpretation, Kant's argument is
wrongly viewed as a syllogism, and consists rather of two
judgements. In the first judgement we recognise the schema
contained in a particular category — we recognise, for example,
that the category of cause and effect contains, not only grounds
and consequents, but the necessary succession of grounds and
consequents; and only so can it be regarded as the category
of cause and effect. In the second judgement we recognise
that all objects, so far as they are substances whose accidents
succeed one another in time, fall under the category of cause
and effect ; or in other words that all changes happen in accor-
dance with the law of cause and effect.2
There is manifestly nothing artificial in making a distinction
between the concept of ground and consequent and the concept
of cause and effect. It is vital to Kant's argument to specify
the transcendental schema which is contained in each category
and thereby distinguishes the category from the concept of an
empty form of judgement supposed somehow to determine
objects.
§ 2. Category and Schema
On this view the pure category is an abstraction : the only
category which we can legitimately apply to objects is the
schematised category. This I believe to be Kant's own doctrine,3
and he habitually insists, especially in the second edition,
1 Compare A 246 where they are said to have absolutely no relation
to any determinate object.
2 We shall have to consider later whether this is properly described
as a judgement in the technical sense; see Chapter XXXVI § 4.
3 Compare A 145-6 = B 185.
XXXIV § 2] THE SIGNIFICANCE OF THE SCHEMA 69
that the pure category is obtained when we abstract from
the references to time and space contained in the schematised
category.1
It may be suggested that if this is so, Kant's paraphernalia
of pure categories, schematised categories, and transcendental
schemata is unnecessarily elaborate. All we require is the
schematised category, and the schematised category can be
identified with the transcendental schema.2
This suggestion has some value as indicating a possible
way of reconstructing Kant's doctrine, if we are unable
to accept his derivation of the categories from the forms of
judgement.3 It has no value as an interpretation of Kant's
own thought.
We may indeed say with propriety that, on Kant's view, the
transcendental schema is revealed concretely to sense and
imagination4 and is conceived or 'contained' in the schematised
category. There is a minor difficulty even in this; for the
schematised category may be said to be a concept of the com-
bination of the manifold in time, while the transcendental
schema is rather the sensuous characteristic which results
from such combination.5 If we set this aside as an unnecessary
complication, we must not forget that for Kant more is con-
tained in the schematised category than is given in the trans-
1 Sec, for example, B 162 and B 163.
2 Compare Kemp Smith, Commentary ', pp. 339-40. Kemp Smith
even goes so far as to say that 'what Kant means when he speaks of
the categories are the schemata'; but it should be noted that the
names by which Kant alludes to the different schemata are other
than the names by which he alludes to the schematised categories.
3 See § 6 below.
4 Kant himself sometimes speaks as if the transcendental schema
were a concept; see A 146 = B 186. The transcendental schema
can of course be conceived, like any other sensuous characteristic;
but the concept of the transcendental schema * con tains' less than
the schematised category.
6 As, for example, beauty may be said to result from harmony or
coherence in the object. I believe myself that such language is too
external. Beauty is neither the logical consequence nor the practical
effect of harmony or coherence; and it would be truer to say that
beauty is manifested or embodied in such harmony or coherence.
70 THE SCHEMATISM [XXXIV § 2
cendental schema ; for the category is enriched by its connexion
with the form of judgement. This is true at any rate in regard
to the categories of substance and cause — the two categories
which we may not unreasonably conjecture to have been
the starting-point of Kant's thought.
Thus, in the traditional doctrine which Kant inherited,
substance is regarded (i) as the ultimate subject of all predicates
and (2) as the permanent substratum of change. Both of these
are conceived in the schematised category. The first Kant
derives from the form of judgement. The second is given
in the transcendental schema and is derived from the synthesis
of the manifold in time and space. If the schematised category
were a concept of the transcendental schema and nothing
more, then the category of substance would for Kant be
impoverished.
This consideration is more important when we consider
the category of cause and effect. For Kant causality means
(i) that the succeeding event has its ground in the preceding
event, and (2) that the succeeding event follows upon the
preceding event in accordance with a rule of necessary succes-
sion. Here again (i) is derived from the form of judgement,
and (2) is derived from the synthesis of the manifold in time
and space. The schematised category, if it contained only
the transcendental schema without the principle of synthesis
present in the form of judgement and conceived in the pure
category, would for Kant be impoverished.
No doubt it may be thought to-day that if causality is to
be admitted at all, it must be reduced to necessary, that is,
invariable, succession; but the plain man, and for this purpose
Kant is a plain man, believes that the effect is really grounded
in the cause, so that such a modification of the Kantian doctrine
would mean for him a definite loss.1
1 The same considerations apply to the category of interaction. I
feel more doubt in regard to the categories of quantity, quality, and
modality.
XXXIV § 3] THE SIGNIFICANCE OF THE SCHEMA 71
§ 3. The Transcendental Synthesis of Imagination
So far we have considered Kant's doctrine with reference
to categories and schemata. We must now consider it in relation
to the active synthesis necessary for knowledge.
It is easy to see that all judgement involves the unification
or synthesis of ideas,1 and that the transcendental synthesis
of imagination involves the unification of ideas in time and
space. Granted that the second (or concrete) synthesis might
be a species of the first (or abstract) synthesis, we have still to
ask what is the relation between them. Does the synthesis
present in judgement control and determine the synthesis
whereby the given manifold is combined in one time and space ?
Kant clearly holds that the transcendental synthesis of imagina-
tion maintains the unity of time and space in response to the
general demand of thought for unity in the object : the unity
of apperception is Original' and the unity of objects is 'de-
rivative'. But there still remains the question whether the
different aspects of the transcendental synthesis of imagination
are determined and controlled by the different aspects of
synthesis present in the form of judgement as such.
I do not find that Kant is wholly clear on this point, and
perhaps we should keep open the possibility that he believed
the different forms of synthesis present in judgement to follow,
rather than to control, the transcendental synthesis of imagina-
tion.2 Nevertheless it seems difficult to understand his view
except on the supposition that the forms of judgement determine
1 Compare Kant's statement that the categories, even in
abstraction from all sensible conditions, have a logical meaning —
they are concepts of the abstract unity (der blossen Einheit) of ideas ;
see A 147 = B 186.
2 This is suggested chiefly by some obscure statements in Kant's
casual jottings. Thus he distinguishes the real function of ideas from
their logical function, and seems to suggest that the former are the
ground of the latter; sec Nachlass 4631 (XVII 615). He even says
that the sensitive function is the ground of the intellectual function ; see
Nachlass 4629 (XVII 614) and compare Nachlass 4635 (XVII 619).
His statements are, however, so puzzling that I am not sure whether
they arc relevant to the present question.
72 THE SCHEMATISM [XXXIV § 3
and control the different aspects of the transcendental synthesis
of imagination.
In certain instances this is perhaps not so impossible as
it might seem to be at first sight. Granted that the transcendental
synthesis of imagination must impose some sort of permanence
on the manifold in order to maintain the unity of time, it
might be because of the demand of thought that we regard
the permanent as the substratum of change and the ultimate
subject of all predicates. Granted also that the transcendental
synthesis of imagination must impose necessary or regular
succession upon the given manifold, it might be because
of the demand of thought for grounds that we regard the first
event in a regular succession as the cause and the second as
the effect. Even so I do not see how the demand of thought
could control or determine the imposition of permanence
and regular succession by the transcendental synthesis qf
imagination. Still less do I see how the homogeneity of the
times and spaces combined by imagination could be due to
the demand of thought for homogeneous objects — unless
indeed Kant holds that there is in time and space as given
to us by the perception of temporal and spatial objects nothing
which suggests homogeneity apart from the demands of
thought.1 Above all, I can see not the slightest ground for
believing that the degree of intensive quantity given to us in
sensation is due to a combination made by the transcendental
synthesis of imagination in response to the demand of thought
that we should be able to affirm and deny and thereby
delimit.
It is unfortunate that Kant has not given us more help
on these difficult questions, but I think they should be asked
even if we are unable to answer them. All we can say with
confidence is that on his view each aspect of the transcendental
synthesis of imagination falls under an aspect of the synthesis
present in judgement as such: the former gives the species
of which the latter is the genus.
1 Time, for example, seems sometimes to race and sometimes to
drag; yet we think that its parts are homogeneous.
XXXIV §4] THE SIGNIFICANCE OF THE SCHEMA 73
§ 4. The Schematism of the Understanding
Kant may have thought that questions of the type I have
raised are too difficult to answer. Thus he asserts that the
schematism of our understanding, in its relation to appearances
and their mere form, is a hidden art in the depths of the
human soul: its true operations we shall hardly ever divine
from nature and lay open to our gaze.1
This is one of the statements which have been used in
support of the view that Kant believed the syntheses which
are the conditions of experience to be necessarily unconscious
and even noumenal. I do not believe that it can be properly
interpreted in this way,2 but here I wish to ask only what
Kant meant by the phrase 'schematism of the pure under-
standing'.
This schematism is said to be the procedure of the pure
understanding with the transcendental schemata.3 This pro-
cedure is a kind of 'exhibition'4 — that is, an exhibiting of the
object to which the pure category applies. We are said to
'exhibit* the object of a concept, or more commonly to 'exhibit*
the concept, when we supply the intuition to which the concept
applies. When we exhibit an empirical concept, we provide
the corresponding empirical object or intuition. When we
exhibit a mathematical concept, we construct the corresponding
object in pure intuition. When we exhibit a pure category,
we supply the sensuous condition or schema under which
alone the pure category can be employed.5 This exhibition
of the pure category is what Kant calls the schematism of
the pure understanding. In this way we give objective reality,
or sense and significance, to the pure categories.6
1 A 141 — 13 180-1. Compare A 78 — B 103.
2 The fact that we have to divine the schematism from nature
suggests that it is not noumenal. 3 A 140 — B 179.
4 'Exhibitio* or ' Darstellutig* ; see Fortschntte der Metaphysik (Phil.
Bib. 460, pp. 106-7, iSJ* and J65). Compare A7i3 — B74i and also
(for perhaps a rather different usage) A 727 = B 755.
6 Compare A 136 -- B 175.
6 In the case of the Ideas of Reason there is no schematism, but
only a symbohsation by analogy (sometimes called analogical or
VOL. II C*
74 THE SCHEMATISM [XXXIV § 4
I take it that by 'schematism* Kant means primarily, not
the reflective exhibition of the pure category which takes
place in the Krittk itself, but the unreflective exhibition which
takes place in ordinary experience. It is this unreflective pro-
cedure which is 'a hidden art in the depths of the human soul'.
There is one other, and rather obscure, passage to be men-
tioned.1 The schematism of the understanding through the
transcendental synthesis of imagination is said to result in2
the unity of all the manifold of intuition in inner sense, and
so indirectly in the unity of apperception as a function which
corresponds to inner sense (a receptivity).3 Kant must mean,
I think, that the schematism of the understanding supplies
us, not with intuitions corresponding to the pure category,4
but with kinds of unity (or combination) in intuitions; and
that it is these kinds of unity (or combination) of the temporal
and spatial manifold which correspond to the pure categories.
We may regard these different kinds of unity as aspects of
the one necessary synthetic unity of all the manifold in inner
sense ; and the one necessary synthetic unity of all the manifold
in inner sense corresponds to the necessary synthetic unity
of apperception. Indeed the necessary synthetic unity of
apperception finds its concrete embodiment only in the neces-
sary synthetic unity of the manifold given in time and space.5
symbolic schematism), an indirect (as opposed to a direct) exhibition
of the concept; compare the passages in the Fortschritte der Meta-
physik given above and also K.d.U. § 59 (V 351).
XA 145 = Bi85.
2thinauslaufe.' This word seems obscure in the present passage:
it can hardly have its more common meaning of * being equivalent to'.
3 Compare statements about the transcendental synthesis of imagina-
tion in A 118, A 123, and B 151; also A 119. See especially Chapter
XXXVI § 7.
4 Other kinds of exhibition supply us with intuitions corresponding
to the concept.
6 Hence the schematism may be said 'to result in' the unity of
apperception 'indirectly'. Compare Kant's statement that the schema-
tism is 'the synthesis of the understanding when it determines inner
sense in accordance with the unity of apperception'; see Nachtrage
LVII. Compare also the statement that the schematism concerns
appearances and their mere form ; see A 141 — B 180.
XXXIV § 5] THE SIGNIFICANCE OF THE SCHEMA 75
The schematism of the understanding, it appears, must
work 'through the transcendental synthesis of imagination*.
So far as it differs from this synthesis, it must do so in virtue
of the fact that it involves a judgement (however 'obscure')
that the product of the transcendental synthesis is an instance
or 'case' to which the pure category applies. It must be present
whenever we judge that A is the cause of B, and indeed when-
ever we make any judgement of experience. Needless to say,
it is not made explicit in ordinary experience. What Kant
is attempting to give is an analysis of elements which must
be present in experience as such, not a description of experience
as it appears to the unreflective mind, and still less a description
of the successive stages which precede experience or are
found in experience.
§^5. Value of Kant's Doctrine
Kant's doctrine, if we view it as a whole, has little or nothing
of that perversity commonly attributed to him by his critics.
His fundamental contention that judgement as such requires
a synthesis of the given manifold is perfectly sound, and it
is not unreasonable to suppose that judgement as such requires
certain definite kinds of synthesis. To accept the forms of
judgement in Formal Logic as giving us an infallible clue
to these definite kinds of synthesis is certainly a trifle ingenuous.
Yet even here it is possible to maintain that the principles
of synthesis which Kant finds by this method are really involved
in all judgement as such; and I am inclined to believe that
we are justified in taking this as the correct expression of his
own view. The theory that the forms of judgement are forms
of analytic judgements only, and are nevertheless the source
of principles of synthesis, is undoubtedly perverse; but this
perversity is entirely the creation of the commentators and
has nothing whatever to do with Immanuel Kant. To treat
the derivation of the categories from the forms of judgement
as wrong-headed and inexcusable pedantry indicates, to my
mind, only the failure of the critic to think himself into Kant's
point of view.
76 THE SCHEMATISM [XXXIV § 5
In any case if we start from this derivation of the categories,
an account of the transcendental schemata is absolutely essential
to the consistent development of the theory. Kant would
merely display incompetence as a thinker, if his account of
the schemata had no relation to his derivation of the categories,
however perverse that derivation might be. It is unreasonable
to blame a man twice over for the same mistake ; and to con-
demn him because his argument is consistent with his premises
is wholly unjustifiable.
The doctrine of the schemata is not the result of formalism
or of a so-called 'architectonic': it is a necessary part of his
argument. Indeed even if we attribute his derivation of the
categories to formalism in a bad sense, we ought to recognise
that in his account of the schemata and of the Principles
Kant is breaking away from mere formalism. He is deriving
the categorial characteristics of objects from the fact that
all objects must be temporal; and in this there is surely a
considerable measure of truth. The connexion of the categories
with the synthesis of imagination and the form of time is the
most important, and the least artificial, part of the Critical
Philosophy. We must not allow the difficulties of an unfamiliar
and antiquated terminology to obscure the real significance
of the argument.
My own complaint about this chapter is not that it follows
too closely the pedantic methods of the schools, but on the
contrary that it is too brief, and is lacking in clarity and pre-
cision. The schemata are obscurely described, and their con-
nexion with the corresponding category receives no elucidation.
If we have patience with Kant's elaborate terminology,
which is the terminology of his time and not of ours, and if
we make allowances for a carelessness at least partly excused
by the circumstances in which he wrote, I think we shall see
that it is the connexion between form of judgement and category
and schema which clamps together his whole argument into
the firmly knit structure which it was intended to be. One
part of that structure — the account of the forms of judgement
given by Formal Logic — has now crumbled, and the whole
XXXIV § 6] THE SIGNIFICANCE OF THE SCHEMA 77
edifice may therefore seem to be in ruins, unless we admit
the possibility of reconstruction on the lines I have suggested.
But even at the worst we ought to recognise that ruin has
resulted, not because the building was so loosely put together,
but because the different parts were so closely and firmly
joined. The failure, if it be a failure, is due not so much to
the incompetence of the architect as to the use of materials,
hitherto believed to be sound, which have proved unable to
withstand the march of time.
§ 6. The Possibility of Reconstruction
Kant's doctrine rests upon two main foundations, firstly
the forms of judgement, and secondly the transcendental
synthesis of space and time. It is possible that the second
may stand, even if the first has been undermined. The trans-
cendental schemata are not deduced from the forms of judge-
ment, but from the nature of time.
If we cease to lay stress upon the different forms of judge-
ment, and refuse to admit the possibility that these forms
may be involved in judgement as such, we shall certainly
lose something which Kant believed to be of importance,
particularly, as I have pointed out,1 in regard to the category
of cause and effect. Yet on the other hand there might still
be much which we could retain. We might still retain the view
that judgement is necessary in order that there may be objects
for us, and that judgement presupposes the unity of apper-
ception and demands a corresponding unity in the empirical
manifold. If we accept this, we may still hold also that the
required unity is imposed by the transcendental synthesis
of the imagination, which combines the given manifold in
one time in accordance with the demand of thought. It seems
to me obvious that this implies the necessity of certain categorial
characteristics in all objects: we have only to await a further
description of these characteristics and a satisfactory proof
that without them the world as known to us would be in-
1 See § 2 above.
78 THE SCHEMATISM [XXXIV § 6
compatible with the unity of time. Hence we can still approach
Kant's Principles in the hope of discovering a proof of the
necessity of certain categorial characteristics; for his proofs
rest, not upon the forms of judgement, but upon the unity
of time. The appeal made to the forms of judgement serves
only to enrich some of the categories and to guarantee the
completeness of Kant's list ; and the latter point is quite cer-
tainly a mistake.
It must be added, however, that Kant is hampered through-
out by his attempt to restrict the schemata to the form of
time. This attempt is based on the view that space is the form
of outer sense only, while time as the form of inner sense is
the ultimate condition, not merely of inner, but also of outer,
intuition. If we are to make a satisfactory doctrine, we shall
have to work with space and time (or perhaps space-time),
and it is clear that Kant's owrn mind was steadily working
in this direction: space is not wholly neglected even in the
first edition, and it becomes much more prominent in the
second. Such a development of Kant's view will certainly
give rise to new difficulties; for it may tempt us to regard
the mind itself as spatial, and this will have consequences
which Kant at least is not prepared to accept. But even in
Kant's own doctrine there are many puzzles about the mind,
which it is doubtful if he ever solved.1
1 Professor Alexander's derivation of the categories in Space, Time,
and Deity is, I think, partly an attempt to improve and develop
Kant's doctrine along the lines suggested by the second edition of
the Kntik. He accepts the theory that the mind is spatial as well as
temporal, but I think that this leads to views of freedom and immor-
tality which are fundamentally opposed to the views of Kant.
BOOK VIII
THE PRINCIPLES
OF THE UNDERSTANDING
CHAPTER XXXV
THE SUPREME PRINCIPLE OF SYNTHETIC
JUDGEMENTS
§ i. The Nature of Kant's Argument
The Principles of the Understanding set forth the main
positive conclusions of Kant's metaphysic of experience; that
is to say, they are the ultimate synthetic a priori judgements
which we are entitled to make about objects of experience. To
estimate their value we must understand, not only the nature
of the proof by which they are established, but also their place
in Kant's argument as a whole.
The Metaphysical Deduction has shown, according to Kant,
that the categories are derived from the forms of judgement;
and the Transcendental Deduction on its objective side has
demonstrated the objective validity of categories so derived.
The Transcendental Deduction on its subjective side showed
generally that the transcendental synthesis of imagination
imposes the principles of synthesis thought in the pure
categories upon appearances given under the form of time;
but no attempt was made to deal with the separate categories,
or to determine the special nature of the link which connected
each category with objects. This link has been treated in the
chapter on Schematism, where Kant has maintained that
corresponding to each category there is a sensuous condition,
or schema, which entitles us to apply the category to objects
in a synthetic a priori judgement.1 It is now our task to
establish such a synthetic a priori judgement for each category.
Each of these synthetic a priori judgements is called a Principle
of the Understanding.
The argument is complicated by the difference between
the pure category and the schematised category. If we look at
Kant's Principles we see that what they affirm of objects is the
1 A 148 = B 187.
82 THE PRINCIPLES [XXXV § i
schematised category.1 Kant himself says2 that appearances
must be subsumed, not directly3 under the categories, but
under their schemata ;4 and the lack of homogeneity between
appearance and category indicates that the subsumption —
that is, the direct subsumption — of appearances under the
categories is impossible.5 The very fact that the Principles are
principles of the empirical use of the categories implies that
they are concerned with the schematised, and not with the
pure, categories.6
For reasons already given I do not think that subsumption
under the category by means of the schema involves a syllogism.7
Kant's exposition is not sufficiently clear, but the easiest inter-
pretation seems to be that the chapter on Schematism shows
how the categories must be schematised, while the Principles
show how the schematised categories must apply to all objects
of experience.8
There is an obvious difficulty in the fact that the Principles
have to be 'proved'. The assertion of the Principles is the
work, not of reason, but of judgement; and the Principles,
although they are grounds of other judgements, are not
themselves grounded in higher, or more general, judge-
1 This fact is obscured by Kant's use of 'substance* and 'cause
and effect* as names for the pure categories; but the pure categories
have strictly no reference to time, and the categories proved in the
Analogies, as in all the other Principles, must have a reference to time.
2 A 181 = B 223 ; compare Chapter XL § 3. 3 ' schlechthin.'
4 This applies to all the Principles, but preeminently to the
Analogies. Kant adds that in the Principle we do indeed make use
of the category, but in its application to appearances we set the schema
in its place, or rather set the schema alongside the category as a
restricting condition (A 181 - B 224). In other words the Principles
use the category only as schematised. 5 A 137 == B 176.
6 Compare A 180-1 — B 223. The empirical use of the categories
is their use with regard to objects of experience ; see Chapter XI § 4.
In A 161 - B 200 the Principles are said to be rules for the objective
use of the categories. The only legitimate objective use of the categories
is their empirical use. 7 See Chapter XXXIV § i.
8 Hence the Analytic of Principles is not concerned with the prin-
ciples laid down in the Aesthetic in regard to space and time ; still
less is it concerned with the principles of mathematics. See A 149 -=
B 188-9 and A 159-60 — B 198-9, and compare Chapter XXXVI § i.
XXXV § 2] THE SUPREME PRINCIPLE 83
ments.1 Hence the 'proof' of the Principles must have a very
special character. A Principle cannot be inferred from some-
thing else that we know about objects : it is itself the basis of
all our knowledge of objects. The proof of it depends on our
seeing that without it all knowledge of objects would be im-
possible;2 and Kant very properly feels himself obliged to
explain the nature of his proof, and to set forth what he calls
'the supreme principle of all synthetic judgements'.
§ 2. The Principle of Analytic Judgements
In order to avoid misunderstanding3 Kant first of all explains
the supreme principle of analytic judgements. This is the law
of non-contradiction, which he expresses in the form 'Nothing
can have a predicate which contradicts it'.4
The purpose of this formula is to avoid reference to time,
stjch as is found in the statement that a thing cannot both be
and not be at the same time,5 or that A cannot at the same
time be both B and not-B.6 A statement of this kind is defective;
for a logical principle is not restricted to temporal relations.
The reason for a formulation which refers to time is the fact
of change, which means that the same thing can have contra-
dictory predicates, not at the same time, but successively.
In such a case, however, the predicates are incompatible with
one another, but not with the concept of the subject to which
they apply. It is only because both predicates are separated
from the subject-concept that we have to say they cannot be
attributed to the subject at the same time. If the first predicate
is really a part of the subject-concept, the second predicate
cannot be attributed to the subject at all.7
1 A 148 = B 1 88. The German word for Principles (Grundsatze)
is itself an indication of this.
2 A 149 = B 1 88. The proof cannot be carried further Objectively',
and must be derived from 'the subjective sources of the possibility
of knowledge of an object in gcnerar. To say this is to say that it
must be a transcendental proof. 3 A 150 -- B 189.
4 A 151 = B 190. 8A 152 = B 191. °A 152 = B 192.
7 Thus we can say 'No unlearned man is learned', while we can
say only 'No man can be both learned and unlearned at the same
time'. See A 153 -- B 192.
84 THE PRINCIPLES [XXXV § 3
All judgements, whether analytic or synthetic, must conform
to the principle of non-contradiction, which is a universal,
though negative, condition of truth.1 If a judgement is not in
conformity with this principle, it is false ; but if it is in con-
formity with this principle, it need not be true.2
In the special case of analytic judgements conformity of
the judgement to the principle of non-contradiction is a
guarantee of truth.3 Given a subject-concept, we can make
analytic judgements by the principle of non-contradiction alone.
Hence the principle of non-contradiction is a sufficient prin-
ciple of all analytic judgements. It is their highest or supreme
principle, because we require no other.4
§ 3- Different Kinds of Synthetic Judgement
The primary concern of Transcendental Logic, as indeed
of the wrhole Critical Philosophy, is with synthetic a priori
judgements, whose origin, objective validity, extent, and limits
it seeks to determine.5 Nevertheless Kant attempts to formulate
the supreme principle of all synthetic judgements, and we must
suppose that this principle is meant to cover a posteriori, as
well as a priori, synthetic judgements. He is, however, less
interested in the former than in the latter, and this makes it
1 A 151 =- B 190. Compare A 152 — 13 191 for synthetic judgements.
2 Compare Chapter IX § 2,.
3 A 151 =- B 190-1. It should be noted that Kant js assuming the
subject-concept to refer to an object. Compare also A 736 - B 764.
4 This doctrine offers not the slightest justification for supposing
that the laws of thought or the forms of judgement belong for
Kant only to analytic judgements. On the contraiy the law of non-
contradiction, as he points out in A 150 -- B 189 and A 152 -=- B 191,
applies to all judgements (including synthetic judgements); and so
docs his account of the forms of judgement. Kant, it should be noted,
asserts in A 154 — -= B 193 that Formal Logic has nothing to do with
the problem of explaining the possibility of synthetic judgements,
and should not even know the name of such judgements This implies,
and I think correctly, that the distinction between analytic and
synthetic judgements does not arise for Formal Logic at all. Kemp
Smith takes the 'name* to be the name of the problem, but the general
result is much the same.
6 Compare A XII, A 10, B 23, A 57 — B 81, A 154 — B 193.
XXXV § 3] THE SUPREME PRINCIPLE 85
difficult to disentangle his exposition. It is not always
certain whether he is speaking of all synthetic judgements
or only of synthetic a priori judgements; and his view
of synthetic a posteriori judgements is not made sufficiently
clear.
We should naturally expect to find a common principle at
work in all synthetic judgements, just because they are synthetic ;
but Kant regards the different kinds of synthetic judgement as
connected by something more than being species of the same
genus.
It will be remembered that in his first account of synthetic
judgements he suggested that the problem of synthetic a
posteriori judgements was capable of a simple solution.1 Such
judgements are dependent upon further intuition of the object
referred to in the subject-concept, and so are justified by our
complete experience of the object. I see no sign that Kant ever
modified this belief, which is obviously true ; but we have since
learnt that such experience of objects is impossible apart from
the application of the categories to given intuitions.2 The
justification of such application is to be found only in the
Principles of the Understanding, which are themselves synthetic
a priori judgements ; and Kant believes that synthetic a posteriori
judgements presuppose the Principles of the Understanding
and consequently presuppose the ultimate principle which is
embodied in them.
The Principles of the Understanding are not the only syn-
thetic a priori judgements, and here again it is at times uncertain
whether Kant is speaking of all synthetic a priori judgements
or only of the Principles. I think we can say both that the
Principles are presupposed by all other synthetic a priori
judgements, and also that one and the same general principle
is at work in the Principles and in other synthetic a priori
judgements, such as those of mathematics.
1 A 8, B 12. Compare Chapter III § 8.
2 When we judge that this white sugar is also sweet, we are pre-
supposing that we have before us an object which is a substance
with accidents and so on.
86 THE PRINCIPLES [XXXV §4
To sum up — Kant's account deals mainly, but not entirely,1
with the principle of synthetic a priori judgements ; and he is
concerned above all with the way in which this principle is
manifested in those synthetic a priori judgements which he
calls the Principles of the Understanding. Nevertheless his
account is, I think, intended to give the supreme principle, not
only of all synthetic a priori judgements, but of all synthetic
judgements without exception.
§4. The 'Third Thing9
Kant begins his account by a general statement which does
apply to synthetic judgements of every kind. In all synthetic
judgements the predicate-concept falls outside the subject-
concept, and we must pass beyond the subject-concept, which
is supposed to be given.2 In order so to pass we require 'some-
thing else', or a 'third thing', to justify our synthesis of subject
and predicate.3 We have consequently to ask what is the 'third
thing' which is the 'medium' of all ynthetic judgements.
The key to the problem is to be found in the Transcendental
Deduction. Kant therefore begins his enquiry by a summary
statement of his previous conclusions.4 There is only one
whole5 in which all our ideas are contained. This whole is inner
sense and its form, which is time. The synthesis of our ideas in
time depends on imagination, and the unity of this synthesis6
1 In A 155 = B 194, where he asserts that the possibility of synthetic
judgements is to be found in sense, imagination, and apperception,
he is manifestly referring to all synthetic judgements, and not only
to synthetic a priori judgements ; for he adds that the possibility of
pure synthetic judgements is also to he found in sense, imagination,
and apperception, because these are sources of a priori ideas. There
are also other passages which refer to all synthetic judgements, but
there is no attempt to deal with synthetic a posteriori judgements
by themselves. 2 Compare A 6 = B 10 and Chapter III § 5.
3 A 155 = B 194. Here we have a 'third thing* which manifestly
does not involve a syllogism. 4A 155 = B 194.
5 'Es tst nur em Inbegnff.' Mellm's emendation 'Es gibt nur einen
Inbegnff' seems to me unnecessary.
6 The word 'derselbert refers, I think, to 'the synthesis of ideas*
rather than to 'ideas* as in Kemp Smith's translation. Compare A 158
= B 197.
XXXV § 4] THE SUPREME PRINCIPLE 87
(a unity which is required for judgement) depends upon the
unity of apperception. Hence it is by reference to the three
powers of inner sense, imagination, and apperception that we
must seek to explain the possibility of all synthetic judgements.
And since all three powers are the sources of a priori ideas,1
it is by reference to these powers that we must seek to explain
the possibility of synthetic a priori judgements. Indeed synthetic
a priori judgements basedon these sources2 are not only possible,
but also necessary, if we are to have a knowledge of objects
which rests solely on the synthesis of ideas. Such a knowledge
of objects is synthetic a priori knowledge :3 it can take no account
of the empirical matter of experience, but only of its form, that
is, of its synthetic unity.4
The implication of these statements is that in order to make
synthetic judgements we require, in addition to the subject-
concept, a knowledge of the object5 to which the subject-
concept refers. Such knowledge, as Kant has pointed out,
depends on the three powers of inner sense, imagination, and
apperception. He now proceeds to examine this knowledge from
the side of the object.
If any cognition is to have what Kant calls 'objective reality',6
that is, if it is to be knowledge of an object, the object must
1 Inner sense is the source of the pure intuition of time, imagination
is the source of the transcendental schemata, and apperception is
the source of the pure categories ; compare A 94. All three powers
are involved in every synthetic a priori judgement, and indeed in
every synthetic judgement.
2 Note that it is synthetic a priori judgements (and not the three
powers, as in Kemp Smith's translation) which are necessary. The
phrase *aus diesen Grunden* is puzzling. I incline to take 'Grunden*
not as 'reasons', but as the 'grounds' or 'sources' (Quellen) of a priori
ideas. If we interpret the phrase as signifying 'for these reasons',
it must mean 'because these three powers arc sources of a priori ideas'.
3 Knowledge which rests on the synthesis of ideas is synthetic
knowledge. Knowledge which rests solely (ledighch) on the synthesis
of ideas is synthetic a priori knowledge: it does not rest partly on
given sensations, but contains 'nothing except what is necessary for
synthetic unity of experience in general' (A 158 = B 197). Such
synthetic unity involves the three powers which arc said to be sources
of a priori ideas. 4 Compare A 156-7 — B 196.
5 Compare A 157 -= B 196. a A 155 = B 194.
88 THE PRINCIPLES [XXXV § 4
be capable of being given in some way or other. Apart from
given objects our concepts are empty; and although we can
think by means of such concepts, thinking of this kind is not
knowledge but a mere play of ideas. The difficulty is to explain
the exact sense in which objects are 'given'.
Kant's explanation is too compressed to be clear. To be
given, an object must be immediately exhibited in intuition:
it is not enough that it should be given mediately.1 Apart
from immediate intuition no object can be given; but Kant
is seeking a general formula which will cover the way in which
objects are given both when we make synthetic a posteriori,
and when we make synthetic a priori, judgements. He therefore
says that to give an object is to relate the idea2 of the object to
experience, either to actual or to possible experience.
We may take the 'idea' of the object to be the concept of the
object. Where this concept is empirical, it must be related to
actual experience. Where the concept is a priori, it must be
related to possible experience. Only in this way can we show
that a concept is the concept of an object which is, or can be,
given.
In what sense is the concept 'related' to experience? An
empirical concept is related to experience when it is borrowed
or derived from experience,3 when in short we can indicate an
object of experience containing the combination of marks which
is thought in the concept.4 An a priori concept is related to
experience when it is a concept of the conditions (or the form)
1 Kant docs not explain what he means by 'given mediately'. I take
it that an object might be said to be given mediately in a concept:
for example, the concept of chimaera refers to a descnbable object,
but unless the object can be given immediately to intuition, the concept
does not refer to a real object, and the use of the concept in mere
thinking cannot give us knowledge.
2tVorstellung.' Kant must have in mind primarily concepts, but
the wider word 'idea* may be used because he is thinking also of the
ideas of space and time, which are intuitions although he describes
them as concepts. 3 Compare A 220 - B 267.
4 We need not have actually experienced the object ourselves : it is
sufficient if it is connected, by means of the Analogies, with objects
we have actually experienced.
XXXV § 4] THE SUPREME PRINCIPLE 89
of experience. In this case the concept is related to possible
experience; for experience is possible only if it conforms to
such conditions.1 Although the concept of such conditions is
a priori, it nevertheless 'belongs' to experience, because its
object can be found in experience alone.2
Kant's main point is that a priori concepts can have objective
reality or validity only if we can prove that they must neces-
sarily apply to all objects of experience ;3 and we can prove this
only by showing that they contain or express the necessary
conditions of experience, to which all objects of experience
must conform. He illustrates his point by the examples of space
and time, which strictly speaking are not pure concepts but
pure intuitions.4 Even in their case his principle holds. Our
ideas of space and time have objective validity, because we
can show that objects must be spatial and temporal ;5 for space
and time as conditions (or forms) of intuition are conditions
of experience. He adds that our idea of space and time is in
itself a mere schema: it is dependent on the reproductive imagi-
nation which calls up the objects of experience, and apart from
them it would have no meaning.6
We may conclude provisionally that the 'third thing' which
makes synthetic judgements possible is experience — actual
experience if the judgement is empirical,7 and possible experi-
ence if the judgement is a priori.
1 Compare Chapter XLIX § 6.
2 See A 220 - 13 267. Its object is an 'object in general' so far as
that object conforms to the conditions of experience.
3 Mathematical concepts, however, apply necessarily only to some
objects of experience ; but they too express a possibility contained in
the conditions of experience.
4 A 156 — B 195. 5 Compare B 147.
6 This statement should be taken as qualifying the doctrine pro-
visionally stated in A 24 =• B 38-9 and A 31 — B 46. Although our
intuitions of space and time are completely a priori, we can separate
them from experience only by an act of abstraction, and apart from
their relation to experience they would be mere 'phantoms of the
brain*.
7 Compare A 8 and B 12. Even this, as we shall see later, pre-
supposes the forms or conditions under which alone is experience
possible.
90 THE PRINCIPLES [XXXV § 5
§ 5. The Possibility of Experience
Although Kant is professedly dealing with all synthetic
judgements, his main interest is directed to synthetic a priori
judgements. He sums up his position by saying that it is the
possibility of experience which gives objective reality to all
our a priori cognitions.1
The phrases 'possible experience* and 'possibility of experi-
ence' are thus treated as equivalent, but Kant indicates that it is
the second phrase which best expresses his meaning.2 The
'third thing* is not just some experience or other which we might
possibly have : it is rather the form of experience itself or the
necessary conditions without which no experience is possible.
We should indeed get into logical puzzles if we identified
the possibility of experience with the form (or the conditions)
of experience ;3 but we can say that so far as experience has
the form of experience it is possible, and so far as it is possible
it has the form of experience.
What then is the form upon which experience depends for
its possibility ? The form of experience is the synthetic unity of
appearances, and experience is possible only if it 'rests1 on
a synthesis which conforms to the categories4 and to the unity
of apperception. Without this there would be no experience
or knowledge, but a mere 'rhapsody* of sense-perceptions.
Hence experience has certain principles as the a priori
basis of its form.5 These are the Principles of the Understanding,
and they are universal rules of unity in the synthesis of appear-
1 A 156 — B 195. For the possibility of experience see also Chapter
XLIX§6. 2A 157 =- B 196.
3 Compare such questions as whether beauty can, or can not, he
identified with coherence (or harmony).
4 The categories are here called 'concepts of the object of appearances
in general'. This description may be intended to indicate that the
categories in question are the schematised categories. Similarly the
synthetic unity of appearances is a synthetic unity in space and time.
5 A 156 — B 196. 'Form', I think, does not go with 'principles',
as in Kemp Smith's translation, but rather with 'a priori zum Grunde
hegen\ These principles are the a priori basis of the form of experience
because they express the conditions of experience and of its objects.
XXXV § 5] THE SUPREME PRINCIPLE 91
ances, rules which state the ways in which appearances must be
combined in all experience. Inasmuch as these rules state the
necessary conditions of experience, their objective reality can
always be shown in experience, and indeed, in the very possi-
bility of experience.1
The same doctrine holds, not only for the Principles of the
Understanding, but for all synthetic a priori judgements.
Unless they were related to possible experience (in the sense of
describing the conditions of experience), they would be
impossible; for they would have no 'third thing', that is, no
object,2 in relation to which the synthetic unity of concepts
(which is affirmed in the judgement) can exhibit objective
reality.3
Kant illustrates his point by the example of mathematical
judgements.4 We do not need experience to make synthetic
a .priori judgements about space in general5 or about the
figures which productive imagination describes in it. Neverthe-
less we should be occupying ourselves with a mere phantom of
1 Kemp Smith's translation wrongly attaches 'the possibility of
experience* to 'conditions'. For the idiom compare 'auf diescr ihre
Moghchkeit* a few lines further down.
2 The conditions of experience are also conditions of the objects
of experience.
3 The German is 'an dem die synthctische Einheit ihrer Begnffe
objektive Realitat dartun konnte*. Vaihinger's emendation (accepted
by Kemp Smith) substitutes after Einheit 'die objektive Realitat ihrer
Begrtffe*. This misses the whole point of the argument. We are here
concerned, not with the objective reality of the separate concepts
employed in the judgement, but with the objective reality of their
union which is affirmed in the judgement. Compare below 'the
objective validity of their synthesis', that is, of the synthesis present
in pure synthetic judgements.
4 A 157 = B 196; compare A 159-60 = B 198-9.
5 1 take these to be such judgements as 'Space has three dimensions'.
Kant may have in mind also the judgements m the Aesthetic, but
it is unsafe to hold this in the absence of an explicit statement. The
judgements in the Aesthetic are synthetic a pnoii judgements; but
I am not sure whether Kant would say of them, as he does of mathe-
matical judgements, that they relate mediately to experience, unless
he means that they relate immediately to outer intuition (which is
only an element in experience). If he had in mind the Aesthetic, we
should expect a reference to time also.
92 THE PRINCIPLES [XXXV § 5
the brain, unless we could regard space as the condition of
appearances, and so of outer experience. Hence these synthetic
a priori judgements also are related to possible experience,
or rather to the possibility of experience,1 and on this alone
do they base the objective validity of their synthesis ; but this
relation is mediate, since the mathematician deals with space
in abstraction and need not judge that it is the condition
of outer intuition and so of all outer experience.2 In the case of
the Principles this relation is immediate, since they affirm
directly what are the necessary conditions of experience.
The conclusion of this discussion can now be formulated.
Experience, as empirical synthesis, is in its possibility the only
kind of knowledge which can give reality to every other syn-
thesis'.3 This must mean that the possibility of empirical
experience alone can give objective validity to every other
synthesis. We may take 'every other synthesis' to mean 'every
a priori synthesis';4 but in view of what follows5 I am inclined
to think it means 'the synthesis of concepts in judgements'.6
When this synthesis is an a priori cognition, that is, when
it is a synthetic a priori judgement, it has truth7 (or agreement
with the object) only so far as it contains nothing save what is
necessary for the synthetic unity of experience in general.8
1 Notice Kant's preference for the latter phrase.
2 Kant does not explain what he means here by 'mediate'. lie
explains later that mathematics depends primarily upon pure intuition ;
hut its application to experience, and therefore its objective validity,
depends upon pure understanding; see A 160 = B 199. If so, it
depends upon the Principles of the Understanding, and not merely
upon the Aesthetic. Compare also A 149 ~ B 189, where the possi-
bility of mathematical judgements is said to be made intelligible by
the principles of the Understanding. 3 A 157 — B 196.
4 This is Kemp Smith's view in his translation.
6 The formulation of the principle of all synthetic judgements.
6 Compare 'the synthetic unity of concepts' and 'the objective
validity of their synthesis' above. Every synthetic judgement is
a synthesis of concepts; and Kant is saying that experience in its
possibility gives reality to all synthetic judgements.
7 This is equivalent to 'objective reality' or 'objective validity'.
8 Compare A 118, A 123, B 151, and A 145 = Bi8s ; also Chapter
XXIX § 7. It may be objected that mathematical judgements contain
more than this ; for they state the conditions of a particular experience,
XXXV § si THE SUPREME PRINCIPLE 93
In other words synthetic a priori judgements have objective
validity only in so far as they express the necessary conditions
(or form ) of experience and are thus related to the possibility
of experience.
If I am right in interpreting the phrase 'every other synthesis'
to cover synthetic a posteriori as well as synthetic a priori
judgements, then Kant is maintaining that tor all synthetic
judgements without exception, the possibility of experience is
the 'third thing' which gives them objective validity. The actual
experience which justifies our synthetic a posteriori judgements
does so, not in virtue of mere sensation, but in virtue of those
conditions of synthetic unity without which no experience is
possible.1
It is unfortunate that Kant does not deal more explicitly
with synthetic a posteriori judgements. It is also unfortunate
that he does not give separate treatment to the judgements
of the Aesthetic2 as well as to the judgements of mathematics
and the Principles of the Understanding. There too we have
synthetic a priori judgements which depend upon the possibility
of experience. They do so in the obvious sense that they affirm
space and time to be forms of sensibility and necessary condi-
tions of intuition, and so of experience. But I think they do so
also in a deeper sense ; for they depend upon the necessary
synthetic unity of experience which is expressed in the Prin-
ciples of the Understanding.3 This could not be made clear
in the Aesthetic,4 because Kant was considering pure intuition
in abstraction from the rest of experience, and because a com-
plicated system of philosophy cannot be explained in a few
pages. Nevertheless even the judgements of the Aesthetic,
since they depend upon the possibility of experience, depend
that of triangles, circles and so on. Nevertheless their objective
validity for Kant depends only on the fact that the space with whose
particular determinations they deal is a condition of experience in
general.
1 Compare B 142.
2 They are mentioned in A 149 = B 188, but only in order to mark
them off from the Principles of the Understanding.
3 Compare A 149 = B 188-9. 4 Compare B 160-1 n.
94 THE PRINCIPLES [XXXV § 6
upon the Principles of the Understanding, which set forth the
form, or the necessary synthetic unity, of experience in general.1
We do well to remember that the Principles of the Understand-
ing are formulated in the light of all that has gone before.
In setting forth the necessary form of experience they are con-
cerned, not only with the pure categories, but also with the
transcendental synthesis of imagination and the forms of space
and time.2 They state the conditions of the possibility of
experience and so have themselves objective validity. And
all other synthetic judgements without exception have objective
validity in virtue of the possibility of experience whose con-
ditions are adequately and explicitly expressed in the Principles
alone.
§ 6. The Principle of All Synthetic Judgements
In the light of these considerations Kant formulates the
supreme principle of all synthetic judgements: Every object
stands under the necessary conditions of the synthetic unity
of the manifold of intuition in a possible experience?
This formula expresses Kant's supreme principle from the
side of the object. It is another way of saying that synthetic
judgements can have objective validity only from their relation
to the possibility of experience.
It should now be clear that this formula applies to synthetic
a posteriori judgements. These are made in virtue of actual
1 A 156-7 = B 195-6. For this reason it is, I think, possible, but
not certain, that Kant has in mind the judgements of the Aesthetic,
as well as those of mathematics, when he speaks of judgements
which are related mediately to the possibility of experience.
2 Compare A 158 -= B 197 and also A 155 = B 194.
3 A 158 = B 197. We may be tempted to abbreviate the formula
and say, more simply, that every object must stand under the
necessary conditions of a possible experience. Kant, however, wishes
to indicate that these conditions are all involved in the necessary
synthetic unity of the manifold of intuition, a necessary synthetic
unity which constitutes the essential character of all objects of
experience; compare A 105, A 109, B 137, etc. The paragraph which
follows in regard to synthetic a priori judgements shows that these
conditions are not to be taken in abstraction from one another.
XXXV § 6] THE SUPREME PRINCIPLE 95
experience of an object, as Kant never ceases to hold ; but in
them we presuppose that their object stands under the neces-
sary conditions of a possible experience as formulated in the
Principles of the Understanding. Apart from such a presup-
position we should have before us, at the most, a stream of
momentary appearances, and we should be unable to make any
synthetic judgements at all.
Kant himself makes no special reference to synthetic a
posteriori judgements. His attention is concentrated on synthetic
a priori judgements. Since every object must stand under the
conditions of possible experience, we can see that synthetic
a priori judgements have objective validity1 so far as they express
the necessary conditions of a possible experience.
No attempt is here made to distinguish between the synthetic
a priori judgements of mathematics, of the Aesthetic, and
of the Analytic; and I need not raise again the questions
already discussed. 1 take Kant to refer to all synthetic a priori
judgements without exception, though he may have in mind
primarily the judgements of the Analytic. If we are to under-
stand the objective validity of any kind of synthetic a priori
judgement, we must 'relate the formal conditions of a priori
intuition, the synthesis of imagination, and the necessary unity
of this synthesis in a transcendental apperception to a possible
experiential knowledge2 in general'; that is to say, we must
perform that analysis of the conditions of experience which
has been set forth by Kant in the Kritik and especially in
the Analytic. More simply, we must recognise that the con-
ditions of the possibility of experience in general are also conditions
of the possibility of objects of experience. This is the principle
upon which the whole of the Transcendental Philosophy
rests. It is the basis of the Transcendental Deduction3 as it is
1 In this passage — A 158 = B 197 — when Kant says that synthetic
a priori judgements 'are possible*, he is clearly referring not to their
logical, but to their real possibility, that is, to their objective validity.
2 'Erfahrungserkenntms. '
3 This is stated expressly in A in (compare also A 93 = B 125-6
and A 125-6), and it applies equally to the arguments in the first
and second editions.
96 THE PRINCIPLES [XXXV § 6
the basis of the separate proofs given for the Principles of the
Understanding. And indeed it is the basis of all synthetic
a priori judgements without exception; for, as we have seen,
such judgements can have objective validity only so far as they
express the necessary conditions of possible experience.1
1 The judgements of the Analytic do so directly. The judgements
of the Aesthetic perhaps do so also directly, but their full implication
is made intelligible only in the Analytic; and it may be that they do
so only indirectly, since (if we speak strictly) while they show space
and time to be conditions of intuition, it is only in the Analytic that
we understand space and time to be conditions of experience in general.
The judgements of mathematics do so indirectly: they deal with
determinations of space and time, but it remains for philosophy to
show that space and time, and the synthesis of the given manifold
in space and time, are conditions of experience.
CHAPTER XXXVI
THE PRINCIPLES OF THE UNDERSTANDING
§ i . Different Kinds of Principle
The discussion of the principle of synthetic judgements
is intended primarily to explain the nature of the proof which
must be given for the Principles of the Understanding. The
proof of these Principles is a matter of judgement', but Kant
declines to regard them as self-evident.1 They are proved,
when they are shown to express the conditions of experience ;
and we can judge that they do express these conditions, only
when we understand the part played by sense, imagination,
and understanding as sources of knowledge.2
The Principles to be proved are concerned with the appli-
cation of the categories, and this narrows the range of our
present enquiry. Needless to say, it excludes all empirical
principles. An 'empirical principle' is a contradiction in terms,
for it is derived by generalisation from experience; and such
generalisations, however universal they may be, are totally
lacking in necessity, and particularly in that 'necessity according
to concepts' which is the mark of the Principles of the Under-
standing.3 The principles of the Aesthetic are also excluded,
for they are concerned, not with the application of the cate-
gories, but with the conditions or forms of intuition.4 And finally
the principles of mathematics must be excluded, because
they pass from intuitions to concepts and not from concepts
to intuitions.5 Nevertheless the possibility and objective validity
1 Compare A 149 — 13 188. The self-evident is commonly regarded
as intelligible itself without reference to anything beyond itself, but
the Principles are intelligible only in relation to experience. If we
could not * prove* the Principles by showing their relation to experience,
they would incur the suspicion of being surreptitiously introduced.
2 The pi oof is 'from the subjective sources of the possibility of a
knowledge of the object in general'. See A 149 — B 188.
3 A 159 = B 198. A principle, as an aprf or Grundsatz, cannot
be derived from anything else. 4 A 149 = B 188.
6 A 149 =- B 188-9, A 159-60 = B 198-9, and A 712 = B 740 ff.
Compare Chapter V § 8.
VOL. II D
98 THE PRINCIPLES [XXXVI §2
of the principles of mathematics depends upon the Principles
of the Understanding.1
In all this Kant is assuming that the categories are derived
from the forms of judgement, and so are products of pure
understanding.2 Even if we reject this derivation, the distinction
between the different kinds of principle will still remain.
The proof of the Principles of the Understanding cannot be
intuitive like a mathematical proof,3 but must be conceptual
or discursive, as we shall see below.4
§ 2. The Principles of the Understanding
Kant divides the Principles of the Understanding into
(i) Axioms of Intuition, (2) Anticipations of Sense-Perception,
(3) Analogies of Experience, and (4) Postulates of Empirical
Thought.5 These correspond to the headings of quantity,
quality, relation, and modality, under which the categories
are arranged.6
1 A 149 = B 189 and A 160 — B 199. The relevant Principles of
the Understanding are primarily the Axioms of Intuition and the
Anticipations of Sense-Perception.
2 Note Kant's repetition of the distinction between undei stand ing
as a lawgiver and understanding as a discoverer of laws. See A 126-7
and compare A 114 and B 165; also Chapter XXVII § 4. What arc
ordinarily called the laws of nature are all subject to the Principles
of the Understanding, and this is why they convey a suggestion of
necessity.
3 See especially A 719-20 - B 747-8 The difficulty that some of
the Principles have immediate or intuitive ceitainty (or 'evidence')
— see A 1 60 = B 1 99-200 and A 1 80 •= B 223 — is discussed in § 3 below.
4 In § 3 ; compare also Chapter XXXII § 5. At present it is sufficient
to say that we cannot construct an object in a priori intuition for the
categories, as we can for mathematical concepts.
5 These titles must not be thought to describe the Principles. We
have a Principle of Axioms, a Principle of Anticipations, and a
Principle of Analogies, but this does not mean that one Principle is
an axiom, another an anticipation, and another an analogy ; compare
Chapter XXXVII § 7.
6 A 161 — B2oo. There is, it need hardly be said, nothing artificial
in the correspondence between the categories and the Principles. If
there were not such a correspondence, the whole of Kant's argument
would be absurd. The fact that the Axioms and Anticipations have
only one Principle each, while there are three Principles both for the
XXXVI § 2] PRINCIPLES OF THE UNDERSTANDING 99
The categories of quantity and quality are concerned with
the objects of intuition (both pure and empirical), while those
of relation and modality are concerned with the existence
of these objects in relation either to one another or to the
understanding.1 The categories of quantity and quality are
called mathematical categories, and the corresponding Prin-
ciples (the Axioms and Anticipations) are called the Mathe-
matical Principles. The categories of relation and modality
are called dynamical categories, and the corresponding Prin-
ciples (the Analogies and Postulates) are called the Dynamical
Principles.2
It must not be thought that the Mathematical Principles
are principles of mathematics, or that the Dynamical Principles
are principles of dynamics. All the Principles of the Under-
standing are supposed to be general, and are not restricted,
as^ are the principles of geometry and dynamics, to objects
of outer sense.3 They are called Mathematical and Dynamical,
because they account respectively for the possibility of mathe-
matics and (physical) dynamics.4
Analogies and for the Postulates, is due to the fact that the Principles
are concerned primanly with the schematised categories. The reason
why there is only one schematised category of quantity and one of
quality I have already explained in Chapter XXXIII § 7.
1E 1 10. In A 160 -= B 199 Kant asserts that the mathematical
principles concern mere intuition, and the dynamical principles
concern the existence of an appearance in general. For reasons to be
stated later, I think this way of expressing the distinction to be less
satisfactory. See Chapter XXXVII § 5.
2 See B no and A 162 = B 201.
3 This is what Kant means when he says in A 162 = B 202 that the
Principles are those of pure understanding in relation to inner sense
(without regard to the difference in the ideas given in inner sense). The
Principles do not exclude objects of outer sense, for all our ideas,
even those of physical objects, belong as modifications of the mind
to inner sense; see, for example, A 98-9. Time and inner sense are
in the first edition stressed unduly at the expense of space and
outer sense, but even in the first edition the Principles are concerned
primarily with objects in space.
4 A 162 = B 202. They are the presuppositions, rather than the
principles, of mathematics and dynamics, and they find their chief
application in these sciences. In the Nachtrage LXIV-LXV, as given
ioo THE PRINCIPLES [XXXVI § 3
In the second edition1 Kant added a footnote, which is
important as a statement of his technical terms. The Mathe-
matical Principles deal with the synthesis of the homogeneous,
a synthesis of homogeneous elements which do not necessarily
belong to one another. Such a synthesis is divided into aggre-
gation (the synthesis of extensive quantity) and coalition (the
synthesis of intensive quantity). The Dynamical Principles
deal with the synthesis of the heterogeneous, a synthesis of
different elements which necessarily belong to one another,
such as substance and accident, or cause and effect.
All this will become clearer when we study the Principles
themselves.
§ 3. Intuitive and Discursive Certainty
Kant asserts that the Mathematical Principles possess
intuitive certainty, while the Dynamical Principles possess
only discursive certainty.2
by Benno Erdmann, Kant seems to express dissatisfaction with this
division. The Mathematical Principles are divided into formal (the
Axioms) and real (the Anticipations). The formal Principles are con-
nected with pure and applied mathematics, and also according to
Erdmann with dynamics; but it seems to me that this must be a
misunderstanding of Kant's note, and that Kant must have intended
to connect the real Principles (the Anticipations) with dynamics, as
he does in Nachtrage LXV and in the Metaphysiithe Anfang\t>rnnde
der Naturwissenschaft. The Analogies and Postulates are called physio-
logical, and are divided into physical (the Analogies) and metaphysical
(the Postulates), as in the footnote added in the second edition of
the Kntik (B 201-2 n.). Rational 'physiology' is the philosophical
science of nature (whether corpoieal or spiritual) , sec A 846 — B 874,
and Metaphysiky p. 12.
1 B 201-2 n. Kant's Latin terms often throw light on the ordinary
German expression.
2 A 162 = B 201 ; compare A 160 — B 199-200 and A 180 — B 223.
Intuitive or mathematical certainty (intuitive Gewissheit or anschauende
Gewissheit) is called 'evidence* (Evidens). See Log. Eml. IX (IX 70)
and A 734 = B 762. 'Evidenz' seems to be used in a more general
sense in A 180 = B 223, but 'evident' is used in the technical sense
in A 733 - B 761. 'Certainty* is here 'objective certainty* (certainty
for everyone) : that is to say, the ground (Erkenntmsgrund) of these
Principles is objectively (and not merely subjectively) adequate. See
A 823 = B 850, A 820 = B 848, and Log. Eml. IX (IX 70).
XXXVI §3] PRINCIPLES OF THE UNDERSTANDING 101
In spite of this assertion intuitive certainty is usually said
by Kant to belong to mathematics only, while philosophical
certainty is always discursive.1 Philosophical knowledge is
rational knowledge from concepts; mathematical knowledge is
rational knowledge from the construction of concepts? A philo-
sophical proof is always a proof by means of concepts, and so
is discursive; a mathematical proof is by the construction
of concepts and is intuitive.3 Kant even says that axioms are
synthetic a priori principles which possess immediate cer-
tainty, and that philosophy has no principles which deserve
the name of axioms.4 In other words, the synthetic a priori
principles of philosophy never possess intuitive or immediate
certainty.5
Unless I have overlooked one of Kant's subtle distinc-
tions, we have here a contradiction, at least in words. At the
same time there is a real difference between the proof of the
Mathematical, and the proof of the Dynamical, Principles, and
it is this real difference which Kant is trying to express. Per-
haps the contradiction can be at least partly explained, if we
1 Log. Eml. Ill and IX (IX 23 and 70-1). Compare A 734-5 ==-
B 762-3.
2 A 713 — B 741. Compare Log. Eml. Ill (IX 23). Rational know-
ledge is opposed to empirical knowledge : it is grounded not on
experience, but on reason. To 'construct a concept* is to exhibit
a pnon the intuition which corresponds to the concept. We cannot
const! uct an object lor the categories in pure intuition: we can only
show that, although they arc not derived from experience, they
express the necessary conditions of a possible experience.
J A 734-5 - B 762-3. Compare Log. Eml. Ill and IX (IX 23 and
70-1). A philosophical proof is also said to be 'acroamatic' because
it uses woids, not intuitions. Only a mathematical proof can be called
a 'demonstration'; for 'demonstration* implies the use of intuition.
This doctrine has a close affinity with Plato's account of the mathe-
matical sciences and dialectic in the Republic.
Compare also A 714 = B 742 : 'Philosophical knowledge considers
the particular only in the universal ; mathematical knowledge considers
the univeisal in the particular, or rather in the individual, yet always
a priori and by means of reason'. The whole passage should be
consulted. 4 A 732 = B 760.
6 Kant says expressly in A 733 --. B 761 that even the principle
of the Axioms of Intuition is not itself an axiom, but a principle
derived from concepts.
102 THE PRINCIPLES [XXXVI § 3
remember the difference between the category and the schema.
The schema of extensive quantity (i.e. number1), and perhaps
even the schema of intensive quantity (i.e. degree2), can be
constructed in intuition a priori, and this may be the reason
why Kant says that the Mathematical Principles have intuitive
certainty.3 I presume that the categories of quantity and
quality cannot be so constructed, and so far as these are
involved in the Mathematical Principles, the Mathematical
Principles, like all other Principles of the Understanding, have
only discursive certainty. In the case of the Dynamical Principles
there is no possibility of constructing even the transcendental
schemata, let alone the categories.
Kant himself implies that we are not yet in a position to
understand his doctrine in regard to this point.4 He bases
this contention on the view that the Dynamical Principles
exhibit an a priori necessity only under the condition of empiri-
cal thinking in an experience: the Mathematical Principles are
unconditionally necessary.5 The emphasis in this statement
appears to rest on the word 'thinking' (which I have italicized) ;
but the difficulty remains that even the Mathematical Principles
must be necessary only in relation to experience. Kant appears
to recognise this, and to suggest that a necessity in relation to
experience can be absolute or unconditioned; for he asserts
that the a priori conditions of intuition (with which the Mathe-
matical Principles deal, and from which they derive their
character) are absolutely (durthaus) necessary m relation to a
possible experience. The Dynamical Principles have their
conditional necessity (in relation to empirical thinking), because
they deal with the conditions of the existence of objects of a
possible empirical intuition, and these conditions are in them-
selves contingent.6 This is obscure, and I am uncertain of its
1 For the construction of number, see A 724 == B 752.
2 Such at least is Kant's own view in A 179 = 13 221.
3 As I have pointed out in Chapter X § 7, this does not mean that
there is no discursive or conceptual element present.
4 A 161 = B 200. 6 A 160 = B 199.
6 'Contingent* does not mean 'due to mere chance,' but 'necessary
under a condition'. See also A 766 — B 794.
XXXVI § 41 PRINCIPLES OF THE UNDERSTANDING 103
precise meaning; but we can perhaps say at present that the
unconditional necessity of the Mathematical Principles is due
to the fact that these are concerned with objects primarily
as appearances given to intuition, while the conditional necessity
of the Dynamical Principles is due to the fact that they are
concerned with objects primarily as judged to exist in time and
space. The factor of intuition is dominant in the first case* the
factor of thought in the second; but in both cases the necessity
is derived from the relation of the Principles to a possible
experience, which is always a combination of intuition and
thought.1
§ 4. The Ptoof of the Principles
What then are we to say of the proof of the Principles?
Whatever be the intuitive element involved in some cases,
the proof is always a discursive proof, a proof from concepts,
like all other proofs in philosophy ;2 but it is not for this reason
either illegitimate or uncertain.
The Principles of the Understanding are synthetic a priori
judgements and cannot be derived from mere analysis of
concepts.3 They cannot be proved by mathematical methods
of construction, nor can they be proved directly from concepts,
for in that case they would be mere dogmas.4 If they can be
proved at all, they must be proved indirectly from concepts.
1 For the subsequent development of this doctrine, see A 178 =
6220 if., and also A 216-17 = 6263-4. It may be added that the
schemata of number and degree can be constructed because of their
close connexion with intuition. Number and perhaps degree seem
to be necessary for knowledge of time and space: the categories of
relation have no meaning apart from change, which is simply an
empirical fact , compare B 3. This is why the proposition 'Every change
has its cause', although it is a priori, is not a pure a priori proposition.
2 Compare especially A 719-20 = B 747-8 and A 722 = B 750.
3 1 have shown in Chapter X § 7 that discursive judgements are
not necessarily analytic. Compare A 733 — B 761.
4 A 736 - - B 764. The philosophy which Kant condemns as dog-
matic offers us synthetic a priori judgements which arc supposed to
arise directly from concepts and to apply to thmgs-in-themselves.
The only judgements which we can be j'ustified in proving directly
from concepts are, I take it, analytic judgements.
104 THE PRINCIPLES [XXXVI § 4
An indirect proof depends upon the relation of concepts
to something wholly contingent, namely possible experience.
The Principles of the Understanding can be apodeictically
certain only if possible experience (or 'something' as an object
of possible experience) is presupposed.1 They are nevertheless
properly called 'principles' (Grundsatze), because they have the
peculiar property that they make possible the very experience
which is their own ground of proof, and in experience itself
they are always presupposed.2
This is the clearest expression in Kant of the doctrine
which has already been set forth. Such a doctrine must always
raise the question whether Kant's method of proof is, or is not,
circular. To take the most important case, the case of causation,
it would be (as I have already pointed out3) a vicious circle,
if Kant argued that because we commonly assume causation
in ordinary experience, therefore causation is a necessary con-
dition of experience ; and that because causation is a necessary
condition of experience, therefore we are justified in our com-
mon assumption.
Kant's argument, whether it be right or wrong, does not
merely accept our common-sense assumptions, and then argue
that because these are present in experience, they must be the
conditions of experience. What he assumes in his proof of the
Principles is that for experience of objects (i) there must be
sensuous intuitions given under the forms of time and space ;
1 A 736-7 =-- B 764-5. To say this is only to repeat what has already
been said. We establish the Principles, not directly from the concepts
which they employ, but by showing that these concepts express the
conditions of possible experience, and consequently must apply to
all objects of experience.
It may be observed that when Kant says that a proposition is
apodeictically certain, he means that it is universally and objectively
necessary (valid for all). It can be this only if its ground (Erkenntms-
grund) is objectively adequate. Apodeictic certainty is connected with
rational certainty, the certainty of mathematics or of philosophy.
But certainty can be rational and empirical at the same time, when,
that is to say, we know an empirically certain proposition from a
priori principles. There may therefore be apodeictic certainty even
in connexion with an empirical truth. Sec Log. Einl. IX (IX 66 and 71).
2 A 737 - B 765. 3 Chapter XXX § 5.
XXXVI §4] PRINCIPLES OF THE UNDERSTANDNG 105
(2) there must be an imaginative synthesis of such sensuous in-
tuitions in one time and space; (3) there must be judgement.1
These assumptions, I suggest, are all sound, as is also the
assumption that if different objects are judged to belong to
one and the same objective world, they must be judged by
one and the same self.2 The one doubtful assumption which he
makes is that all the forms of judgement, including the hypo-
thetical, are essential to judgement as such ; but this assumption
— although it undoubtedly increases his confidence in the
argument of the second Analogy and, as I have suggested above,3
is probably regarded as enriching his conclusion — does not play
any part in that portion of his argument which seeks to show
that all objective succession is necessary or regular succession.
If the principle of causality (in the sense of necessary succes-
sion) could be established on the basis of the assumptions
which I have asserted to be sound, I do not think that the
argument could be described correctly as a vicious circle.4
Whether his more doubtful assumption can be so interpreted as
to justify us in regarding causality as more than necessary
succession can, for the present, be left an open question.
Kant has given us his general analysis of what must be
involved in every human experience, and has explained what
the categories are and how they are schematised. lie now
asks us to judge whether the Principles, which affirm the
necessary application of the schematised categories to objects,
state the conditions necessary for any experience of the kind
he has analysed. His 'proof is, as he says, a judgement made in
1 Compare A 158 = B 197. Hence our proof is said in A 149 =
B 1 88 to be a proof from the subjective sources of a knowledge
of the object in general.
2 This is the simplest way of asserting the necessity of the unity
of apperception, and has to be understood in the light of Kant's
doctrine of the self.
3 See Chapter XXXIV §2.
4 The argument for the assumptions themselves might still be a
vicious circle, but I do not think that it is so. We must always remember
that for Kant the conditions of experience are not merely necessary
m relation to experience, but have an intelligible necessity in them-
selves when considered in isolation ; see Chapters VII § 4 and XXX § 5.
VOL. II D*
106 THE PRINCIPLES [XXXVI § 5
the light of his previous analysis, and not a syllogistic inference
from the truths which he claims to have established.
§ 5. Modern Science and the Principles of the Understanding
It should be clearly understood that Kant's main, although
not his sole, object in the Analytic of Principles is to establish
the ultimate philosophical basis of mathematics and the
physical sciences.1 He is attempting to justify the application
of a priori mathematical thinking to the actual world of physical
objects and to establish the principle of the uniformity of
nature. The problems which he attempts to solve are, I believe,
no less important now than they were in the eighteenth century,
but his solutions must be judged in the light of the science of
his time.2
In recent years we have been informed that science has no
need for the category of substance nor even — what is muqh
more remarkable — for the category of cause and effect. If this
is true, cadit quaestio: Kant's proof of substance and causality —
and these are in some ways the most important of his categories
— can be no more than a squaring of the circle. I must confess,
however, to some sympathy with the view that these categories,
and especially the category of cause and effect, are not to be
lightly set aside. Some of the distinguished exponents of the
philosophy of modern physics seem to take a delight, a delight
which is certainly human and probably also useful, in stressing
the paradoxes of modern theory rather than in showing the
continuity of its development. The plain man, and even, if
I may use the phrase, the plain philosopher, is merely foolish
when he attempts to criticise the physicist in his own domain ;
but physics cannot be identified with the whole of human
experience, nor can the practical devices which it uses at a
particular moment claim to be accepted without further exami-
1 The more special principles of these sciences he seeks to establish
in the Metaphysische Anfangsgrunde dcr Naturwnsensthaft.
z 1 must confess that 1 feel myself handicapped in this matter,
since my acquaintance alike with past and present science is that
of an outsider.
XXXVI §s] PRINCIPLES OF THE UNDERSTANDING 107
nation as eternal philosophical truths. It seems to me probable
that when the historian looks back upon the present age, he
will see our modern theories developing continuously out of the
old, and will perhaps be surprised that they appeared so
paradoxical and so revolutionary. It is clear enough to-day —
was it ever really doubtful ?— that the traditional theories of
space and time are in need of modification ; and if Kant were
right in holding that experience of a world in space and time
is impossible apart from substance and causation, we should
expect that the traditional theories of substance and causation
would also require to be modified. Nevertheless modification
is very different from mere blank rejection,1 and I doubt
whether we are at present obliged to say that the category of
substance, and still more the category of causality, must be
abolished for ever from the sphere of human thought.
§ It would be futile upon my part to discuss the ways in which
Kant's doctrine of the categories must be modified. He
assumed Euclidean space, and if we are to understand his
argument, we must do the same. It is our task to estimate the
value of his argument as it stands ; and if we conclude that it
is sound on the basis of his assumptions, 1 see no reason to
suppose that it is now wholly without value, or that the method
of his proof (as opposed to the details) could not be of use for
the modern theory of science.
1 Professor Alexander, who has done so much to modify Kant's
doctrine, says (Space, Time, and Deity, Vol. I, p. 191): 'I cannot
think that this part of Kant's doctrine is so innocently inadequate
as is often believed'.
BOOK IX
THE MATHEMATICAL PRINCIPLES
CHAPTER XXXVII
THE AXIOMS OF INTUITION
§ i . The Principle of the Axioms
The Principle of the Axioms of Intuition is: All intuitions
are extensive quantities.
This is the formula of the second edition.1 Both here and
in the Anticipations and Analogies Kant seems to have been
dissatisfied with his original formulation of the Principle. In
each case he offers us a new formula in the second edition, and
the reason for the change is not always easy to see. In each
case he offers us also a new proof in the second edition, which
he places immediately in front of the first proof. The obscurity
of the original proof, obscurity complained of from the publi-
cation of the Krihk to the present time, is the reason why he
attempts what he believes to be a better version.2
In the first edition Kant very properly began his proof by
defining his terms. In the second edition these definitions
are retained in their original position ; and the placing of the
second proof before the first has the unfortunate result that
if we are reading the second edition, we have to face Kant's
most important argument before we have learned the exact
meaning of the terms employed.3
1 B 202. In A 162 the Principle is: All appearances are, as regards
their intuition, extensive quantities. It is difficult to say why in the
second edition Kant should have altered this formula, especially as
the conclusion of the argument in the second edition conforms more
closely to the formula of A than to that of B. Mellin believed that
in the formula of B Kant really intended to assert that all appearances
(not all intuitions) are extensive quantities. This is supported by
the conclusion of the argument in B, and Kant is not speaking of
intuition qua intuition, but of intuition qua appearance of an object.
a Compare B XXXVIII.
J For this reason the reader, or at any rate the beginner, is well
advised to consider the A proof with its definitions before he examines
the B proof.
ii2 THE MATHEMATICAL PRINCIPLES [XXXVII §2
§ 2. The Proof in the First Edition
In the Principle of the Axioms the argument turns on the
nature of extensive quantity. Extensive quantity is defined
as that in which the representation of the parts makes possible
(and therefore necessarily precedes) the representation of the
whole.1 This definition is by no means clear, and Kant does
not give us any further elucidation of its details except such
as may be extracted by inference from his argument. His main
point appears to be that an extensive quantity — and by this, I
think, he must mean a determinate extensive quantity2 — is one
which can be known only by a successive synthesis of the parts.3
1 A 1 62 = B 203 . 1 use the word 'representation* here for * Vorstellung9
(rather than the word 'idea') because Kant may mean 'the representing*
or — since the word 'represent* is full of ambiguities — 'the knowing*.
Here, as always, we are handicapped in English, because we have no
satisfactory word which covers indifferently 'sensing* and 'conceiving*
or 'thinking*. The word 'precedes* must, I think, be used in a temporal
sense ; for Kant's point appears to be that the synthesis of the parts
must be successive.
2 We can intuit an indeterminate quantum as a whole, if it is enclosed
within limits, without requiring to construct its totality through
measurement, that is, through the successive synthesis of its parts;
see A 426 n. -= B 454 n. Furthermore we can recognise that something
is a quantum — here, I take it, an indeterminate quantum — from the
thing itself without any comparison with others (as units of measure-
ment), namely when a multiplicity of the homogeneous constitutes
one whole. To decide how great it is, we always require something
else (which is also a quantum) as its measure ; see K.d.U.§2$ (IV 248).
When we measure, we must have a successive synthesis, and only
thus can we have a determinate extensive quantum.
3 Compare A 163 — B 204 and A 167 - B 209. It might be objected
that this statement (if true) is rather a consequence than a definition
of the nature of extensive quantity — the synthesis must be successive
because the parts of an extensive quantity are external to one another ;
but Kant, I imagine, holds that the proper definition of an extensive
quantity is a statement of the way in which it can be constructed,
and that a determinate extensive quantity can be known (and so can
be an object) only through successive synthesis.
The argument of the second edition suggests that an extensive
quantity is one which can be known only by a (successive) synthesis
of homogeneous parts ; and this is implied in the category of quantity
itself. Nevertheless homogeneity is not the distinguishing mark of
extensive quantity; for according to B 201 n. it belongs to intensive
quantity as well.
XXXVII §2] THE AXIOMS OF INTUITION 113
Since space and time are extensive quantities, Kant's defini-
tion makes explicit a presupposition which runs through the
whole of his argument1 — the presupposition that the parts of
space, like those of time, can be known only one after another.
He concerns himself first of all with pure space and time, the
space and time which we study in mathematics in abstraction
from sensible objects ;2 and he maintains that any space and
time about which we think must be constructed by an act
which is a successive synthesis of parts. In geometrical thinking
we must construct in pure intuition a figure corresponding to
our concept, and the construction must be a successive synthesis.
The same principle applies when we think of any determinate3
stretch of time.
From this general principle Kant proceeds to draw conclu-
sions as to the necessary character of all objects as appearances.
Empirical appearances are commonly regarded by him as
intuitions, but here4 he distinguishes within appearances what
he calls 'mere intuition',5 that is, intuition in abstraction
from sensation. Such 'mere intuition* is intuition of the space
or time occupied by the appearance, the form of the appear-
ance as opposed to its matter.6 Since every appearance contains
this element of mere intuition, it must be known in appre-
hension through the successive synthesis of parts;7 that is
1 It is present throughout the Transcendental Deduction.
2 This is true also of B 154 where it is said that we must think
a line, a circle, and even time itself, by means of a successive spatial
construction or synthesis.
a The word 'determinate* is important, I hclievc, in the argument
of both editions.
4 A 163 = B 203; compare A 167 — B 208-9.
6 'bhsse Anschauung.9
6 The 'mere intuition* is presumably the empirical form of the
appearance, namely, that determination of space or time (or both)
which belongs to the appearance : the matter of the appearance is
what is given in sensation. Compare A 128, B 207, and also Chapter
VI § 8.
7 Compare A 224 = B 271: 'The figurative synthesis by which
we construct a triangle in imagination is wholly identical with
that which we exercise in the apprehension of an appearance in
order to make for ourselves an empirical concept of it*.
ii4 THE MATHEMATICAL PRINCIPLES [XXXVII §3
to say, it must be an extensive quantity. In other words every
appearance is intuited as an aggregate, that is, a plurality of
previously given parts. As we shall see in the following chapter,
there is another kind of quantity to which such a description
does not apply.
It should be noted that we must synthetise the spatial,
as well as the temporal, element in appearances, and so far
space is as important as time.1 The special importance of time
arises from the fact that the synthesis must be a successive
synthesis. This necessary successiveness of the synthesis is
the special mark of extensive (as opposed to intensive) quantity.
It also enables us to find by abstraction a common element,
namely number, which is present whether extensive quantity
be spatial or temporal ; for number is produced by a successive
synthesis (or addition) of homogeneous units, whatever these
units may be.2
The proof given in the first edition is in some ways defective.
In spite of the fact that number was said to be the schema of
quantity, there is no explicit reference to number, or even to
the successive synthesis of the homogeneous with which number
has been connected.3 Kant's proof in the second edition is
more elaborate; and although it does not refer to number, it
does refer to the synthesis of the homogeneous.4
§ 3. The Proof in the Second Edition
In the second edition Kant again regards appearances as
'containing' form and matter, the form being an intuition of
space and time, the matter being given in sensation. Hence5
1 Like time it may be the source of the homogeneity of the parts.
2 The internal character of the units synthetised is for arithmetic
a matter of indifference ; compare A 720 --- 13 748 and A 724 = B 752.
3 A 142 - B 182.
4 Curiously enough, he does not in the second edition assert this
synthesis to be successive, but the omission seems to be a mere
oversight.
5 B 202 ; compare B 207. Kant says that 'all appearances contain,
as regards their form, an intuition in space and time'. I take this to
be an intuition of the determinate space or time referred to immediately
XXXVII §3] THE AXIOMS OF INTUITION 115
if we are to apprehend appearances,1 there must be a synthesis
of the manifold2 whereby the idea of a determinate space
or time (namely, of the determinate space or time occupied
by the appearance) is produced.3 This means that there is a
combination of the homogeneous manifold of space or time, and
consciousness (clear or obscure) of the synthetic unity of the
homogeneous manifold.
Now consciousness of the synthetic unity of the homogeneous
manifold of intuition in general is consciousness of the pure
category of quantity (or totality). Consciousness of the synthetic
unity of the homogeneous manifold of space or time is con-
sciousness of the schematised category of extensive quantity.4
thereafter, the space or time which the appearance occupies. If so,
it is identical with the 'mere intuition' of the first argument.
An appearance can hardly be said to contain the intuition of all
space and time; and the fact that the intuition is said to be in space
ami time suggests that it is an intuition of a part of space and time.
The phrase 'space and time1 may imply that Kant is thinking primarily
of physical objects ; but it may perhaps be due to the greater importance
attached to space in the second edition — we always require outer
intuition to show the objective reality of the categories (B 291).
Kant adds that an intuition in space and time is the a priori condition
of all appearances. This need not, I think, imply that he is immediately
concerned with intuitions of space and time as infinite wholes; but
it must imply that in knowing the determinate space and time of an
object we are knowing these as parts of the one infinite space and
time.
1 'Apprehension* is used, as generally by Kant, to mean 'the taking
up into empirical consciousness' ; compare A 99 ff and A 120. Here,
as usual, it is a successive synthesis (in which reproduction plays a
necessary part).
2 This manifold I take to be the pure homogeneous manifold of
space or time, the synthesis of this manifold conditions the con-
current synthesis of the empirical manifold in space or time.
3 This is the doctrine of all the versions of the Transcendental
Deduction, whatever their differences in terminology. Note that Kant
speaks here of 'space or time', not 'space and time', presumably
because the synthesis need not be concerned with spatial appearances.
4 See Chapter XXXI II § 2. Kant himself says that the consciousness
is the category. The name he gives to the category — the concept of
a quantum — suggests that he has in mind the schematised category,
as we should anticipate ; but the reference to intuition in general may
suggest that he has in mind the pure category. Perhaps 'intuition
in general' is not intended to have the usual technical sense (which
n6 THE MATHEMATICAL PRINCIPLES [XXXVII §3
It is not wholly clear whether Kant is concerned primarily
with the pure category or the schematised category. If we
take him to be concerned with the schematised category,1
the argument is relatively simple. We can have sense-per-
ception of an object as an appearance only by synthetising the
pure and homogeneous manifold of the determinate space or
time which it occupies. Hence one condition of the sense-
perception of an object is the synthetic unity of the pure and
homogeneous manifold of a determinate space or time.2 But
synthetic unity of the pure and homogeneous manifold of space
or time is precisely what is thought in the category of extensive
quantity. Therefore all objects as appearances must fall under
this category, or in other words they must be extensive quan-
tities.3
associates it with the pure category) : it may indicate only that the
difference between space and time can be ignored. Such a usage
seems to be found in A 724 - B 752 (and perhaps in A 142-3 = B 182)
in speaking of number, but there it indicates that we are concerned
with a quantitas (see § 8 below), not with a quantum. Furthermore
the category is identified with consciousness of the synthetic unity
of the homogeneous manifold of intuition in general only so far as
thereby the idea of an object first becomes possible; and this perhaps
suggests that the category in question is schematised.
Kant, it should be noted, does not in this passage use the phrase
'the synthetic unity of, which has been introduced by Vaihmger
(and is accepted by Kemp Smith). The insertion of the phrase makes
for clarity, but I am not sure that it is necessary.
1 If we take him to be concerned with the pure category, there
is no real difficulty, but in that case the reference to the schematised
category is introduced only when he comes to deal with extensive
quantity at the end.
2 Kant himself speaks of 'the synthetic unity of the manifold of
the given sensuous intuition'. For the sake of simplicity I take the
'given sensuous intuition* to be 'mere intuition* as opposed to sensation.
If we take 'intuition* to be used in the ordinary sense, we must add
that its synthetic unity is, as we have shown, also the synthetic unity
of a pure and homogeneous manifold.
3 Note that appearances or intuitions in space or time 'must be
represented through the same synthesis as that whereby space and
time in general are determined*. This suggests, I think, that in deter-
mining the space or time of an object we arc determining a part of
a wider whole which must be determined in the same way.
XXXVII §4] THE AXIOMS OF INTUITION 117
§ 4. Successiveness of Synthesis
There are many minor difficulties in following Kant's
argument. These arise mainly from his failure to make clear
whether he means 'intuition1 to be taken as 'pure intuition',
and whether he means 'the concept of a quantum' to be the pure
category or the schematised category. Such difficulties are
more in the expression than in the thought; and I do not
believe we need take seriously his omission to state, in the
argument of the second edition, that the synthesis of extensive
quantity is necessarily a successive synthesis.
The more philosophical difficulties centre in the successive-
ness of the transcendental synthesis. If we accept this succes-
siveness as necessary to mathematical construction, its presence
in all empirical apprehension requires a more detailed defence
than Kant has given us. When we know how to construct a
triangle or a circle, we can recognise at sight that a figure
drawn on paper is an example of what we are thinking about;
and although such a recognition takes time, it seems impossible
to believe that (for example) we construct each side of the seen
triangle by running successively through its parts. Neverthe-
less it may fairly be said that if there were any doubt on the
subject, we should test the figure by considering whether it
could be constructed in this way; and that a successive syn-
thesis is the basis on which our recognition rests. Indeed, if
Kant is right, to recognise this figure as a triangle is to recognise,
however 'obscurely', that it is the product of such a construction.
If Kant were going further than this, and were maintaining
that when we see a triangle, we always do construct what we
see by running our eye successively along the three sides,1
then I think we should have to say that he is mistaken. When
I look at the rafters on the ceiling I see a series of parallel
lines, and I have no reason to believe that I must follow suc-
cessively the contour of each line before I can see such a series.
1 To maintain this is like maintaining that when we judge three
people to be approaching, we must count them in succession. For
a further discussion of this point see Chapter XLII § i.
n8 THE MATHEMATICAL PRINCIPLES [XXXVII §4
Kant's language may in places suggest that he took the more
extreme view, though I find it hard to believe that he could
have advanced, without any attempt at argument, a doctrine
which on the face of it finds no corroboration in experience.
The psychological question whether we can, in the case of
familiar figures, recognise wholes at a glance is in any case
irrelevant. Kant is maintaining that we must think of any space
and time, however small, as a whole to be constructed by the
successive synthesis of parts. He is also maintaining that in
the case of any spatial or temporal intuition we must traverse
the parts successively, if we are to make the intuition deter-
minate.1 If we take him to be concerned only with determinate
extensive quantities, his contention seems to me to be true
— it is certainly true when we are concerned with determination
by measurement — and it is sufficient for his argument.
If we grant the necessity of construction in all mathematical
thinking, Kant's insistence on the successiveness of the syn-
thesis is not to be dismissed as manifestly irrelevant. There
is a successiveness also in our thinking and in our sensing;
but such successiveness does not constitute the essential nature
of thought as such or sensation as such.2 From the Critical
standpoint, which refuses to accept the view that the pheno-
menal world exists in its own right independently of thought,
successiveness of synthesis is essential to the presence of
determinate (though not of indeterminate) extensive quantity;
and it is the successiveness of the synthesis of apprehension
(so far as this is concerned with space and time) which guaran-
tees the applicability of the mathematics of extension to the
phenomenal world. I do not wish to dogmatise on these difficult
matters, but Kant's view is not to be refuted merely by assuming
the transcendental realism which he denies. It is also to be
1 1 find some difficulty in understanding how far Kant regards
shape or figure as kind of quantity. Broadly speaking, he is concerned
in this chapter with determinate quantity, quantity determined by
measurement, and for this we do require a successive synthesis.
2 Compare A 143 - B 183, B 208, A 168 -= B 210, for the gradual
changes in degree of sensation. This will be considered in the follow-
ing chapter.
XXXVII §5] THE AXIOMS OF INTUITION 119
noted that the intuitionist school of mathematicians, who have
rejected the Kantian view of space, attempt to base the whole
structure of mathematics on a doctrine which, so far as I under-
stand it, appears to follow Kant's view pretty closely in this
respect.1
The successive synthesis of extensive quantity, so far as it
is concerned with the pure manifold of time or space, is a
continuous synthesis2. The fact that we must run through all
the parts in order to know the whole does not mean that the
whole has a finite number of parts. In measuring we choose
a unit (such as a foot) arbitrarily, and interrupt our synthesis
whenever we have traversed the length of the unit.3 The possi-
bility of such interruption in a continuous synthesis does not
make the object measured a discrete quantity; and Kant would
have been very much surprised to learn that his view was
incompatible with the continuity of space and time.4
§ 5. Intuition and Object
It may be thought that the Principle of which Kant has
offered a proof applies to intuitions as intuitions, and not
to intuitions only so far as they are intuitions of an object.
Kant's own language supports this view when he says that the
Mathematical Principles arc concerned only with intuition?
1 See Black, The Nature of Mathematics, especially pp. 186 ff. 1
must, however, add that Mr. Black's account of Kant's doctrine is
so astonishingly inaccurate as to disturb my confidence in him when
he deals with other matters on which he is doubtless better informed.
2 A 169-70 -= B 211-2.
3 For Kant's view of measurement see KdU. § 26 (V 251 if).
The unit must be taken as the product of a continuous synthesis.
I think Kant means to assert this in A 171 - B 212, when he says
that appearance as a unity (or unit) is a quantum and so a continuum.
4 See Sidgwick, The Philosophy of Kant, p. 92. It is of course
true that by means of number we can represent any quantum as
discrete, but we must distinguish a quantum which is discrete in
itself fiom a quantum which is continuous in itself, but represented
by us as discrete. See Metaphyuk, p. 31.
5 A 1 60 - B 199. In B 1 10 he says, more correctly, that the mathe-
matical categories are concerned with objects of intuition (as opposed
to the existence of these objects). Even in A 160 = B 199 he adds
120 THE MATHEMATICAL PRINCIPLES [XXXVII § 5
If these words were to be taken literally, the Principle of the
Axioms would be out of place here — as many commentators
have held — and ought to be relegated to the Aesthetic.
This view, it seems to me, in spite of the support given by
some of Kant's looser expressions, is incompatible with the
argument of the second edition ; and it fails to recognise the
interconnexion of the different Principles of the Understanding,
all of which without exception are directed towards establishing
the necessary characteristics of every object of experience.
In the Mathematical Principles we consider the object in
abstraction from its relation to other objects, and we find that
the object in such abstraction must have extensive and inten-
sive quantity; but these categorial characteristics are products
of the one transcendental synthesis which also imposes upon
objects the categories of relation and modality. We must not
imagine that because we can consider in abstraction aspects
of what is essentially one synthesis, we are therefore concerned
with something other than an object of experience.
It is true that every intuition, and even that every image
of our fancy and our dreams, is spatial and temporal, and
may therefore be described in a loose sense as an extensive
quantity ; but if it is to be an extensive quantity in the strict
sense, it must occupy a determinate* space and time. Kant
means, I think, that it must be determined by measurement,
and so must be a determinate part of the one space and time
in which all objects are. When we perceive an object, the
appearance given in intuition occupies such a determinate
space and time, and can be measured exactly. The images or
that the a priori conditions of intuition arc absolutely necessary in
relation to a possible experience. In the Analytic \ve arc concerned,
not with conditions of intuition in abstraction, but with conditions
of intuition as conditions of a possible experience and its objects;
and one of these conditions is the successive synthesis of the pure
and homogeneous manifold of our common time and space.
1 B 202 , compare 'a determinate quantity of time* in A 163 — B 203.
The infinity of time is said to mean that every determinate quantity
of time is possible only through limitation of the one individual
whole of time; sec A 32 = B 47-8.
XXXVII §6] THE AXIOMS OF INTUITION 121
pseudo-objects of our imagination and our dreams cannot be so
measured,1 because they do not occupy such a determinate
space and time. What Kant is trying to show is that all
objects of sense must be exactly measurable or numerable —
and this means (although the momentary abstraction fails to
bring this out) measurable in relation to all other objects of
experience. It is only as intuitions (or appearances) of objects
that our intuitions are measurable as extensive quantities ; and
it is only as appearances of objects that they must be repre-
sented by the same synthesis which determines time and space
in general?, and must be subject to the category of quantity
without which no object can be thought.3
§ 6. The Doctrine of the Aesthetic
For these reasons I regard it as an error to maintain that Kant
is» repeating unnecessarily the doctrine of the Aesthetic, and
that he does so through the influence of an artificial plan
described by some commentators as 'architectonic'. The doc-
1 They arc indeterminate quanta.
2 B 203. Time and space in general are the one time and space
in which all objects are
n I cannot here enter into the more elaborate aspects of this conten-
tion. To determine the size of anything we always require thought
as well as sense, and \ve always presuppose that it occupies a deter-
minate part of our common space. This is obvious when we deter-
mine the size of the heavenly bodies, but it is equally true, although
less obvious, when we determine the size of a table. An image has
no measurable size, unless we assign to it, however arbitianly, a
position in space at a definite distance from ourselves; and to do
this is to make it a sort of pseudo-object When we imagine castles
in Spain or dream of marble halls, these edifices have no exact
dimensions; and if we find that dream-measurements are assigned
to them, we may equally find that they are dream-substances and
the product of dream-causes. There is no difference in this respect
between the Mathematical Principles and the Analogies. Both are
concerned with objects in a common time and space, and both find
a sort of imitation of themselves in the world of dreams and fancy.
We can of course measure the time through which an image or
a dream lasts, but to do this is to measure the time of our apprehension,
and to make our apprehension itself an object. Similarly we can
explain the causes of our dreams, but then we arc no longer dreaming;
we are making our acts of dreaming into objects of thought.
122 THE MATHEMATICAL PRINCIPLES [XXXVII § 6
trine of the Aesthetic is in manifest need of the additions here
supplied, and it is all-important to recognise that when we
determine an object, there must be present the same synthesis
of a homogeneous space and time as is necessary for the deter-
mination of space and time in general. This is a matter, not of
mere intuition, but of thought by means of the categories.
There is a greater show of plausibility in the criticism that
Kant, so far from repeating the doctrine of the Aesthetic, is
actually contradicting it. The charge of contradiction can
be repelled only when we realise that in the Aesthetic Kant is,
as he says, abstracting from the element of thought; and that
consequently the doctrine of the Aesthetic is provisional, and
must be supplemented and corrected by what comes later.1
In the Aesthetic it was argued that times and spaces are
known only as limitations of one infinite time and space ; and
consequently the 'original' idea of infinite space and time must
be a pure intuition, from which the concepts of temporality
and spatiality are derived. Kant even went so far as to say of
space that it is represented as an infinite given quantity.2 The
Aesthetic, in short, regards the idea of the whole as making
possible the idea of the parts ; whereas we have now been told
that it is of the essence of extensive quantity for the idea of
the parts to make possible the idea of the whole.3
The contradiction is due partly to the fact that in the
Aesthetic, since Kant abstracts from the element of thought,
he is bound to ignore the presence of synthesis.4 Hence he
has to speak as if the unity of space and time were dependent
merely upon intuition, and as if the pure intuitions of space and
time were given as one and even as infinite (or at least were
'represented' as an infinite given quantity). He has now
1 Compare Chapter V, especially § 8.
2 B 39. Compare A 24 and see Chapter V § 8.
3 A 162 = B 203. It should, however, be noted that if the whole
precedes the parts logically (or objectively) and the parts precede
the whole temporally (or subjectively) there is no contradiction. The
whole makes possible the parts in a sense different from that in which
the parts make possible the whole.
4 Except in so far as it is presupposed by synthetic judgements.
XXXVII § 6] THE AXIOMS OF INTUITION 123
explained that although the ideas of space and of time must
be intuitions, since they are ideas of one infinite whole, the
unity of these intuitions, like the unity of every intuition
of an object, depends on a synthesis of imagination in con-
formity with categories and the unity of apperception.1 When
we are told that space is represented as an infinite given quantity,
we must add that it can be so represented only because the
manifold is combined or synthetised by the understanding,2
although Kant makes no reference to synthesis in the Aesthetic.3
In this way at least some part of the contradiction can be
explained, but there remains an element of truth in the
Aesthetic which Kant fails to express in the Analytic. The
synthesis which constructs space and time by the addition of
part to part is itself dominated by an idea of the whole, and this
fact is here ignored by Kant, except in so far as he implies
that the synthesis of quantity, like every other, must accord
with the unity of apperception. To understand fully his view
of space and time we must supplement the doctrine of the Aes-
thetic and the Analytic by the doctrine of the Dialectic.4
1 Compare 13 160-1 n. and A 107.
2 Sec B 130, B 134, B 161, and compare A 105.
J In A 24 space was said to be represented as an infinite given
quantity because of the absence of limits in the advance of intuition.
This advance manifestly requires synthesis, but Kant makes no
attempt to emphasise this. lie omits the passage in the second edition.
Compare Chapter V § 7.
4 Especially in the Antinomies Kant's doctrine is elaborated further
in the Metaphysische Anfangsqrunde der Naturwissenschaft (IV 481-2).
There he recognises a relative or material space which is movable
and is capable of being perceived or sensed, that is, can be symbolised
(bezeichnet) through that which can be sensed. Such a relative or
movable space, if its movement is to be perceived, presupposes a
wider relative space in which it moves, and so on ad infimtum. Absolute
space on the other hand is not material and cannot be perceived;
it means only a wider space which is relative to every other, a space
which I can always think as outside others and extend indefinitely.
Such a wider space is still in a sense material, but as I know nothing
of the matter which symbolises it, I abstract from the matter and
represent it as a pure and absolute space, an immovable space in
which other spaces move. To regard it as an actual thing is a mistake,
and a misunderstanding of reason in its Idea. For Kant's doctrine
of Bezeichnung (signatid) see Anthr* § 38 (VII 191).
i24 THE MATHEMATICAL PRINCIPLES [XXXVII § 7
Such an investigation is beyond the scope of the present
book, but I believe that his theory is more coherent than many
of his critics are prepared to admit.
§ 7. The Axioms of Geometry
Although Kant's primary aim is to establish the applicability
of the categories to objects of experience, he regards the
Principle of the Axioms as the basis of the objective validity
of pure mathematics, that is, of its application to physical
objects. He discusses briefly (i) geometry, (2) arithmetic, and
(3) the application of these, but especially of geometry, to objects
of experience. The discussion does not profess to be other than
elementary, and on that level it must be judged.1
The mathematics of extension (that is, geometry) rests on
the successive synthesis of the productive imagination in the
construction of figures. This is true in particular of the axioms
of geometry, and consequently the Principle is called the
Principle of the Axioms.2 Axioms, we must remember, are
a priori synthetic principles which are immediately certain,
and this immediate certainty is due to the possibility of 'con-
structing* concepts, that is, of 'exhibiting' a priori in intuition
an object corresponding to the concept.3 As principles, the
axioms of geometry express or formulate the conditions of
a priori intuitions of space and of spatial figures, the conditions,
that is to say, of our rules for constructing geometrical figures.4
1 For further remarks on this point, see Chapter VII §§ 5-8. In
the present chapter I ignore the many difficulties raised by the develop-
ments of modern mathematics.
2 Compare A 733 == B 761. As distinguished critics have objected
that this Principle is not an axiom, it is necessary to point out that
although Kant in A 161 — B 200 speaks loosely of the Principle as
if it were an axiom, when he comes to formulate it, he describes it,
not as an Axiom, but as a Principle of Axioms.
3 See A 732 - B 760 and Log. Einl. Ill (IX 23).
4 A 163 = B 204. Kant says they formulate the conditions under
which alone the schema of a pure concept of outer appearance can
arise. The schema would seem to be the rule for constructing a triangle,
square, and so on; see A 141 — B 180. It may possibly be space
itself (see A 156 — B 195), though space is also referred to as the pure
image (Bild) of the quanta of outer sense (see A 142 =•= B 182).
XXXVII § 8] THE AXIOMS OF INTUITION 125
Such axioms are that between two points there can be only one
straight line, and that two straight lines cannot enclose a space.
In the Aesthetic Kant had already presumed such axioms
to be intuitively certain.1 He now adds that this intuitive
certainty depends on an imaginative construction which,
in conforming to the particular concept involved, conforms
also to the category of quantity. He makes no reference to the
axioms concerned with time which he mentioned in the
Aesthetic, but the same considerations would apply in this
case also.2 All these axioms are concerned with extensive
quantities which Kant calls quanta, which we may here take
to be figures in space and durations in time.3
§ 8. Quantitas and Quantum
At this point4 Kant makes a distinction between 'quanta'
and 'quantitas\ This distinction raises problems of Kantian
terminology through which it is not easy to thread one's way.
In English we can distinguish between 'quantum' and 'quan-
tity', although the words are often used ambiguously and
without precision. The ambiguity in German is increased by
the fact that the same word5 has to do duty for both.
The pure category of quantity (or totality6) — which I
1 See 13 41. The example there given is that space can have only
three dimensions The presence of intuitive ceitamty does not imply
the absence of thought; compare Chapters X § 7 and XXXVI § 3.
2 See A 3 1 - B 47. The axioms are that time has only one dimension,
and that different times are not simultaneous but successive.
3 Time, it may be noted, is sometimes descnbed as 'protensive1
instead of 'extensive' (see Metaphysik, p. 37), and Kant has here
confined the mathematics of extension to geometry.
4 A 163 — B 204.
5 'Grossed Strictly speaking, quantitas is 'die blosse Grosse or 'Grosse
uberhaupt' ; compare A 717 — B 745 and A 242 -— B 300.
6 Totality includes in itself the moments of plurality and unity,
and is definitely said to be the category to which number belongs
(as a schema) ; see Bin. Curiously enough in the Prolegomena §21
(IV 303), when Kant gives the three moments of quantity (Quantitat),
he speaks of unity as the measure or unit (das Mass), plurality as
quantity (die Grosse), and totality as the whole (das Ganze). Similarly
in Metaphysik, pp. 3 1-2, he connects 'quantum' primarily with plurality
126 THE MATHEMATICAL PRINCIPLES [XXXVII § 8
have defined as the concept of the synthesis of the homogeneous1
— may be called 'quantitas'? The schematised category I have
called the category of extensive quantity, and defined as the
concept of the synthesis of the homogeneous in time and
space.3 Though Kant, so far as I know, does not employ the
phrase, the schematised category might be called 'quantitas
extensive?*
The concrete instances in which quantitas is manifested
are naturally called quanta, and the word 'quantum' is applied
by Kant both to space and time (the only original quanta5)
and to empirical objects so far as these are extended in space
and time. We might indeed express the Principle of the Axioms
itself by saying that all appearances are extensive quanta.6
As I have already pointed out,7 Kant habitually uses concrete
words for the purpose of expressing concepts ; and the category
may be referred to indifferently as the concept of quantitas
or the concept of quanta in general or even as the concept of a
quantum*
So far there is no real difficulty. But quantitas may also be
used for a special kind of instance in which quantitas (the
(multitude). Perhaps this is part of his doctrine that the infinite is
a quantum without being a whole; see Chapter XV § 2. Perhaps
(like the use of 'reality* for the category of quality) it has no special
significance.
1 See Chapter XXXIII § 2.
2 See A 142 = B 182. The same usage is implied in A 146 -= B 186.
3 Kant does not distinguish the schematised category from the pure
category with sufficient precision, but it is manifestly the schematised
category with which he is concerned in the present passage. The
'homogeneous in time and space* is here the pure homogeneous
manifold of time and space.
4 In Metaphysik, p. 32, he speaks of quantitates as extensive and
intensive, but there the usage is concrete, not abstract.
6 A 725 =- B 753.
6 The word is sometimes translated as 'magnitude*. This tends
to obscure its connexion with the category of quantity, and Kant
uses 'magnitude* in a different sense; see K.d.U. § 25 (V 248).
7 Chapter IX § 4.
8 The last usage is the one employed in B 203. We can add the
word 'extensive* to make clear that we are dealing with the schematised
category.
XXXVII § 8] THE AXIOMS OF INTUITION 127
category) is present, and we can speak of quantitates in the
plural. We must distinguish between such quantitates and
quanta* although they have the common characteristic that
they can be constructed a priori in mathematics. Examples of
quanta are the spatial figures of geometry2 and also durations.3
These have a quality as well as mere quantity — in the case of
spatial figures that quality is shape or figure.4 When we abstract
entirely from the quality,5 then we have quantitates, which
Kant identifies with numbers 6 These I take to include the
constants and variables of algebra as well as the numbers of
arithmetic.7
The only source of difficulty here is the use of the word
'quantitas' both for the universal and for certain special
instances of the universal, namely numbers; but there is, I
fear, still a further complication. I will put it in my own way
by saying, although Kant does not use the phrase, that we can
treat any quantum (even an empirical object) as itself a
quantitas. We do so by abstracting from all its qualities, and
this happens when we measure it, that is, when we ask how big
it is.8 This question can be answered only by saying how many
units it contains, and the answer must be by means of numbers.9
Such a quantitas, although not a number, always involves
1We may ignore the cases where these words are used without
being distinguished. E.g. in Metaphysik, p. 32, quantitates clearly
covers quanta.
2 A 717 - B 745. 3 A 720 --= B 748, A 724 = B 752.
4 'GestalV '; see A 720 — B 748. Kant does not say what the corre-
sponding quality is for durations, m which he is less interested; but
I suppose that every duration has the quality of being one-dimensional.
*'Quahtaty or 'Bcsthajfenheit'; see A 720 = B 748 and A 717
= B 745.
6 A 717 = B 745 and A 720 = B 748. Compare Chapter VII § 6.
7 In K.d.U. § 26 (V 251) Kant speaks of the estimation of quantity
as mathematical if it is by means of number-concepts or their signs
in algebra. In A 146 = B 186 number is quantitas phacnomenon.
8 A 163 = B 204. In Metaphysik, p. 32, Kant speaks of things as
quantitates.
9 We may of course have to be satisfied only with approximations
obtained by means of number-series which progress ad infimtwn\
see K.d.U. §26 (V 251).
i28 THE MATHEMATICAL PRINCIPLES [XXXVII § 8
number and comparison with a standard or unit of measure-
ment: I think it is better called a determinate quantum. A
quantum can be recognised at sight and need not be compared
with anything,1 but it is then, I think, an indeterminate
quantum.
Every determinate quantum, since it is the product of a con-
tinuous and successive synthesis, can (as I have already pointed
out2), be measured by interrupting the synthesis whenever
we have traversed the length of the unit chosen as our standard
of measurement.3 We may ignore for the present the difference
between continuous and discrete quanta,4 and we may also
ignore the fact that there are some quanta which are not exten-
sive.5 Granting Kant's presuppositions, we may take him to
have proved that every object must (in one aspect of it) be a
determinate continuous extensive quantum; we can always
determine its objective quantity by numbers or measurement.
This seems to me to be the essence of Kant's doctrine.
If we take the schematised category to be concerned only
with determinate extensive quantity,6 we can understand why
he insists on the successiveness of the synthesis and on the
presence of number. It is only by counting or measuring — a
procedure which is necessarily successive — that we can deter-
mine the extensive quantity of any object. In this as in all
other cases (though Kant does not make his view too clear)
1 K d U. §§ 25 and 26 (V 248 and 251) and compare again A 426 n.
= B 454 n. All estimate of quantitas is relative to the unit we take,
and in the last resoit this is a quantum which is not itself estimated
mathematically as a quantitasy but only aesthetically in mere intuition
by the eye (or I suppose by touch). Compare also A 240 — B 299.
2 See § 4 above.
3 The quantitas of anything may be described as the quantitas of
my progression in space and time ; see Metaphysik, p. 39.
4 See A 526-7 -= B 554-5.
5 See A 143 = B 183 and A 170 =^ B 212.
0 I think Kant is entitled to define his technical terms as he pleases ;
and it does not seem to me to be too paradoxical to say that we have
extensive quantity only so far as we have exact measurement. I
confess that I discovered this only at the last moment — partly from
reading the Master of BalhoFs book on Kant — but it seems to me
to solve many difficulties.
XXXVII § 9] THE AXIOMS OF INTUITION 129
the schema has to be established if we are to justify our appli-
cation of the pure category. The schematised category combines
in itself the pure category and the schema: it is not only a
concept of the synthesis of the homogeneous, but a concept of
that successive synthesis of the homogeneous manifold of time
and space whereby alone an object can be quantitatively
determined in regard to its extent.1
Needless to say, we do not require to measure an object
before we can regard it as an object ; but in regarding it as an
object we presuppose that it can be measured. We know a
priori that an object must have extensive quantity, but we do
not know a priori what extensive quantity an object must
have. Its actual measurements are to be determined by empirical
methods alone.2
§ 9. The Formulae of Arithmetic
Arithmetic (under which we may include algebra) is a
more abstract science than geometry and is concerned, not with
quanta, but with quantitates, which may be described generally
as numbers.3
Arithmetical propositions have intuitive certainty,4 and
depend upon a construction; they are synthetic and not
analytic. In the judgement 7 + 5 = 12 the left-hand side of
the equation gives us the idea of 7, the idea of 5, and the idea
of an operation (namely adding) ; but we have to perform that
operation by means of a construction before we can get the
1 I still have difficulties as to the distinction between the schematised
category and the schema, but I do not wish to waste time on subtleties.
2 These general considerations are true as regards all the categories.
It is interesting to note that in the Nachtrage LXX Kant explains
that the homogeneous manifold must be taken together in accordance
with concepts of quantity, because we cannot intuit space and time
for themselves. The fact that we cannot intuit empty or absolute
space and time is a reason which he repeatedly gives for the necessity
of employing all the categories.
3 See A 163 ~ B 204, A 717 = B 745, A 724 = B 752, and compare
K.d.U. §§ 25-6 (V 248 ff.). Compare also A 146 - B 186.
4 A 164 — B 205. They are Evident' in the technical sense. See
Chapter XXXVI § 3.
VOL. II E
i3o THE MATHEMATICAL PRINCIPLES [XXXVII § 9
right-hand side of the equation.1 Such a construction Kant calls
symbolic, and believes to be impossible apart from intuition.2
According to Kant there can be no axioms in arithmetic,
only formulae.3 Arithmetic, like geometry, does presuppose
certain general principles — if we may call them so4 — of a purely
analytic character, for example that if equals be added to,
or subtracted from, equals, the results are equal;5 but axioms,
strictly speaking, are synthetic. On the other hand the pro-
positions of arithmetic — such as 7 + 5 = 12 — although they are
synthetic, are not universal, and an axiom must be universal.
Such propositions are therefore called by Kant 'number-
formulae'.6
The proposition 7 + 5 = 12 Kant regards as a singular
synthetic a priori proposition. He must mean that the pro-
position is concerned originally with this 7 and this 5, although
he admits that the use of these numbers afterwards is universal.
I take his view to be that when we have seen this 7 and this 5
to be equal to 12, we can affirm that the sum of any 7 and any 5
is equal to 12 :7 we do not require to repeat the operation of
adding the separate units in every case.
1 Here again, as in the case of recognising a triangle, we need not
go through the process of adding 7+1 + 1 + 1 -hi ]-i, but our
addition of 7 + 5 rests ultimately upon such a process. In the
Nachtrage LXXI Kant proposed to omit this insistence on the synthetic
character of the judgement in view of the discussion introduced in B 16.
2 Compare Chapter VII §§ 6 and 7. 3 A 164 — B 204-5.
4 Kant himself calls them principles (Grundsatze) in B 16, but
immediately denies that they serve as principles (Pnnzipieri).
5 The examples given in B 1 7 for geometry are : the whole is equal
to itself or a — a ; and the whole is greater than the part or (a + b) > a.
These 'principles' are said to be valid even in mere conception (nach
blossen Begnffen); they are admitted in mathematics because they
can be 'exhibited' in intuition. This is another case where analytic
judgements are not 'about' concepts — as is maintained by Kmkel
and Hermann Cohen — but 'about' objects.
6 ' Zahlformeln.' Schulz (Prufung der Kantischen Kntik, Vol. I,
p. 2 19) argued in 1789 that there are two axioms in arithmetic, namely
a + b = b + a and c + (a + b) = (c -\ a) + 6.
7 It may be objected that there is only one 7 (the number 7) although
there are many groups of 7 things. This seems to me to be an error
which is refuted every time we say that 7 + 7 = 14. There is only
XXXVII § IG] THE AXIOMS OF INTUITION 131
On the other hand we have to remember that the axioms
of geometry, although they are stated as universal propositions,
also rest according to Kant's theory on the construction of
individual instances, as do all mathematical propositions
without exception. Mathematics as such deals with the universal
in the particular, or rather in the individual j1 and the difference
between geometry and arithmetic on which Kant is here
insisting seems to be little more than a difference in expression.2
On his view both sciences deal with individual instances;
both sciences construct these instances a priori in accordance
with a principle; and both sciences extend their conclusions
to all other individual instances constmcted on the same
principle. This is possible because we can see in the individual
instance that the conclusion follows only because of the prin-
ciple of construction employed.3
§ 10. The Application of Mathematics to Objects of Experience
The Principle of the Axioms is intended to show the objective
validity of pure mathematics : it is our justification for applying
pure mathematics to objects of experience. Kant's contention
is general, but his argument is confined to geometry.4 He
states his case first of all in terms of the Aesthetic: empirical
one seven-ness, but it has many instances. Such is the doctrine which
I believe to have been held by Plato in the Republic. It is certainly
attributed to him by Aristotle; see Metaphysics, A 6, gSyb, 14 ff. But
these matters arc highly controversial, and I have no wish to speak
dogmatically on a matter where I have no claim to expert knowledge.
1 Sec A 714 = B 742 and also A 734 = B 762.
2 The fact that we can construct a triangle in different ways and
a number in only one way has surely no direct connexion with the
difference between an axiom and a number-formula (or between a
universal and a singular proposition). The variation in triangles rests
on the fact that they are figures of two dimensions; and it may be
true that we require axioms in geometry because space is a continuum
of more than one dimension.
Kant's further objection — that if we call number-formulae axioms,
there will be an infinite number of axioms in arithmetic — is valid
only if we assume that there cannot be an infinite number of axioms.
3 Compare A 715-16 = B 743-4 and Chapter VII § 7.
4 His failure to deal with arithmetic is very remarkable, since the
schema of quantity is number.
132 THE MATHEMATICAL PRINCIPLES [XXXVII § 10
intuition is possible only through the pure intuition of time and
space, and what geometry asserts of pure intuition must
undoubtedly apply to empirical intuition.1 For the full under-
standing of his doctrine it must be added that the synthesis
which is necessary for knowledge of empirical objects must
involve a synthesis of time and space, and this point he duly
proceeds to make. The synthesis of spaces and times, which arc
the essential forms of all intuition, is what makes apprehension,
and therefore outer experience, and therefore all knowledge of
physical objects, possible; and what pure mathematics proves
about space (by means of its a priori constructions) must be
valid of objects in space.2 It is mere sophistry, he maintains,
to suggest that though mathematical lines are infinitely divisible,
the actual lines in nature might be made of simple parts or
physical points.3
All such sophistical doctrines rest on the supposition that
physical objects are things-in-themselves, and consequently
cannot be known a priori to conform to theories which have
been proved independently of experience. Granted this
supposition, Kant believes the doctrine to be true, and adds
that on this supposition geometry itself would be impossible4
— presumably upon the ground that it would deal only with
the creations of our own fancy.5
Such an argument would manifestly have no weight with
those who hold that mathematics does deal only with a world
of fancy, and that there is no known reason why it should
sometimes apply to actual things. For those who hold such a
view Kant's argument is a petitio principii? and in any case it
1 A 165 = B 206. 2 A 165-6 = B 206.
3 Compare Prol. § 13 Anmerk. I (IV 288).
4 A 1 66 — B 207. Yet Kant admits that mathematics is possible
on the Newtonian view.
6 Prol. § 13 Anmerk. I (IV 287). In A 165 == B 206 Kant says we
should deny objective validity to space and consequently to all
mathematics, and should not know why or how far mathematics
could be applied to appearances.
6 He assumes that we can construct only Euclidean space, and
consequently that the space of the actual world and of physics must
be Euclidean.
XXXVII § IQ] THE AXIOMS OF INTUITION 133
is too elementary to meet the difficult problems of the present
day. Nevertheless I cannot believe it to be a mere accident
that geometry — whether Euclidean or any other — should be
developed a priori, and yet should be found to apply to the
actual world. There must be an intelligible connexion between
the development of pure mathematics and its application to
the physical world, and the reasons for that connexion ought
to be found in an analysis of experience such as Kant has
offered. We cannot afford to ignore the fact that our experience
depends essentially upon an imaginative construction based
upon sensation and controlled by thought, and that this imagi-
native construction is always a synthesis of space and time
or of space-time. However much Kant's doctrine may be in
need of modification, it is by no means merely to be set aside.
CHAPTER XXXVIII
THE ANTICIPATIONS OF SENSE-PERCEPTION
§ i . The Principle of the Anticipations
The Principle of the Anticipations is : In all appearances the
real, which is an object of sensation, has intensive quantity, that
is, a degree.
This is the formulation of the Principle in the second edition.1
In the first edition the Principle is formulated thus: In all
appearances sensation, and the real which corresponds to it in
the object (realitas phaenomenon), has intensive quantity, that
is, a degree* Since the argument added in the second edition
conforms to the formulation of the Principle in the first edition,
the change in expression would seem to imply no change in
the thought, and I can see no reason for it other than a desire
for brevity.3
There is some uncertainty as to the meaning of the terms
employed by Kant, and these must be considered before we can
estimate his proof.
The word 'Anticipation* might be applied to all the Principles4
(and indeed to all synthetic a priori judgements): they all
anticipate experience and inform us, before any particular
experience, what necessary characteristics an object of that
experience must have. The word is, however, peculiarly
appropriate to the Principle we are about to consider. It is
most remarkable that we should be able to anticipate experience
on its empirical side and to have a priori knowledge of its
matter, a matter which must be given through empirical
sensation .5
1 B 207. 2A 166.
3 The brevity both here and in the Axioms is secured at the expense
of details which do not cease to be parts of Kant's doctrine.
4 A 166-7 = B 208. For a similar statement about the word
* Analogy', see A 180-1 — B 223.
5 A 167 — B 208-9. The Principle of the Axioms dealt only with
the form, as opposed to the matter, of appearances. The Principle
XXXVIII § i] THE ANTICIPATIONS 135
Since all the Principles are concerned with the application
of the categories (or the schematised categories) to objects,
I think we may take 'appearances' to mean appearances as
determinate objects. In the Anticipations1 we consider one
characteristic which must belong to every determinate object —
Kant is thinking primarily about physical objects — and although
we consider this in abstraction from the other characteristics
which every object must have, we must understand this
Principle in the light of the others, and we are certainly not
examining the nature of sensation in itself without regard to the
fact that it is sensation of an object.2
'Intensive quantity' is identified by Kant with 'degree'.3
of the Anticipations may be said to deal with the foim of the matter
of appearances, an essential characteristic which belongs to the matter
as such (and to sensation as such) apart from the time and space
which it fills; compare A 176 — 6 218. Every Principle must be
foVmal, and the present Principle is no exception. In A 161 — B 201
Kant himself indicates that the Anticipations are concerned only
with the form of quality.
1 I use this as a shorter way of saying 'the Principle of the
Anticipations'.
2 Compare Chapter XXXVII § 5 for further development of this
general view.
3 See A 1 68 = B 210. Degree is degree (or intensive quantity) of
a quality, and by quality — which is not here defined — Kant means
such things as colour, taste, heat, weight, and resistance. See A 176
— B 218 and (for the particular qualities) A 168 = B 210, A 169 =
Ban, A 174 = 6216, and also Prol. §24 (IV 306). In A 173 = 6215
impenetrability t>eems also to be regarded as a quality comparable
with weight; this is presumably the same quality as resistance It is
not made clear whether all these qualities are on the same level.
Colour and taste are said to be qualities of sensation in A 175 — 6217,
and are contrasted with the real which corresponds to sensation ; in
A 176 - B 218 quality is identified with 'the real of appearances*
(rcahtas phae nomenon) ; and in A 1 73 — B 215 impenetrability and
weight (the result of the forces of repulsion and attraction) are implied
to be identical with the real in space. For the purposes of dynamics
Kant identifies the 'real' or the 'matter' of objects of outer sense
with 'moving forces' (betoegende Krafte), that is, with a combination
of the forces of repulsion and attraction. See M A.d.N. 2. Hauptstuck
(IV 523) and compare A 265 = B 320-1. We must remember that
for Kant the primary qualities are in a special sense objective, and
to these impenetrability — see Prol. § 13 Anmerk. II (IV 289) — and
presumably weight belong. Compare Chapter II § i.
i36 THE MATHEMATICAL PRINCIPLES [XXXVIII § i
It is defined as 'that quantity which is apprehended only as
unity, and in which plurality can be represented only through
approximation to negation = o'.1 An extensive quantity
is made up of parts (quantities) outside one another in space or
time, while an intensive quantity is given as a whole and all
at once. A foot is made up of so many inches and an hour of
so many minutes, and it is because we have separate ideas of
the parts that we can have an idea of the whole ;2 but when we
experience a degree of heat we have an idea of the whole without
having separate ideas of its parts.3
The chief difficulty of Kant's account is to be found in the
words 'real* and 'sensation*. Are these meant to be the same or
are they meant to be different ? The formula in the first edition4
distinguishes them explicitly, and so does the argument in
1 A 1 68 — B 210. This, I think, explains what Kant says in A 99
— that every idea, as contained in one moment (that is, in abstraction
from the synthesis of spaces and times), can be nothing but absolute
unity. Compare Chapter XIX § i. Extensive quantity is also a unity,
but its plurality is represented by parts outside one another. The
plurality of intensive quantity is not represented by parts outside
one another, but every degree contains a plurality, because it contains
all lesser degrees down to zero. This is what Kant means by saying
that its plurality is represented through approximation to negation.
2 See A 162 = B 203.
8 Kant believes that in experiencing a degree of heat we pass
successively and continuously fiom our starting-point through the
intermediate degrees to the final degree; but at every stage we have
before us a degree which is one and indivisible.
Prichard (Kant's Theory of Knowledge, p. 262) points out that
this is true of velocity. *A mile can be said to be made up of two
half-miles, but a velocity of one foot per second, though comparable
with a velocity of half a foot per second, cannot be said to be made
up of two such velocities; it is essentially one and indivisible/ Kant
does not use velocity as an illustration — I think because it is not directly
sensible — but he recognises it elsewhere as an intensive quantity,
pointing out that its parts are not outside one another as are the parts
of space. See M.A.d.N. i. Hauptstuck (IV 493-4).
4 The formula in B says only that the real, which is an object of
sensation, has intensive quantity, and does not say that sensation
has intensive quantity; yet even here the real seems to be distinct
from the sensation, if it is the object of sensation. Sensation is essen-
tially subjective, although we use it for knowledge of objects — see
K.d.U. Einl. VII (V 189).
XXXVIII § i] THE ANTICIPATIONS 137
both editions.1 The real is what corresponds to sensation, and
what corresponds to sensation must be different from sensation
itself. Nevertheless the carelessness of Kant's language, together
with the fact that he is keeping in the background some of his
doctrines as unsuited to Transcendental Philosophy,2 makes it
difficult to determine the precise meaning of 'sensation' and 'real'
and the precise sense in which the real 'corresponds to' sensation.
There would seem to be three possibilities: (i) that sensation
is our sensing and the real is the sensum ;3 (2) that sensation is
the sensum considered as a modification of the mind, while
the real is the quality of the object revealed or given in the
sensum,4 and (3) that sensation is the sensum considered as
revealing a quality of the object, while the real is the moving
forces (bewegende Krdfte) of repulsion and attraction which
fill space and constitute the solid bodies of common sense and
the substances of physical science.5
1 In the argument of the second edition Kant does not speak of
the real corresponding to sensation; but he does speak of 'the real
of sensation' , and he says that corresponding to the degree of sensation
we must ascribe a degree to objects of sense-perception, so far as
sense-perception contains sensation. The distinction is also supported
by his ascribing to objects a degree of influence upon sense.
2 In opposition to 'Rational Physiology' (the a priori science of
corporeal and spiritual nature). Compare A 171 = B 213; A 846-7
— 13 874-5 > an(l also § 7 below.
3 This receives some support from A 172 — - B 214. There every
reality in sense-perception has a degree, and every sense (Sinn) has
also a determinate degree of the receptivity of sensations.
4 When we are actually perceiving an object, the sensum and the
quality would seem to be the same thing regarded from different
points of view, but the sensum is thought to be only at the moment
of sensing, while the quality has a semi-independent existence (in
space and time) which we determine by thought. When we see white
sugar, we think that it is sweet, even although we are not tasting it.
Such is the simple statement of Kant's view. It has to be modified
by the further doctrine that secondary qualities exist only in relation
to the individual, while primary qualities are the same for all men.
All these statements anticipate the doctrine of the Analogies.
6 Compare A 265 = B 320-1, A 273 — B 329, A 277 = B 333,
A 284 =- B 340. Note particularly that realitas phaenomenon is identified
with moving forces in A 265 - B 320-1, and in A 273 -^= B 329
with the obstacles and reactions in nature (Hmdermsse and Gegen-
wirkungen) which are due to such forces.
VOL. II E*
138 THE MATHEMATICAL PRINCIPLES [XXXVIII § i
Of these possibilities the first is unimportant and may be
neglected ; the third is a statement of Kant's dynamical theory
of matter and has strictly no place in a Kritik of Pure Reason ;
the second alone must be adopted for the interpretation of
Kant's argument.1 The Anticipations can tell us only that
the quality of objects must have a degree corresponding to the
degree of our sensations.2 This is the universal principle of
which the dynamical theory of matter is a particular applica-
tion.3
The Principle of the Anticipations is concerned with the
matter as opposed to the form of objects, and here also there
is an ambiguity. Sensation is itself spoken of as the matter,
but usually as the matter of intuition (or sense-perception or
experience);4 the matter of the object is what corresponds to
sensation.5 Kant has in mind, at least partly, matter — or the
qualities of matter — as it is known to physical science;6 but
1 If we take this interpretation, we can understand why Kant does
not maintain a sharp distinction between 'sensation' and 'the rear:
to say that there are degrees in sensation is also to say that there are
degrees in the qualities of the objects revealed in sensation.
2 This is in accordance with the second possibility suggested above ;
but we must add that while some qualities are revealed directly in
sensation, others are known indirectly by inference from sensation.
3 In M A.dN. (IV 523) the following is said to be the universal
principle of dynamics — that all the real of objects of outer sense,
which is not merely determination of space (place, extension, and
shape), can be regarded only as moving force. This abolishes the notion
of the solid, or absolute impenetrability, and sets in its place the
forces of repulsion and attraction which are necessary for the idea
of matter.
4 In A 42 = B 60 and A 167 --- B 209 sensation is the matter of
sense-perception ; in A 50 = B 74 the matter of sensuous knowledge ;
in A 267 = B 323 the matter of intuition; and again in A 167 =
B 209 the matter of experience. It will be remembered that in
A 146 = B 1 86 reahtas phaenomenon is itself identified with sensatio.
6 A 20 — B 34, A 143 = B 182. I concern myself here only with
the matter of the phenomenal object. The inner nature of that matter
as it is in the thmg-in-itsclf is to us unknown.
8 Matter is identified by Kant with substance, and perhaps the
real should be regarded as the qualities of matter. In A 176 — B2i8
quality is identified with the real of appearances (reahtas phaenomenon) ,
and it is quality which has a degree. In A 186-7 = B 229-30 Kant
XXXVIII §2] THE ANTICIPATIONS 139
on the whole the matter of an object as treated in the Antici-
pations is its sensed qualities, which are distinguished from its
extensive quantity, that is, from its size and duration and
perhaps its shape.1
Broadly speaking, Kant is about to argue that an object is
more than the space which it occupies and the time through
which it lasts. It is real as filling a determinate space and time,
and what fills space and time must have intensive quantity
or degree.
§ 2. The Proof in the First Edition
We have seen that 'apprehension* involves a successive
synthesis of what is given in sensation, and therefore a synthesis
of the times and spaces occupied by what is given; and that
consequently every object must have extensive quantity.
But apprehension is more than a successive synthesis of times
and spaces ; and we can abstract from the successive synthesis
and consider apprehension as a mere momentary 'taking up'
of the given. We can therefore say that in the appearance, or
object, there is something the apprehension of which is not a
successive synthesis producing a whole by the addition of part
to part. What is apprehended in this way can have no extensive
quantity.
So far at least Kant would seem to be right. He does not
mean that we can sense something in a mere point of time and
space without reference to anything else;2 that is utterly
points out that the determinations or accidents (and so presumably
the qualities) of a substance are always real', but he warns us against
the danger of separating the accident from the substance, and reminds
us that the accident is only the way in which the substance exists.
1 Shape is not an extensive quantity, but (like extension and also
position) it is a determination of space rather than of the real con-
sidered in abstraction from the space which it fills; see M.A.d.N.
(IV 523).
2 1 do not think Kant holds that we cannot be aware of the colour
red as extended without running successively through its parts : he
does hold that we cannot determine its extent except by running
successively through its parts; see A 426 n. = B 454 n.
i4o THE MATHEMATICAL PRINCIPLES [XXXVIII § 2
opposed to the doctrine of the Second Analogy. He does mean
that when we are aware of anything in space and time, it must
have a quality distinct from being spatial and temporal. We
are aware of colour, taste, or resistance ; and whether we regard
these as sensa (that is, modifications of our mind) or as qualities
of objects, they fill time and space, and their complete absence
would mean that time and space were empty.1 When time
(and space) is filled, we have reality (realitas phaenomenori)\
when it is empty we have negation = o.
Now, Kant asserts, every sensation is capable of diminution
so that it can decrease and gradually vanish. Therefore between
reality (realitas phaenomenorif and negation, or between any
given sensation and complete absence of sensation, there is a
continuous sequence3 of possible intermediate sensations.4
This means that the difference between any given sensation
and such an intermediate sensation is always less than the
difference between the given sensation and zero.5 Hence
there is a more and a less of what fills time and space, and this
is distinct from the more or less of time and space which is
filled. That is to say, sensation (and the real corresponding
to sensation) has intensive quantity or degree.6
There is in this proof no reference to synthesis, but \\c
1 Kant docs not of course suggest that we can perceive empty
space and time; his whole argument throughout the Principles rests
on the view that we cannot. Empty time and space is a mere limit
at the most.
2 What Kant calls Reality in the appearance' (Reahtat in der
Enchemung) is equivalent to 'realitas phaenomenon*.
3 A 168 ~ B 210, ' Zusammenhang* .
4 The continuous sequence or gradation is present both in the
sensation and in the quality of the object.
5 If, for example, we see a red colour, there is always possible a
less red colour which is still red. See A 169 -= B 211.
6 This should be compared with the argument in A 143 = B 182-3.
There Kant points out that a sensation can fill the same length of
time more or less, until it ceases altogether. There is therefore a
sequence (Zusammenhang), or rather a continuous transition (Obergang),
from reality to negation ; and this means that reality must be recognised
as a quantum quite apart from the quantum of time (or space) which
it fills.
XXXVIII § 3] THE ANTICIPATIONS 141
already know that the schema of quality 'contains and makes
rcpresentable* the synthesis of sensation (or sense-perception)
with the idea of time.1 This point is brought out later.2 Needless
to say, unless there were an act of synthesis involved, it would
be impossible on Kantian principles to have any a priori
knowledge in regard to sensation.
§ 3. The Proof in the Second Edition
Sense-perception is empirical consciousness, and must
contain sensation.3 Appearances, since they are objects of
sense-perception,4 are not merely pure intuitions like space
and time, which indeed can never be perceived in the strict
sense.5 The spatial and temporal form of appearances cannot
be known apart from pure intuition, but appearances themselves
contain matter as well as form, the matter for some object in
general.6 This matter is described as that through which we
represent something as existing in space and time,7 and is
said to be the real of sensation;8 it would seem to be a
1 A 145 = B 184.
2 A 175-6 = B 217-8. It is also brought out in the proof added
in B 207-8.
3 B 207. Strictly speaking, empirical consciousness of an object
need not contain actual sensation of the object, but sense-perception
must.
4 To be such objects, they must be known by thought as well as
by sense-perception.
6 That is, 'wahrgenommen', which is the verb corresponding to sense-
perception (Wahrnehmung). This point about space and time was
not brought out in the first proof; it is repeated again and again
throughout the Principles.
6 Kant says 'the matters' (Mater ten). I suppose he is referring to
the different qualities of the object. He is referring also to his view
that every individual object is thought under the concept of an object
in general.
7 The existence or actuality of a thing depends on its connexion
with the material conditions of experience, namely sensation; see
A 218 = 6266.
8 Kant here explains, though obscurely, what he means by matter
as the real of sensation. He speaks of it (i) as a subjective idea which
gives us only the consciousness that the subject is affected, and
142 THE MATHEMATICAL PRINCIPLES [XXXVIII § 3
quality given to us in sensation1 and attributed by us to an
object.
Now a continuous change is possible from empirical con-
sciousness (or sense-perception) to pure consciousness (or
pure intuition); the real (the sensed quality in time and space)
might diminish and finally disappear from our consciousness,
so that nothing would be left but a formal or a priori conscious-
ness of the pure manifold of time and space. Hence there is
possible a synthesis which is the production of a quantity (a
more or less) of sensation, beginning from pure intuition
(=•== o or complete absence of this sensation) and arriving at
any particular quantity.2
Sensation has therefore a quantity peculiar to itself, and this
(2) as related by us to an object in general. Both these things arc
necessary if we are to have the real of sensation; compare Benno
Erdmann, Beitrage zur Geschnhte und Revision des Tc\tcs von Kants
Kntik der remen Vernunft, p. 56. On this view sensation, or rather
the sensum, can be regarded in abstraction as a mere modification
of the mind ; but as related to an object and brought under the categories
it is the real of sensation, a real quality of a phenomenal object When
we see a red colour, we see it as the colour of an object in space ; this
is not due merely to sense, but to the transcendental synthesis of
imagination by which we complete the object in accordance with
the categories.
1 Qualities are given to us directly in sensation, but physical science
is able to infer other qualities not given directly in sensation ; compaie
A 226 - = B 273.
2 Kant is stating only a possibility. Time and space cannot be
perceived in themselves, but only as filled, and we do not begin
with empty space and time and then proceed to fill them. On the
other hand I think Kant does believe that when we open our eyes
and look at a red colour, we pass from complete absence of colour
through various degrees up to that particular shade of red; and
again that if we are looking at the colour on a dull day, and the sun
suddenly shines on it, we pass continuously through different degrees
from the dull to the bright colour.
It should be noted that there can be a transition from reality to
negation as well as a transition from negation to reality, but the
transition from negation to reality is the one which is described by
Kant as a synthesis. If this is a synthesis, the transition from reality
to negation looks more like omitting elements from a synthesis, but
there is still a synthesis of the elements retained.
XXXVIII § 3] THE ANTICIPATIONS 143
quantity is not extensive, since1 in sensation qud sensation2
there is no intuition of time or space, and so no parts outside
one another. It is therefore an intensive quantity, and it arises
because in apprehension empirical consciousness can3 pass
in a certain time4 from absence of the sensation to the given
amount of sensation. Since sense-perception of objects always
involves sensation (in addition to intuitions of time and space),
we must ascribe a corresponding intensive quantity to such
objects.5
We should expect Kant to mean by this that the sensed
qualities of objects — colour, sound, taste, etc., and especially
resistance and weight, if these can be said to be sensed qualities
— must have intensive quantity. I believe this is what he does
mean, but he suddenly asserts6 that this intensive quantity is a
degree of influence7 on sense. Such a statement may suggest
that Kant has at the back of his mind a doctrine of physical
matter as the cause of sensation8. But this doctrine is here
1 Kant gives as another reason that 'sensation qud sensation is not
an objective idea.' I do not see why the subjectivity of sensation
should be a ground for saying either that it involves no intuition
of space or time or that it must be an intensive quantity — unless
indeed Kant means that sensation as subjective can be nothing more
than a consciousness of being 'affected'; compare B 207.
2 B 208, 'an sick*. Here again we are dealing with sensation in
abstraction. 3 Kant again is speaking of a possibility.
4 The fact that it takes time, however brief, to pass from absence
of sensation to a given degree shows it is only by abstraction that we
separate intensive from extensive quantity. At every moment during
the period of transition we have a different degree before us.
6 'Such objects' seems to be an abbreviation for 'the qualities of
such objects', but it is a legitimate abbreviation which it would be
pedantic to avoid.
8 This may be compared with his equally sudden assertion in
B 225 that the quantum of substance in nature can neither be increased
nor diminished.
7 'Influence' (Emfluss, influ\us or actio transiens) is the technical
term for the action of one substance on another, and so indicates
a particular kind of causality. Compare Baumgarten, Metaphystca
§211 (XVII 71).
8 The same doctrine is present in the first proof, if we regard that
proof as continuing to the end of the first paragraph of B 2 1 1 . It is,
144 THE MATHEMATICAL PRINCIPLES [XXXVIII § 4
irrelevant, and on the whole it seems better to suppose that
these words arc used without any very precise or definite
significance.1
§ 4. Intensive Quantity
Let us set aside for the moment the view that our sensations
are caused by physical objects. Even so, Kant's Principle
requires working out in detail,2 and the exact bearing of his
argument is not always certain. Nevertheless we may say that
he is directing attention to an important element in experience,
and to one which has at least some appearance of being known
a priori?
Needless to say we cannot tell a priori that any particular
shade of colour must be found in nature. The most we can
say a priori is that in passing from a paler to a darker shacje,
we must pass through all the intermediate shades. If a psy-
chologist informs us that there is no such transition and that
our sensations are discontinuous, I certainly do not feel myself
however, there touched upon only in passing, because (as Kant
points out correctly in A 169 = B 210) this Principle has nothing
to do with causality.
1 If we consider the quality of the object to be directly given in
sensation, it is not unnatural to say loosely that the quality is the
cause of the sensation, and that objects have different degrees of
influence on sense.
2 Thus sound, for example, has loudncss, pitch, and timbre. Do
all of these have degrees or only the first? A similar distinction can
be made in colour, and possibly in other sensible qualities. It seems
best to suppose that Kant is here concerned only with degrees of
loudness in sound and of depth in colour; but there are other con-
tinuous gradations — such as higher and lower in pitch — the relation
of which to gradations of intensive quantity ought to be con-
sidered.
3 Curiously enough, this was partially admitted by Hume, who
asserted — contrary to the central principle of his philosophy — that
if there were a man who had never seen a particular shade of blue,
and if all other shades were put before him, 'descending gradually
from the deepest to the lightest', he would be able to have an 'idea*
of the missing shade, even although it had never been conveyed to
him by his senses. See Treatise, Book I, Part I, Section i.
XXXVIII § 4] THE ANTICIPATIONS 145
in a position to contradict him.1 Yet I find it hard to think
my belief in degrees of sensible qualities due merely to gene-
ralisation from experience. No doubt I could not have such a
belief apart from experience ; but just as I know, when I see
a line, that a shorter line is possible, so I seem to know, when
I see a shade of colour, that a paler shade is possible,2 and that
the paler shade could fill the same area and last for the same
time. And it seems as reasonable to say that there is an infinity
of possible paler shades between any given shade and zero,
as it is to say that there is an infinity of possible shorter lines
between any given line and zero. We may well hesitate nowadays
to assert that we know anything a priori^ but is there any ground
for saying that one of these statements is known a priori and
the other not ? And can we really maintain that either of these
statements rests on precisely the same basis as the statement
that forget-me-nots are blue ?
Kant believes that the Principle of the Anticipations, like
that of the Axioms, has immediate or intuitive certainty,3
and we must, I think, agree that if it has certainty at all, the
certainty must be intuitive. But for Kant such intuitive cer-
tainty implies the possibility of constructing in intuition an
object corresponding to a concept, and this at once raises
difficulties. His own doctrine is that qualities cannot be con-
structed a priori* and yet he asserts that I can determine
1 The physical stimulus can be gradually increased for some time
before we recognise any change in the sensible quality, but I doubt
whether that proves change of sensation to be discontinuous. The
sensation may vaiy continuously with the stimulus even when the
variation is not perceptible. The fact that we can watch a moving
body for some time — for example, the sun or the hands of a watch —
without recognising that there is a change of position does not prove
that motion is discontinuous; and the same principle may, I think,
hold also of change in the perceived qualities of objects.
2 This seems to be all that is necessary to justify Kant's contention,
even if he himself thought he could go further. He believes that the
continuity of all change — including change of degree — can be proved;
but the fact that he excludes such a proof from Transcendental Philo-
sophy (see A 171 = - B 2 13) suggests that continuity of change may not
be necessary to his present argument. 3 A 160-2 — B 199-201.
4 See A 714-5 =- B 742-3, and compare Log. Einl. Ill (IX 23).
i46 THE MATHEMATICAL PRINCIPLES [XXXVIII § 4
a priori, that is, construct, the degree of the sensation of sun-
light by combining some 200,000 illuminations of the moon.1
We may perhaps admit, with Hume, that we could in imagi-
nation fill up a gap in the shades of one colour ; but if we were
acquainted only with the degree of brightness produced by one
moon, we manifestly could not create in imagination the
brightness which would be produced by 200,000 moons, nor
could \\e know a priori that such a degree of brightness would
not be blinding. Such considerations are, however, irrelevant.
Kant is not concerned with the extent to which we can create
images in imagination, a question to be settled only by empirical
psychology. He is concerned, as he says, with the rules of a
mathematical synthesis.2 If we are given a foot, we know how
to construct a line 200,000 feet long, but we do not know
what such a line would look like without actual experience.3
Similarly it may be maintained, not that we could construct
a priori the actual appearance of the sun, but that we know
the principle (or schema) of such a construction.4 Kant must
mean only that we can construct the degree in abstraction,
giving it a place in the scale of degrees and so making it numer-
able— not that we can imagine every possible degree of a given
quality.5
1A 179 -•= B 221. This seems to imply that, given a particular
quality, I can construct its different degrees a priori.
2 A 178 ~- B 221 ; compare the difference between the mathematical
and the aesthetic estimate of quantity in K.d.U. § 26 (V 251 ff.).
3 Compare A 140 — - B 179.
4 This is supported by Kant's assertion in A 175-6 B 217 that
the real means merely the synthesis in an empirical consciousness in
general; and again in A 723 — B 751 that we can have a priori only
indeterminate concepts of the synthesis of possible sensations (so far
as they belong to the unity of apperception). Compare A 143 = B 183
where the schema of reality, as the quantity of something so far as
it fills time, is the continuous and uniform production of reality in
time; and see also A 720 = B 748.
6 Compare again Kant's statement mAi6i— B2Oi that in the
a priori determination of appearances we are concerned only with
the form of a quality (or a quantity). In A 176 — B 218 he says that
about the qualities of appearances we know a priori only that they
have a degree — all else is left to experience.
XXXVIII § 5] THE ANTICIPATIONS 147
A fuller account of the intuitive certainty claimed for the
proof of this Principle, and also a more elaborate treatment
of the details, would have been welcome. In particular we
require to know a great deal more about the relation between
the concrete constructions of imagination and the abstract
constructions of mathematics.1 Nevertheless if we know that
there is possible a continuous transition from any given degree
of intensity to zero (just as there is possible a continuous
transition from any given line or area or volume to zero), we
know that there is a possibility of measuring such a degree
(just as there is a possibility of measuring a line or area or
volume), and that such measurements can be expressed in
numbers. It is this point alone — the applicability of mathematics
to appearances — which Kant is attempting to establish.2 He
has not adequately brought out the differences of the two
cases,3 but, so far as I can see, his doctrine is sound.4
§ 5. The Synthesis of Quality
It may be thought that Kant has no right to use the word
'synthesis' for our apprehension of degree, and that he has
failed to connect this kind of synthesis with the nature of
time and space.
The first objection seems to me one of terminology, and if
synthesis means the holding together of a plurality in unity,
there certainly is a synthesis of degrees as well as of extensions ;
every degree is a plurality in unity, since although it is an
indivisible whole, it contains all the lesser degrees between it
and zero.
1 We coulcl not know how to construct a line 200,000 feet long
unless we could actually construct short lines in imagination, and the
same principle must, I think, hold in regard to degree.
2 See A 178 = B22i.
3 One of the most important differences is that in measuring a
degree of intensity, for example of heat or weight, we translate it
into terms of extensive quantity; we use a thermometer in the one
case and a pair of scales in the other.
4 For a defence of this doctrine see Cassirer, Kants Lcbcn und
Lehre, pp. 191-4.
i48 THE MATHEMATICAL PRINCIPLES [XXXVIII § 5
The second objection is more weighty. We can say at the
most that time and space must be filled with the real which is
given to sense, if we are to be aware of real objects, or even
to be aware of an actual determinate part of space or time.1
We can hardly assert a priori that this reality must have degrees
if it is to fill space and time.2
The transcendental synthesis of imagination by which we
construct our phenomenal world in space and time is not
merely a synthesis of empty times and spaces, but a filling of
time and space with what is given to us in sensation, or a
synthesis of sensation with time and space. The actual intensity
of the object's qualities, like its actual size or duration, is known
to us through experience alone.3 Nevertheless since experience
always involves a transcendental synthesis, every object must
have both extensive and intensive quantity of some sort, and
our knowledge that it must do so is no generalisation from
experience, liable at any moment to be contradicted, but is
rather a synthetic a priori judgement affirming the necessary con-
ditions apart from which human experience would be impos-
sible. Such is the Kantian doctrine, and I do not think it can be
dismissed as obviously untenable.
As regards the connexion between degree and the categories
of reality, negation and limitation,4 I have already offered
such defence as is possible — see Chapter XXXIII § 3. There
are, however, one or two further points to be noticed. Reality
1 This is why Kant can speak of the schema of quality as a time-
determmation We determine actual spaces and times only through
the synthesis of sensation (or reality) in time Nevertheless the
character of this synthesis (as imposing degrees upon reality) seems
to be proved independently of the nature of time (or space).
2 The theory of atoms and the void (which Kant never claims to
disprove on a priori grounds) seems to offer an alternative view —
unless we hold that, inasmuch as it presupposes that parts of space
are empty, it is not a theory of how space is filled.
3 Compare A 176 =-- B 218. Like the actual size or duration of
objects, it depends on the thing-m-itself. The character of our minds
determines only that the thmg-m-itself must appear to us to have
some size and duration and to have qualities of some degree.
4 It is noteworthy that the proof of the Anticipations is directed
primarily to the schema, not to the schematised category.
XXXVIII § 5] THE ANTICIPATIONS 149
(when schematised) is the given quality which fills time (and
space), while negation is the empty time (and space) which is
filled. For a determinate object we require the combination
of the two. I think Kant holds that the object both fills and
does not fill time (and space), so far as its qualities have a degree
and have not a greater degree ; so that there are different degrees
in wrhich we combine reality and negation (or quality and time)
in order to have a determinate object under the category of
limitation.
The full meaning of his doctrine is, however, apparent
only when we understand his dynamical theory of matter. He
believes that there is a real opposition of moving forces which
is, as it were, logical opposition translated into terms of time
and space, just as the relation of cause and effect is the logical
relation of ground and consequent translated into these terms.
What fills space is matter, which Kant identifies with the
movable;1 and matter fills space through a combination of
the moving forces of repulsion and attraction.2 It is the real
opposition of these opposing forces which explains how space
can be filled, and yet filled in different degrees. This is an
empirical illustration — it is, of course, not a deduction possible
in pure philosophy — of Kant's principle that a real object
must be thought under the category of limitation, which involves
a combination of reality and negation.3
1 'das Beweghche.'
2 For this reason Kant attaches special importance to the quality
which he calls resistance or impenetrability, and also to the quality
which he calls weight. The former reveals the power of repulsion
in bodies, while the latter reveals the power of attraction. It is primarily
through the resistance of bodies (both to our own body and to other
bodies) that we became aware of what is assumed by common sense
to be solidity.
3 The whole doctrine can be understood only by an examination
of Kant's Metaphysische Anfangsgrunde der Naturwissenschaft, but a
sort of summary is to be found in the chapter on Dynamics — the
'general appendix* (IV 523 ff.). There the real in space (commonly
called the solid) fills space through the force of icpulsion; the force
of attraction is negative in relation to the real (the proper object of
outer sense), for it penetrates space and thereby cancels or negates
the solid (or the impenetrable); the limitation of the first force by
i5o THE MATHEMATICAL PRINCIPLES [XXXVIII § 6
§ 6. The Causality of the Object
When Kant maintains that because our sensations must
have a degree, the qualities of objects must have a degree, he
is to some extent anticipating his doctrine of substance and
accident ; but this is at least partly justified by his analysis of
the concept of an object, when he argued that our ideas (includ-
ing sensa) refer to an object, or are appearances of an object,
inasmuch as they are synthetised or united in accordance with
the necessary unity of apperception. To say that our sensa
reveal the qualities or accidents of substances is only an elabora-
tion of this doctrine and a translation of it into terms of time ;
and Kant is perhaps entitled in his present argument to keep
the doctrine of the First Analogy in the background.1
On the other hand the doctrine that physical substances
are the causes of our sensations is as irrelevant to the Antici-
pations as is the doctrine that physical substances are the
causes of changes in each other.2 We completely misunderstand
Kant, if we imagine him to be arguing that we first of all have
a sensation, and then infer that the sensation must be caused
by some quality in an object.3 He is not maintaining that the
cause of that which has degree (namely, sensation) must itself
also have degree.4 He is maintaining that the qualities of objects
the second determines the degree in which space is filled. Kant
believes that either of these forces by itself would result in the emptying
of space. The modern theories in regard to positive and negative
electricity would be equally welcome to him as an illustration.
1 This shows again how all the Principles are bound up together
and must not be considered in isolation, although they have to be
expounded in succession.
2 A 169 = B 210. The first kind of causality is called by Professor
Price Vertical causality* and the second 'horizontal causality', see
Perception, p. 86.
3 Here as always any attempt to interpret Kant as trying to explain
the temporal development of experience results in error.
4 The statement about 'the degree of influence on sense* in B 208
ought not to be interpreted in this sense. Kant does maintain — see
A 168 — 62-10 — that reality in time and space may be regarded as a
cause, and says that the degree of reality as a cause is called a 'moment'
as being apprehended, not successively, but instantaneously, for
example, in the 'moment 'of gravity. To say this is not to say that
XXXVIII §6] THE ANTICIPATIONS 151
as given or revealed to us in sensation must have degree.
Whether scientific thought is able to infer other qualities
which are not revealed directly in sensation we need not here
discuss.1
Nevertheless Kant does believe that human sensations
are caused by a physical stimulus,2 although in his view this
cannot be known a priori: we know a priori only that every
event must have a cause. The cause of any particular event
can be discovered by experience alone ; and it is by experience
alone that we discover certain physical stimuli to be the causes
of our sensations.
The exact method of this discovery it is not Kant's business
to explain, nor does he attempt to do so ; but granted that we
possess the concept of causality and are aware of a world of
physical objects, the fact that when we fall we invariably hurt
ourselves, and when we approach the fire we invariably feel
warm, is itself enough to suggest a causal connexion between
physical bodies and inner states. There is no reason why Kant
should not accept any empirical account (such as is offered
by physiology or by psychology) that explains the nature of
the stimuli causing our sensations or the method of determining
the character of these stimuli.3
the extensive quantity of an object is irrelevant to causation, or even
to the causation of degrees of sensation. One brilliantly illuminated
surface may cause the same degree of sensation as many less bnlliantly
illuminated surfaces of the same extent; see A 176 = B 217 and
compare A 179 •= B 221. In this illustration we are of course not
supposed to be looking at the direct source of the light, but, for
example, at a wall illuminated alternately by one lamp or six candles.
1 Compare his view that there is a magnetic matter pervading all
bodies, and that this could be perceived, if our senses were finer
(A 226 - B 273).
2 Compare, for example, A 213 = B 260. The ultimate cause or
ground is the thmg-m-itself ; see Chapter II §§ 2-3.
J A valuable discussion of this problem is to be found in Price,
Perception, Chapter X. We must not imagine that accounts of the
kind indicated explain how we come to know physical bodies: they
presuppose that we already have this knowledge.
1 52 THE MATHEMATICAL PRINCIPLES [XXXVIII § 7
§ 7. The Doctnne of Continuity
The rest of Kant's exposition1 elaborates the details, and
indicates the applications, of his general theory. It offers little
difficulty in the way of interpretation.
Quantities are said to be continuous, if no part of them is the
smallest possible part, that is, if no part is simple.2 However
small the quantity may be, there is always a smaller quantity
between it and zero. Kant believes he has shown that intensive
quantity is characterised by such continuity, because there is a
continuous gradation between any given intensive quantity
(or degree) and zero. He now maintains that since no part of
time or space is the smallest possible part, space and time are
continuous (extensive) quantities. It follows that points and
moments are not parts of space and time, but only limits or
boundaries. Every part of space is itself a space, and every part
of time is itself a time, so that space and time are made up of
spaces and times, not of points or instants.3 We cannot say,
for example, that any two points on a line are next to one
another; either they are the same point, or else there is a line
between them in which an intermediate point can be taken.
Continuous quantities as so described, whether extensive
or intensive, are the product of a continuous and uninterrupted
synthesis, for which reason they can be called 'flowing'.4
When the synthesis is interrupted, that is, stopped and then
repeated, what is produced is an aggregate. Thus if 'thirteen
dollars' means a particular measure (a mark) of fine silver, it
constitutes a continuous quantity, or quantum5, for no part of
it is the smallest possible.6 If it means thirteen silver coins,
it is an aggregate, or a number, of coins ; for it is composed of
so many discrete units, each of which is the smallest possible
part of the sum of thirteen dollars.7
1 A 169-176 -= B 211-218. 2 A 169 - Ban.
3 I believe that even this doctrine, like so much else, is questioned
by modern mathematics. * A 170 = B 211-12, 'Jhessend.'
5 Kant seems to imply here — as also in A 171 -= B 212 — that a
quantum is necessarily a continuous quantity, but in A 526-7 --B 554-5
he speaks of quanta continua and quanta discreta.
6 Kant believes that matter, like space, must be infinitely divisible.
7 Kant adds that each unit is a quantum, since unity is at the basis
XXXVIII §7] THE ANTICIPATIONS 153
Kant maintains that all appearances or objects are necessarily
continuous quantities, both as regards their extensive quantity
(determined by the synthesis of the space or time which they
occupy), and also as regards their intensive quantity (the degree
of the qualities determined, directly or indirectly, by the synthe-
sis of sensation).1 He maintains also — what is a much more
difficult proposition — that it is easy to prove, with mathematical
evidence, the necessary continuity of all change (all transition
of a thing from one state to another).2 Such a proof he does not
here offer — on the ground that it presupposes empirical prin-
ciples, and so lies outside the limits of Transcendental Philo-
sophy, and belongs to what he calls 'the universal science of
nature'.3 Nevertheless in the Second Analogy he does set forth
what professes to be such a proof.4
of every number. He means, I presume, that in counting objects we
ignore their internal differences, and treat them as homogeneous or
continuous. The identification of number with an aggregate seems to
treat number as discrete, and looks like treating numbers as if they
were only integers.
1 A 170 -— B 212 ; A 171 = B 212. 2 A 171 = B 212-3.
3 A 171 -- 6213. The science referred to, since it is opposed to
Transcendental Philosophy, is presumably Rational Physiology (physio-
logiaratwnahs),sofaras that is immanent and not transcendent. Both
sciences are part of speculative metaphysics; but Transcendental
Philosophy (which covers the Kntik of Pure Reason) deals only with
concepts and principles which apply to objects in general, while
Rational Physiology deals with nature, and since nature is divided into
corporeal and spiritual nature, the science is divided into Rational
Physics and Rational Psychology (physica rationahs and psychologia
rationally). Rational Physics is so much more important than Rational
Psychology that it is at times regarded as the only metaphysical science
of nature — although Kant believes that there is an immanent Rational
Psychology as well as the transcendent Rational Psychology repudiated
in the Paralogisms. Rational Physics is said to realise, that is, to give
'sense and significance' to Transcendental Philosophy. Sec A 845-6
= B 873-4; B 17-18; B 20 n. ; and compare M.A.dN. Vor. (IV 467)
and the final remark to the third mam part which deals with mech-
anics (IV 552-3).
The difficulty of all this is that Rational Physics and Rational Psy-
chology are particular, and not universal, sciences, and the discussion
of change in general cannot be confined to either. For this reason Kant
refuses it a place in his discussion of Rational Physics; see M.A.d.N.
(IV 553). * A 206 = B 252 fT. See also Metaphysik, pp. 54 ff.
154 THE MATHEMATICAL PRINCIPLES [XXXVIII § 8
§ 8. Empty Space and Time
If it be granted that there is an infinity of degrees alike in
our sensa and in the qualities of objects which our sensa reveal,
sense-perception, and consequently experience (which is know-
ledge through combined sense-perceptions1), can offer no
proof of empty space or time. We cannot perceive empty
space or empty time, since sense-perception always involves
sensation; and Kant believes we cannot infer empty space or
time either from the objects we perceive or from the fact that
the qualities of perceived objects have different degrees — he
even goes so far as to say that we ought not to assume empty
space or time for the purpose of explaining phenomena. By this
he means only that wre ought not to assume empty space and
time to be necessary for the purpose of explaining phenomena.
We find by experience that when two bodies have the same
volume, one may be, for example, heavier than the other.
We argue from this that one contains more matter than the
other, and we are tempted to assume that the lighter body must
therefore contain more empty space. This was the doctrine of
the atomists, who maintained that everything was composed of
atoms and the void. Such a doctrine was supposed to rest
upon experience, but it really rests on an unexamined meta-
physical assumption — the assumption that what fills space
can differ only in extensive quantity, so that if a body is lighter,
it must contain fewer atoms, and therefore more empty space.
Once we admit that the same reality can fill space in greater
or less degree, a smaller degree of reality may completely fill
the same volume as is filled by a greater degree. Hence the
inference which argued to empty space from differences in
the qualities of bodies of the same volume was illegitimate.
Kant's contention is, as he says, to be taken only as an illus-
tration of his more general doctrine that the real which fills
determinate times and spaces differs, not only in extension, but
in degree. When we discuss the nature of weight or resistance
or heat, we are passing beyond pure philosophy, and dealing
1 B 161. Compare B 219.
XXXVIII § 9] THE ANTICIPATIONS 155
with problems which must be settled by experience. The theory
of the atomists was a mechanical theory of matter, which
Leibniz and Kant opposed with a dynamical theory. Kant is not
arguing that pure philosophy can decide between these two
theories, but only that the dynamical theory ought not to be
excluded on the basis of what is really a metaphysical assumption.
In this he is undoubtedly right.
§ 9. Kant's Conclusion
As usual, Kant finishes with a short summary of his argument.
He stresses once more the surprising fact that we can anticipate
sensation, which is the empirical element of sense-perception,
although we can do so only in regard to its degree. He points
out — what with his usual carelessness he failed to make explicit
in the argument of the first edition — that degree involves a
synthesis of the given, a synthesis which we can consider in
abstraction from the synthesis of extensive quantity and regard
as complete in every moment.1 Finally he remarks about
quantities in general that we know a priori only one quality
which they must possess, namely continuity;2 about quality
we know a prioj i only that it must have intensive quantity or a
degree.
1 This is consistent with the view that we pass gradually in time
from a lesser degree to a greater or vice versa , see B 208. All the lesser
degrees previously experienced are held together, or synthetised, at
any moment in an indivisible unity.
2 I do not see how Kant reconciles this with his recognition of
aggregates, which are discrete quantities, although the units of which
they are composed arc continuous quantities; see A 170-1 — B 212.
BOOK X
THE ANALOGIES OF EXPERIENCE
CHAPTER XXXIX
THE PRINCIPLE OF THE ANALOGIES
§ i . The Formulation of the Principle
Just as there is one Principle of the Axioms and one Principle
of the Anticipations, so there is one Principle of the Analogies ;
but because the synthesis described in the Principle of the
Analogies is more complicated than the synthesis described
in the other two Principles, Kant finds it necessary first to
state the general l Principle of the Analogies, and then to deal
in detail with the three separate rules or laws or Principles
in which the general Principle is manifested. It must not
be forgotten that in this case, as in the others, there is only
one synthesis (or one aspect of the universal synthesis), and
that this one synthesis involves three categories.2
In the second edition the Principle is formulated as follows :
Experience is possible only through the representation3 of a
necessary connexion of sense-perceptions*
This necessary connexion,5 or nexus, is imposed upon the
given manifold by the transcendental synthesis of imagination,
and is a connexion of correlated, but heterogeneous, elements;
the relations involved are those of substance and accident,
of cause and effect, and of reciprocal causality (or interaction)
between substances.6 The Analogies are therefore concerned
1 'allgememe'; see A 176 and A 177 --- B 220.
2 Compare Chapter XXXIII § 7.
3 * Vorstellung. ' This means the 'representing' or 'conceiving* or
'thinking*.
4 B 218. 'Sense-perceptions' (Wahrnehmungen) are here equivalent
to 'appearances' (Erschemungcn). Compare B 160.
5 ' Verknupfung.' This is identified with nexus in B 201 n. It is a
special case of combination (Vcrbmdung), combination of the manifold
as regards its time-relations. The necessity of 'connexion' should not
be confused with the general necessity of 'combination' proved in the
Transcendental Deduction. Compare Baujngarten, Metaphysica § 14
(XII 27).
6 The first two are the examples given by Kant in B 201 n. The
relation of interaction (reciprocal causality or influence) combines
both. Compare Bin.
160 THE ANALOGIES OF EXPERIENCE [XXXIX § i
with relations of heterogeneous elements which necessarily
belong to one another, while the Axioms and Anticipations
were concerned with homogeneous elements which do not
necessarily belong to one another.1
The Principles of the Understanding are proved by showing
that they express the conditions of experience, through which
alone experience is possible.2 The general Principle of the
Analogies as formulated in the second edition professes to
state such a condition, but it omits to state — perhaps in the
interests of brevity — that the 'necessary connexion' which
is the condition of experience is a necessary connexion in time,
and is concerned with the existence3 of appearances in time.
This point is emphasised in the formula of the first edition,
which is as follows: All appearances are subject, as regards
their existence, to a priori rules in accordance with which their
relation to one another in time is determined.1
The main point of these formulae is a simple one. Kant
believes that every object of experience must have a definite
or determinate position in a common objective time;5 and that
it can have such a definite position only if it is subject to the
rules of necessary connexion in time laid down in the three
1 Sec B 20 1 n. Two extensive quantities or two degrees are homo-
geneous, and we cannot say that where one is, the other must be.
Accident is not homogeneous with substance nor effect with cause,
and we can say that where one is, the other must be.
2 Compare Chapter XXXV §§ 5-6 Necessary * connexion* is a
special element in, or condition of, that synthetic unity of appearances
through which alone experience is possible; see especially A 156
= B 195 and A 158 — B 197.
3 'Dasein.' See A 178 = 6221; also A 179 — 6221-2, A 160 ^= 6199
and B 201-2 n. To exist is 'to be there', to have a definite position in
time or in time and space.
4 A 176-7 Kant says 'a priori rules of the determination of their
relation to one another in one time*. These 'rules' are the Analogies.
6 The theory of Relativity demands a rcmterpretation of the word
'definite'; for the time of an event may be measured differently by
different observers. Nevertheless if the measurements can all be
translated into terms of one another, and if, knowing one measure-
ment, we can say a priori what the others must be, we are, I think,
still entitled to say that every event has a definite position in a common
time (or a common space-time).
XXXIX §2] THE PRINCIPLE OF THE ANALOGIES 161
Analogies. As usual, his formula ignores space, although his
main concern in the Analogies is with physical objects. The
combination of a theoretical insistence on time (at the expense
of space) and a practical concern with objects in space (to the
neglect of mental events in time) is a source of difficulty in his
argument.
§ 2. The Argument in the First Edition
The argument of the first edition is obscurely expressed.
There is, first of all, a short introduction l explaining why
there must be three rules to determine all the relations of
appearances in time. These rules are the three Analogies ; and
the general principle of the Analogies, like that of all other
Principles, rests on the necessary unity of apperception in one
of its different manifestations or aspects. It rests on the fact
that the unity of apperception, in respect of all possible em-
pirical consciousness or sense-perception, is necessary at every
time.2 Hence it rests on the necessary synthetic unity of all
appearances as regards their relation in time? Unless all appear-
ances (or objects) were related in one common objective time,
the unity of apperception, and so experience, would be im-
possible.
If we grant its presuppositions — that the unity of appercep-
tion is the condition of the thought necessary for experience,
and time is the condition of the intuitions necessary for experi-
1 A 177 -- B 219. This is dealt with at the end of the present
subsection.
2 A 177 - B 220. The unity of apperception is not limited to a
particular time, but applies to all times. Compare Chapter XXI § 5.
3 The main difficulty of this inference is the reason obscurely added
by Kant: 'because the unity of apperception is the a priori condition
of all possible empirical consciousness* (da jene a priori zum Grunde
liegt). What rests on something as a condition need not rest on what
that something conditions. The unity of apperception and the unity
of appearances, however, may be said to condition one another
mutually , and indeed Kant often speaks as if they were the same thing;
compare, for example, B 134 and A 108. If 'jcne' could refer forward
to the synthetic unity of appearances, the argument would be easier,
but I doubt whether this is possible.
VOL. II F
i62 THE ANALOGIES OF EXPERIENCE [XXXIX §2
ence — there seems to be little difficulty in this contention;
but Kant supports it by a brief defence. Original apperception
is related to inner sense (the totality of all ideas), and indeed
is related a priori to its form. We should expect this form
to be time, but Kant describes it as 'the relation of the manifold
empirical consciousness in time9. Time as the form of inner
sense is made up of relations1 and seems to be identified here
with the temporal relations of our ideas, though usually it is
regarded as the condition of these relations.2 In any case the
fact that original apperception is related to time, as the form
of inner sense, implies that all our ideas must be united,
as regards their time-relations, in original apperception.3 I think
we may add that Kant means 'as regards their objective time-
relations' ; for he makes his contention depend on the fact that
everything must be subject to the transcendental unity of
apperception, if it is to belong to my knowledge and to be an
object for me.4
There must, then, be synthetic unity in the time-relations
of all appearances or sense-perceptions,5 a synthetic unity
which is determined a priori and is a necessary condition
of experience. This synthetic unity is expressed in6 the law
1 Compare B 67, where time is said to 'contain* the relations of
succession and simultaneity and (curiously enough) of the permanent,
and to 'contain* nothing but relations.
2 See A 30 = B 46. It should, however, be remembered that Kant
has considered (in the Axioms and Anticipations) the time-series and
the time-content ; and he is now expressly concerned only with time-
order or time-relations; see A 145 --= B 184.
3 Compare A 99, B 150-1, B 152, and B 160-1, all of which prepare
us for the present argument. Compare also A 142 — B 181.
4 This is the general argument of the Transcendental Deduction
applied to the special case of temporal relations; compare B 139-40.
Such difficulties as it has are the difficulties of the general argument.
6 'Synthetic unity in the time-relations of appearances' is for Kant
the same thing as 'synthetic unity of appearances as regards their
time-relations'. The simplest statement is that appearances must be
related to one another in one common objective time.
6 Kant says it is the law. This law is more general and ultimate
than the a priori rules which are its embodiments — namely the
Analogies.
XXXIX § 3] THE PRINCIPLE OF THE ANALOGIES 163
that all empirical time-determinations must stand under the
a priori rules of time-determination in general, these rules
being the three Analogies.1
The reason why there are three Analogies is stated in the
introduction.2 There are only three modes of time — perman-
ence, succession, and simultaneity. Hence we require three
rules for all the time-relations of appearances ; and in accord-
ance with them we can determine the existence of every appear-
ance in regard to the unity of all time.3 These rules are prior
to experience and state the necessary conditions under which
alone experience is possible.
The three modes of time, it should be noted, appear to be
identical with the three transcendental schemata of the cate-
gories of relation :4 they arc a priori time-determinations which
concern the time-order, that is, the order of appearances
in time.5
§3. The Modes of Time
The word 'mode' as used in modern philosophy has no very
precise meaning and is frequently a source of confusion.
In the time of Kant a mode of anything was sharply distin-
guished from its essence, its attributes, and its relations. The
essence consists of certain primitive and constitutive marks
called strictly essentialia. The attributes are not part of the
essence, but they have their sufficient ground in the essence
1 A 177-8 = B 220; compare A 217 - B 264. Compare also the
formula of the first edition in A 176-7; this is the formula \\hich he
here professes to prove. If we are to determine the time at \\hieh
any particular appearance exists, we must do so in conformity with
those a priori rules apart from which, according to Kant, there could
be no unity in time or in temporal relations. 2 A 177 — B 219.
3 I should prefer to say 'in one common objective time'. Kant seems
on the whole to avoid such a usage, perhaps because it suggests that
time is a thing in itself and is something complete and whole.
4 See A 143-4 -~- B 183-4 and also Chapter XXXIII §7. Kemp
Smith translates 'Bcharrluhkeit* as 'permanence' in A 143 = B 183
and as 'duration' in A 177 ~ 6219. This fails to bring out the identifi-
cation of the mode of time and the schema.
5 See A 145 - B 184-5.
164 THE ANALOGIES OF EXPERIENCE [XXXIX §3
and are derivative from it. The modes are inner determinations
which have not their sufficient ground in the essence and are
not derivative from it.1 Relations, which are regarded as
external, have likewise no sufficient ground in the essence and
are not derivative from it. Thus a man may be rational (an
essential) without being either learned (a mode) or a master
(a relation).2
According to this usage a mode is clearly a characteristic
or determination of that of which it is the mode. There is an
older usage in which a mode is not such a characteristic or
determination, but is dependent on that of which it is the
mode.3 Thus Descartes speaks of rest and motion as modes
of space.
We have already seen4 that Kant, when he speaks of the
transcendental schemata as time-determinations, does not mean
that they are determinations or characteristics of time itself,5
but rather that they are determinations or characteristics
which must belong to objects so far as these are temporal and
are combined in one time. The same considerations must
apply when he speaks of permanence, succession, and simul-
taneity as modes of time. He could not possibly mean by this
that it is of the essence of time to be permanent, successive,
and simultaneous; and equally he could not mean that time
may be, but need not be, permanent, successive, and simul-
taneous. He must mean on the contrary that only in time can
J Hence the German for 'mode' is 'zufalhge Bcschaffenhcit* (a con-
tingent characteristic). A mode is 'contingent', because we tan have the
essence without the mode, although we cannot have the mode without
the essence.
2 Compare also Chapter III § 6.
3 Compare Spinoza's definition of a mode: Per modum intclltgo
substantiae affectiones, sivc id, quod in alio est, per quod etiam conctpitur.
Time is not a substance, but the temporal characteristics of every
object are dependent on time: they can be, or be conceived, only
through that of which they are the modes, namely, time, and yet
they are not characteristics of time itself.
4 See Chapter XXXI I §6.
5 The definitions of the transcendental schemata are in any case
sufficient proof of this contention.
XXXIX § 3] THE PRINCIPLE OF THE ANALOGIES 165
appearances be conceived as permanent, successive, and
simultaneous.1
Thus he can say that change (or succession) does not affect
time itself,2 but only appearances in time;3 and even that
simultaneity is not a mode of time itself,4 because the parts
of time are not simultaneous but successive.5 At the very
moment when succession and simultaneity are said to be
modes of time, they are also said to be ways in which the
permanent exists.6
It is confusing to be told both that certain characteristics
are modes of time, and that they are not modes of time itself.
Kant ought to have explained clearly what he meant by 'a
mode of time' and 'a mode of time itself; but I can see no
real inconsistency in his thought and no very great difficulty in
understanding what he means.7
From the first mention of modes of time8 Kant seems
to regard them as equivalent to 'time-relations of appear-
1 This usage approximates to the usage of Descartes. Compare
A 30 — B 46 where the idea of time is spoken of as the condition of
simultaneity and succession.
2 Time itself (Zeit selbst, Zeitfur suh, Zcit an sich selbst) is habitually
treated as equivalent to absolute or empty time, particularly in the
statement that it cannot be perceived. Compare B 207, A 172 = B 2 14,
6219, 6225, A 183 =- B226, A 188 = 11231, 6233, A 192 -= 6237,
A 200 == B 245, B 257, A 215 = B 262. 3 A 183 B 226.
4 Kant is either using 'mode* here loosely for a 'characteristic', or
else he means (what would be more consistent) that the modes of time
are not modes of empty or absolute time, but of time as filled.
5 A 183 - B 226. Kant, it should be observed, immediately adds to
this that there can be no succession in time itself, so we must not take
this to mean that succession is a mode of time itself. Nevertheless
succession has a particularly close connexion with time, since the parts
of time are themselves successive.
6 A 182 = B 226. This is apparently equivalent to being modes of
the existence of the permanent (A 183 - B 227).
7 Adickes (followed by Kemp Smith) finds here a flat contradiction
to be explained only on the view that Kant tacked together notes
written at different times without observing their inconsistency.
8 It should, ho\\ever, be noted thatm A 81 = B 107 quando, ubt, situs,
and also pnus and simul, are said to be modes of pure sensibility, by
which Kant means modes of time and space. Here again he seems to
use 'mode* in a sense approximating to that of Descartes.
1 66 THE ANALOGIES OF EXPERIENCE [XXXIX § 3
ances'.1 He says expressly of succession and simultaneity, just
after mentioning them as modes of time, that they are the
only relations in time.2 Later on he again equates the three
modes of time with time-relations: (i) the relation to time
itself as a quantity (the quantity of existence, i.e. duration)?
(2) the relation in time as a series (succession); and (3) the
relation in time as a sum or totality4 of existence (simul-
taneity)^ These statements show that the modes of time are
not modes of time itself.
From all this we may, I think, conclude that when Kant
affirms permanence, succession, and simultaneity to be modes
of time, he does not mean that time itself, speaking strictly,
is permanent or successive or simultaneous — and this he
expresses by saying that permanence, succession, and simul-
taneity are not modes of time itself. He does mean that
the permanence, succession, and simultaneity of objects
is possible only in time, and is inconceivable apart from time.
Permanence, succession, and simultaneity are the three funda-
mental temporal relations which, Kant believes, must be found
in all objects (so far as they are objects in time).
Permanence is not quite on the same footing as succession
and simultaneity, since succession and simultaneity may be
described as modes of the existence of the permanent or ways
in which the permanent exists.6 But this doctrine must be
1 A 177 -- B 219.
2 A 182 - 6226. Compare also A 179 = 6222 where 'time-relation*
and 'mode of time' appear to be equated.
3 Duration seems here equivalent to permanence. 4 'InbegnffS
6A2i5 -= 1*262. This passage explains why Kant says that succes-
sion and simultaneity are the only relations in time, since permanence is
a relation to time. The words in the last two brackets are 'nacheinander*
and 'auglcuh', which I have translated as 'succession' and 'simultaneity*
respectively. Kemp Smith eliminates the brackets.
6 A 183 - B 227; A 182 =--- B 226. Again, as we have seen above,
permanence is described as a relation to time, rather than a relation
in time. If this were taken strictly, permanence would be a relation
and not a mode; but obviously permanence is not merely a relation
between time and something non-temporal, for the permanent must
endure in, or through, time. Further, the category of substance is said
to stand under the head of relation, more as a condition of relation
XXXIX §4] THE PRINCIPLE OF THE ANALOGIES 167
reserved till we consider Kant's account of substance. Here
we are concerned only with the general character of Kant's
argument in the three Analogies. What he proposes to maintain
is roughly this — that since all objects of experience must exist
in time, they must be characterised by permanence, succession,
and simultaneity; and that these temporal characteristics
of objects, if they are objective characteristics, must be neces-
sary, or must be determined in accordance with an a priori
rule. Whether we accept or reject his view, we must at least
recognise that he is attempting to apply the general principle
of the Transcendental Deduction: that what distinguishes
ah object from a succession of subjective appearances is just
the necessary combination of these appearances imposed by
the nature of our thought and by the transcendental synthesis
of imagination working through the medium of time. The
application of that general principle in the Analogies is by far
the most important part of his doctrine; and although Kant
regards his argument as strengthened and enriched by the
connexion between the categories of relation and the categorical,
hypothetical, and disjunctive forms of judgement, the argu-
ment itself rests upon the three modes of time and the general
principle that objectivity involves necessary combination,1 or
necessary synthetic unity, in accordance with the transcen-
dental unity of apperception.
§ 4. The Argument in the Second Edition
In the first edition Kant, as we have seen, lays most stress
on the unity of apperception, although he makes it clear
enough that the necessary synthetic unity of the time-relations
of appearances, in accordance with the unity of apperception,
is the condition of all objects of experience.2 In the proof added
in the second edition he concentrates his attention on the
than as itself containing a relation (A 187 — B 230). Even apart from
these statements, it is in itself obvious that permanence differs from
succession and simultaneity.
1 Necessary 'connexion* is, as I have said, a special case of such
necessary * combination'. 2 A 177 = B 220.
168 THE ANALOGIES OF EXPERIENCE [XXXIX § 4
necessary synthetic unity which is the condition of objects, and
leaves it to us to remember that all synthetic unity is grounded
on the unity of apperception.1 Furthermore he treats the
argument generally, without repeating the details about the
different modes of time.
Experience is empirical knowledge: it determines an object
through empirical sense-perceptions. Since, however, it deter-
mines an object, there must be more in experience than em-
pirical sense-perception ; there must be a synthesis of sense-
perceptions. As we know from the Transcendental Deduction,
what is essential to experience as knowledge of objects (and not
mere intuition or sensation) is the synthetic unity of the given
manifold in one consciousness.2 This synthetic unity is the
necessary synthetic unity which is grounded on the unity
of apperception and is the condition of there being an object.
Synthesis, Kant insists, is not to be found in sense-percep-
tions, and still less can wre find in sense-perceptions necessary
synthetic unity. This is the general principle in which Kant
agrees with Hume; but here he is thinking primarily (if not
exclusively) of the necessary synthetic unity which is to be
found in the connexion, or nexus, of heterogeneous elements
which necessarily belong to one another, as for example cause
and effect. Sense-perceptions, considered in themselves, come
to us in an order in which we can descry no necessity. Appre-
hension— here as always closely connected, if not identified,
with sense-perception — is a mere taking up and putting
together the given manifold; it contains in itself no idea that
the given appearances are necessarily connected in space
and time.3
1 B 218-19. It would be absurd to regard this change of emphasis as
an inconsistency. In the changes added in the second edition Kant
generally lays more stress upon the object, I presume because the
unity of apperception was liable to be misunderstood as merely
subjective. Compare B 139-40 and B 142.
2 This is a clear reference to the unity of apperception.
3 Apprehension — if we may judge by Kant's general view of it —
involves more than a taking up and holding together of appearances
in the order in which they are given. It arranges the given appearances
XXXIX §4] THE PRINCIPLE OF THE ANALOGIES 169
So far Kant is merely summing up the doctrine of the
Transcendental Deduction. He now proceeds to develop his
theory in two sentences, the first of which exhibits that curious
compression and complexity usually to be found at the crux
of his arguments.
First of all he applies his general principle to what he calls
'relation in the existence of the manifold'. By existence1 he
means being in time, and for simplicity's sake we may say
that 'relations in existence' are the relations of succession and
simultaneity.2 An object exists either before or after or along
with another. Since experience is experience of objects, experi-
ence of the temporal relations of objects is an experience
of objective temporal relations. In experience we know the
objective order of objects or events , not merely the order in
which we come to know these objects or events, or the order
in which we can arrange them by the exercise of uncontrolled
imagination.3
in space and time, so that we can apprehend, not merely a succession
of given appearances, but an empirical object such as a house. What
apprehension cannot give us is the necessity of these arrangements or
combinations, and apart from necessity there is, according to Kant,
no difference between an objective, and a merely subjective or
imaginary, combination. Furthermore this necessary connexion (which
is the mark of objectivity or existence in space and time) is not merely
necessary connexion within the object apprehended, but necessary
connexion with other objects to which it is related in space and time.
1 'Dasem' or 'there-being'.
2 Permanence, as I have said, is on a slightly different footing.
3 Kant says that in experience we have to know 'the relation in the
existence of the manifold, not as it is put together in time, but as it is
objectively in time'. The word 'it' presumably refers grammatically to
the manifold, and the words 'put together' (zusantmengestellt) suggest
a connexion with 'apprehension', which was said above to be a
'putting together' (Zusammcnstellung) of the manifold. The general
sense is, I think, that though in apprehension wre 'put together' the
given manifold in certain temporal relations — whether in the order
in which the manifold is given to us or in an order which we create
in imagination — in experience we know that the manifold is in these
iclations, and not merely that we have put it together in these relations ;
compare A 191 = B 236.
Kemp Smith translates ' Zusammenstellung' as 'placing together' and
' zusammcHgestellt' as 'constructed'.
VOT rr F*
170 THE ANALOGIES OF EXPERIENCE [XXXIX §5
In view of the doctrine of the Transcendental Deduction —
that objectivity implies necessity, and that objective unity (or
combination) is necessary unity (or combination) — we might
expect Kant to assert straight away that an objective temporal
order is a necessary temporal order (or a temporal order
in accordance with a rule). He prefers to take a longer way
round to arrive at this conclusion, and indicates that if we
could perceive time itself — that is, empty or absolute time
apart from the events in it—this conclusion would not follow.
There is, however, no possibility of determining the objective
order of events through the direct perception of a time which
is objective and absolute, for time itself cannot be perceived
by sense.1
Kant thus makes two assumptions: (i) that in experience
we are aware of the objective order of events; and (2) that
we cannot perceive time itself. He argues that therefore we
can determine the existence, or the temporal position of
objects, only through their combination in time in general,
and therefore only through concepts that connect them a priori.
Since such concepts always involve necessity, experience
is possible only through representation of the necessary con-
nexion,2 or nexus, of sense-perceptions or appearances.3
§ 5. The Assumptions of the Argument
Kant's exposition is a summary statement of the general
principles which are at work in the detailed proofs of sub-
1 There is indeed an empirical or relative space which is an object
of experience, and can be called sensible, inasmuch as it is symbolised
(bezeichnet) by what can be sensed ; and presumably the same must be
true of time. But m that case we are considering individual spaces and
times as filled (and, I think, as indeterminate), not the one absolute
and infinite space and time which we construct in thought and treat
as a whole in which all relative spaces and times have a determinate
position. See M.A d.N. i Hauptstuck (IV 481-2).
2 The different forms of that necessary connexion are (i) the con-
nexion of permanent substance and changing accident, (2) the con-
nexion of cause and effect, and (3) the connexion of substances acting
causally upon one another.
8 I take sense-perceptions to be here equivalent to appearances.
XXXIX § 5] THE PRINCIPLE OF THE ANALOGIES 171
stance, causality, and interaction. It can hardly be judged till
we have followed the arguments of the Analogies; but since
it professes to be a proof, it deserves to be examined as if it
were relatively self-sufficient.
Firstly as to its assumptions — are we entitled to assume (i)
that we are aware of the objective order of events in time, and
(2) that time itself cannot be perceived ?
The second assumption, which is repeated again and again
throughout Kant's argument,1 is surely sound. What we
perceive is not time itself, but changes in time, and we measure
time, not in itself, but by the changes which take place in it.
Are we entitled also to assume that we are aware of an objective
order of events in time ?
I think it will hardly be denied that we at least seem to
distinguish the order of events from the order in which we
come to know them ; and Kant's statement is true as an analysis
of our experience, even if it is nothing more. For myself,
I cannot even see how we could be aware — as Hume admits
we are aware — of a succession of appearances in time, unless
we distinguished the time of our knowing from the time
of what we know. To be aware of any succession is to be aware
now of what is past.
Even in the simplest kind of experience which we can
imagine — an experience in which the object is only a succession
of appearances in time — we can distinguish the objective
order of the appearances from the subjective order of our
knowings. The order of the appearances is in such a case the
same as the order of our perceivings, but it is not the same
as the order of our rememberings; for we can remember
a later event and then remember an earlier event. Memory
is not merely the recalling of a past event, but the recollecting
1 B 225, A 183 --= B 226, A 188 = B 231, B 233, A 192 = B 237,
A 200 = B 245, 8257, A2i5 — B 263. The same assumption is found
in the Anticipations, see B 207 and compare A 172 = B 214. It is not
found in the Axioms, but Kant's marginal jottings suggest that it
might be used there also; see Erdmann, Nachtrdge LXX. We must
use the category of quantity because we cannot intuit space and
time in themselves.
172 THE ANALOGIES OF EXPERIENCE [XXXIX § 5
of it as past, that is, as having a position more or less definite
in past time, and therefore (since we cannot perceive time
itself) as coming before some events and after others. To have
memory is to be able, as it were, to move backwards and
forwards in the past.
It may be objected that the order of our rememberings
or knowings is just as much an objective order as the order
of given appearances. This is true, but it means merely that
we can make our own knowings an object to ourselves; and
this truth Kant (in spite of some careless statements suggesting
the contrary) can, and does, hold as part of his doctrine.
It remains none the less necessary to distinguish the order
of our knowings from the order of what we know, and there
is no impropriety in using the words 'subjective' and 'objec-
tive* for the purposes of this distinction.
Kant may have in mind also the fact that we can imagine,1
and even think, events to be in an order different from that
in which they actually occurred. Here too we have a subjective
order opposed to an objective order, and to deny this distinc-
tion is to make nonsense of human experience. In the main,
howrever, the subjective order is for Kant the order of events
occurring in the subject, while the objective order is the order
of events occurring in the object.
I suggest then that the assumption which Kant makes
is legitimate and necessary, since apart from it there could
be no experience, even of the most elementary kind.2 Con-
sideration of the details which Kant takes to be implied in the
assumption must be reserved till later.
1 Compare B 233 and also B 140. 1 take it that this second distinction,
the distinction between the real and the imagmaiy, might be made with
reference either to the order of events occurring in the subject or to
the order of events occurring in the object. We can construct an
imaginary account of our own mental history as well as of the history
of objects.
2 The same assumption is made in the Transcendental Deduction
(see especially B 139-40 and B 141-2).
XXXIX § 6] THE PRINCIPLE OF THE ANALOGIES 173
§ 6. The Conclusion of the Argument
Kant's conclusion is asserted in three stages. Of these the
first is not likely to be denied. Granted that we are aware
of an objective order in time, and granted that we cannot
perceive time itself, the position of objects in time1 can be
determined only through 'their combination in time in general*.
The time at which objects exist is determined only by their
relation to other objects which they precede, succeed, or
accompany in a time which is one and the same for all objects.
Kant's second contention is this — that to determine the
position of objects in time 'through their combination in time
in general' is to determine it through concepts connecting2
objects a priori.
This is the Critical solution of the problem, and Kant
believes it is the only possibility that remains; for we have
rejected the view that sense-perception can by itself determine
the temporal position of objects,3 and we have also rejected the
view that we have a direct perception of absolute time itself.
Neither empirical nor pure intuition can account for our
experience of objective relations in time, and we must seek
for an explanation elsewhere. If we are to determine objective
temporal position through the combination of objects in time
in general, we can do so only through concepts which are not
derived either from empirical or from pure intuition; and
these concepts must connect objects a priori , that is, inde-
pendently of experience.
The sense in which these concepts connect objects (or the
1 B 2 19 Kant says the Existence of objects*, but existence is position
in time.
2 Note the transition from the more general term 'combination'
(Verbtndung) to the more specific term 'connexion', or * nexus*
(Verknupfung). I take it that Kant is thinking of 'connexion* in both
cases, in spite of the variation in terminology. The 'connexion* is a
connexion in time, and might be described equally as an objective
connexion of the manifold in time ; compare 'the relation in the existence
of the manifold* in B 219 a little earlier.
3 Apart altogether from Kant's special views about synthesis, it
should be obvious that the order of our sense-perceptions is not the
order of what we ordinarily take to be objective events in time.
174 THE ANALOGIES OF EXPERIENCE [XXXIX § 6
manifold of objects) a priori is not here explained. I take it that
not only do we think (rather than intuit)1 the connexion of
objects in accordance with these concepts: the connexion
is actually imposed on the manifold by the thinking mind.
Kant's view is that objective temporal connexions (which
we all claim to experience) are found in experience only because
they are imposed by the understanding. More precisely, these
connexions are imposed by the transcendental synthesis
of imagination which combines given appearances in one time
and space in accordance with the categories of the under-
standing.2 For example, in all experience we synthetise given
sensible qualities3 as accidents of permanent substances in
time and space. We do so in accordance with the demands
of thought, not in accordance with the deliverances of sense;
and if we did not do so, there could be no such thing as experi-
ence, nor could 'objective temporal position' have any meaning
for us.
We do not make explicit to ourselves the nature of such
concepts as 'substance' and 'accident' till experience is highly
developed; and still less do we ascribe their origin to the
demands of thought. These facts (which are neither ignored
nor denied by Kant) have no relevance as criticisms of his
doctrine. Even when I make so simple a judgement as 'This
apple, which was green, is now red', I have not only combined
the given manifold in accordance with the category of sub-
stance and accident by a transcendental synthesis of the
imagination: I have also presupposed the category in my
judgement itself.
1 Compare Chapter XXXII § 5 ; and also (for the relation of con-
cepts and intuitions) Chapters V § 8 and IX § 5.
2 It is not difficult to see that the unity of apperception involves the
unity of time and of all objects in time, and that this unity might be
impossible unless objects were combined in certain ways by the trans-
cendental synthesis of imagination. The main difficulty is to see how
these different ways of combination can be imposed in response to the
demands of thought. For these demands of thought under the head
of relation see Chapter XIV § 8 and also Chapter XXXIV § 3.
3 Or at any rate sensible qualities given to outer sense.
XXXIX §7] THE PRINCIPLE OF THE ANALOGIES 175
Kant's third contention is that concepts which thus connect
objects (or the manifold of objects) a priori involve necessity ;
and therefore experience (as experience of an objective order
in time) is possible only through representation of the necessary
connexion, or nexus, of appearances.1
This third contention is little more than an expansion of
what has already been said. An a priori connexion must be
universal and necessary : the very concept of such a connexion
involves necessity.2 Kant does not consider the possibility
that the connexion might be purely arbitrary. If it were, there
could be no objective connexion in time, and so no experience.
And indeed Kant already claims to have shown generally
in the Transcendental Deduction that objectivity involves
necessity. In the sequel he will argue that the different forms
of objective connexion in time must involve necessity.3
It may be observed that in this case the argument of the
second edition, as of a more general character, is rightly placed
before the argument of the first edition. It maintains only that
the necessary connexion of appearances in time is a condition
of experience. The fact that there are three forms of such
necessary connexion, and different rules for each of these
forms, is a further development of the general argument.
§ 7. The General Character of the Proof
It must never be forgotten that the proof of the Analogies,
like that of the other Principles, rests upon the possibility
of experience, experience being regarded as 'knowledge in
which all objects must in the last resort4 be capable of being
given, if the idea of them is to have objective reality for us'.5
Kant says expressly that the Analogies could never be proved
1 B 219. 'Representation* (Vorstellung) is here conception.
2 Compare A 2 and B 3-4.
3 See especially B 233-4, where we find a parallel to the present
argument.
4 'zuletzt.' Does this qualification refer to the fact that some objects,
e.g. electrons, are too small to be given directly to our senses? See
A 226 = B 273 and compare Price, Perception, p. 297.
6 A 217 = 6264.
176 THE ANALOGIES OF EXPERIENCE [XXXIX § 7
in regard to objects which were things-in-themselves.1 He
says also that it would be utterly useless to attempt a dogmatic
proof of the Analogies, that is, a direct proof from concepts.2
We may analyse our concepts of objects as we will, but we can
never pass by mere concepts from an object and its existence
to the existence, or mode of existence, of anything else;3 we
could never prove, for example, by an analysis of the concept
of 'event', that every event must have a cause. In Kant's
opinion the proof of the Analogies is incompatible with both
realism and rationalism; and indeed realism and rationalism
can, he believes, offer no proof either of substance or of caus-
ality or of interaction.
Just because Kant's proof rests upon the possibility of
experience, it is to him a matter of indifference whether he
argues from the unity of apperception or from the unity
of objective time-relations; for the synthetic unity which
is necessary for any kind of objectivity is grounded on the
unity of apperception, and the unity of apperception is mani-
fested only in the synthetic unity of objects, and preeminently
in the synthetic unity of their time-relations. He appeals
to experience and its possibility as the 'third thing' which
alone can justify synthetic a priori judgements ;4 and because
the essential form of experience consists in the synthetic
unity of the apperception of all appearances,5 he can discover
the a priori conditions of the necessary time-determination
of all existence in the phenomenal wrorld, conditions apart
from which all empirical time-determination would be im-
possible.6 These conditions are expressed in rules of synthetic
unity a priori? rules through which alone the existence of
1 A 181 = 6223.
2 A 216-7 = B 263-4. Compare A 736 = B 764.
3 A 217 = 6264.
4 Ibid. Compare A 155 = B 194 and A 259 = B 315.
6 I think he ought to add here a reference to the fact that time is
the ultimate form of all our intuitions. Time and the unity of apper-
ception are the ultimate conditions through which alone experience
is possible. fl A 217 = B 264. Compare also A 177-8 = B 220.
7 A 217 = 6264.
XXXIX § 7] THE PRINCIPLE OF THE ANALOGIES 177
appearances can acquire synthetic unity as regards their time-
relations.1
The Analogies in short are rules which must govern all
appearances, if they are to be appearances of objects in one
and the same objective time. The unity of the time in which
all objects exist is grounded on the unity of apperception,
which is manifested only in synthesis according to rules.2
The particular character of the rules of synthesis in regard
to existence in time seems, however, to be determined, partly
at least, by the fact that absolute time cannot be perceived.
If it could be so perceived, we could apparently determine
the temporal position of objects immediately,3 and 'as it were
empirically',4 by reference to absolute time. As absolute time
cannot be perceived, we determine the temporal position
of objects only by their relations to one another in time, and
the rules in accordance with which we do this are a priori
rules which are valid for any and every time.5
We shall be in a better position to estimate the value of this
doctrine when we have considered the proofs in detail. Here
I would only say that Kant has at least a genuine and important
problem; for even if we reject the concepts of substance and
causality, we ought to give some account of what we mean
by an objective order of events which is distinct both from
the order of our knowing and from the order created by mere
imagination.
1 A 215 — B 262. This means, for example, that there can be no
objective succession apart from the law of cause and effect. I take
'rule* in nil these passages to refer to the Analogies, and not to the
empirical laws of nature, which we discover in conformity with the
Analogies.
2 Compare A 216 = B 263. 3 A 215 = B 262.
4 B 233. I presume this means in a way analogous to empirical
observation.
5 A 216 — B 263. I take 'rules' throughout this paragraph also to
mean the Analogies.
CHAPTER XL
THE SPECIAL CHARACTER OF THE ANALOGIES
§ i. The Analogies are Regulative
Kant's further account1 of the special character of the
Analogies is little more than an elaboration of what we already
know.2
The Mathematical Principles wrere concerned with appear-
ances, or more precisely with the synthesis of time and space
and the synthesis of sensation necessary for knowledge of
appearances as appearances of objects.3 The Analogies are
concerned with the existence of appearances as objects, that
is, with their relation to one another in respect of their exis-
tence.4 Kant asserts that we can construct a priori not only
the extensive quantity, but also the degree of appearances.5
We cannot construct the existence of appearances not given
to us, although we can infer some kind of existence from what
1 A 178 = B22off.
2 See A 1 60 -= B 199 ff. and Chapter XXXVI § 2.
3 For the reference to objects, see Bui and Chapters XXXVI § 2 and
XXXVII § 5.
4 A 178 = B 220. This seems to be the same as their position relative
to one another in time.
5 A 178-9 -= B 220-1; compare Chapter XXXVIII §4. Kant's
statement in A 178 -= B 220-1 is particularly obscure. 'The way in
which something is apprehended in appearance can be so determined
that the rule of synthesis can at once, in every empirical example that
comes before us, give this intuition a priori, that is, can bring it into
existence from the example.' The words a priori must, I think, go
with 'give' and not (as Kemp Smith takes them) with 'intuition'. The
word 'darans* I translate as 'from the example' : it is omitted in Kemp
Smith's translation.
Kant is here concerned with the possibility of constructing a priori
both the extensive, and the intensive, quantity of an empirical intui-
tion. I do not understand his references to the empirical example;
but I think he must intend to say, not that we can construct the
empirical intuition a priori, but that we can so construct the quantity
and the degree (and consequently the number) involved in the intui-
tion. Compare A 714-15 = B 742-3.
XL §2] SPECIAL CHARACTER OF THE ANALOGIES 179
is given; for example, we can know that a given event must
have some cause, but apart from experience we cannot say
what that cause must be.1
For this reason the Mathematical Principles are said to be
'constitutive'; to be constitutive always implies for Kant the
possibility of construction.2 The Analogies are merely 'regula-
tive'; they tell us what we must look for in experience, but
they do not enable us to construct it a priori.
§ 2. The First Meaning of 'Analogy*
Hence there is a difference between a mathematical analogy
(or proportion) and Kant's Analogies of Experience, although
both are concerned with what he elsewhere calls an agreement
in relation.3 Mathematical analogies are formulae which
express the equality of two quantitative relations (or ratios);
and just because we can construct quantities, we can determine
the fourth term in a proportion when three are given.4 The
Analogies of Experience are concerned with two qualitative
relations; and since quality cannot be constructed, we are
unable to construct the fourth term, when the other three are
given.5 All we have is a rule for seeking the fourth term in
1 This statement is elaborated in A 766 = B 794. We cannot know
a priori that sunlight will melt wax and harden clay; but we can know
a priori that if wax melts, something must have preceded upon which
the melting has followed in accordance with a fixed law — the law, I
take it, that every event must have a cause.
2 Construction again implies the possibility of immediate certainty
or 'evidence*. See Chapter XXXVI § 3.
3 'Analogia' is equated with 'eine Obereinstimmung des Verhaltmsses* ;
see Metaphysiky p. 90.
4 If 2 : 4 = 3 : x, we can say what x must be.
6 The Analogies are no doubt concerned with qualitative relations,
but the factor of quantity cannot be ignored, as is shown by Kant's
insistence that the quantum of substance can neither be increased nor
diminished (B 224). It is curious that he does not discuss the quanti-
tative equivalence of cause and effect, perhaps he thinks this is
sufficiently indicated in his account of substance. References to
quantity (both extensive and intensive) in connexion with causation
are to be found in A 168-9 — B 210, A 176 = B 217, and A 179
= B 222. In the last of these passages he appears to imply that, for
i8o THE ANALOGIES OF EXPERIENCE [XL § 3
experience, and a mark1 whereby it can be detected. We
know, for example, that effect is to cause as the melting of
wax is to x:2 we cannot say a priori what x must be, but we
know that it must have the mark of invariably preceding such
melting.
§ 3. The Second Meaning of 'Analogy*
There is a further sense in which the term 'Analogy'
is applicable to the Principles with which we are at present
concerned. Kant leads us up to this sense by a remark which,
he declares, applies to all the Principles, but preeminently
example, if we are given an effect, we can say that it must have a
preceding cause, but we can tell a priori neither what that cause is
nor what its quantity is. I do not know how he would deal with the
objection that we can know the cause to be quantitatively equivalent
to the effect. It might almost be said that we are capable of construct-
ing both the existence of the cause and its quantity, but not its empirical
quality. Kant is of course right in holding that although we might be
able to infer some existent or other a priori , we could not know it
determmately ; that is, we could not anticipate the difference between
it and other existents, this difference being revealed to empirical
intuition alone. See A 178 = B 221.
1 I presume that the 'marks* are permanence, regular succession,
and regular simultaneity — the three transcendental schemata. Com-
pare A 136 ~ B 175. Kant suggests later — in A 203 — B 249 — that
sequence in time is the sole empirical criterion by which we distinguish
cause from effect. In that case he is concerned with two events known
to be causally connected, and the only question there is which is the
cause and which is the effect. We may nevertheless take the mark of
a cause to be that it invariably precedes the effect. Needless to say, this
by itself is not sufficient to determine the cause of anything; night,
for example, is not the cause of day. If Kant were writing a treatise
on induction, he would be obliged to discuss in detail the conditions
under which we are entitled to say that A is the cause of B. He is,
however, concerned with something much more general, with the
justification for believing the world to be governed by causality. To
treat the Analogies as an essay in inductive logic can lead to nothing
but misunderstanding.
2 The fact that the melting of wax is taken to be an instance of
'effect', and x to be an instance of 'cause', means that the relation
between them is an instance of the causal relation. Perhaps it might
be better to say that the melting of wax is to x as other events are to
their causes.
XL §3] SPECIAL CHARACTER OF THE ANALOGIES 181
to the Analogies.1 The Analogies have meaning and validity
only in their empirical, and not in their transcendental, use;
that is to say, they have meaning and validity only as applied
to objects of a possible experience, not as applied to things-
in-themselves.2 Hence our proof of them can have reference
only to their empirical use, and appearances must be sub-
sumed, not directly3 under the categories, but under their
schemata.
This doctrine is already familiar to us from the discussion
of the transcendental schemata,4 but Kant deals with it here
in an extremely elaborate and complicated way.5 His main
point is, however, comparatively clear. When we, for example,
say that effect is to cause as the melting of wax is to xy we do
so only in virtue of the schema of necessary succession ; and
in so doing we treat the relation of the necessarily succeeding
1 A 1 80 — B 223. Kant makes a similar statement about the term
* Anticipations' in A 166-7 = B 208-9.
a Sec A 139= B 178 and A 146 - B 185 ; and compare Chapter XI
§ 4 for a fuller statement and also Chapter LIV § 3.
1 'schlechthin* (A 181 - B 223); compare A 138-9 = B 177-8.
4 Compare especially Chapter XXXIV §§ 1-2 and also Chapter
XXX V§ i.
6 Sec A 181 = B 223-4. Kant's statement is unusually full of relative
pronouns which may refer to many different nouns. The commentators
take different views of these references, and even feel compelled
(perhaps not without reason) to make emendations. It is perhaps
impossible to determine the precise meaning of Kant's words, but
Kemp Smith's translation — apart from two sentences — gives what
seems to me an adequate statement of Kant's thought. Of the two
sentences beginning 'But such unity can be thought . . .' the first
seems to me doubtful, and the second seems to me impossible. Of
the correct translation I am uncertain, but Kant, I think, means some-
thing like this : The synthesis of appearances can be thought only in
the schema ; the pure category contains the form (function of unity) of
this synthesis in abstraction from all restricting sensuous conditions;
that is, it contains the form of this synthesis as a synthesis of the
manifold in general (not as a synthesis of appearances in time).
Compare Chapter XXXII §§ 6-7. I take 'synthesis in general' to be
equivalent to 'synthesis of the manifold in general \ compare B 129-30,
B 144-5, and B 150-1. For what the pure category contains, see
A 138 = B 177: for what the schematised category contains, see
A 139-40 — B 178-9.
182 THE ANALOGIES OF EXPERIENCE [XL § 3
to the necessarily preceding as analogous to the relation of
consequent and ground which is thought in the pure category.1
The ways in which we combine appearances in time in accor-
dance with the Analogies of Experience is analogous to the ways
in which the manifold in general is combined in the categorical,
hypothetical, and disjunctive forms of judgement, and so in
the pure categories of relation.2
To say this is, I think, to say that the schemata are analogues
of the pure categories: the synthetic unity of the manifold
of appearances in time (which is thought in the schema) is
analogous to the synthetic unity of the manifold of in-
tuition in general (which is thought in the pure category).3
In this doctrine there is nothing really novel, but only a new
way of expressing what Kant has taught all along.4 Since the
Principles can be proved only in their empirical use, and
since appearances can be subsumed directly only under the
schemata, we must, in applying the Principles to appearances,
substitute the schema for the category as the key to its use,
or rather we must set the schema alongside the category
as its restricting condition.5
I take it that this doctrine holds of all the Principles, although
1 We may expand our previous Analogy' into the form 'The
melting of wax : x — the necessarily succeeding : the necessarily pre-
ceding - consequent: ground*.
2 'By these Principles we are justified in combining appearances
only according to an analogy with the logical and universal unity of
concepts', A 181 == B 224. Compare also A 147 = B 186 and
A 142 -= B 181.
3 For example, the (ultimate) subject is to its predicates as the
unchanging or permanent is to the changing in time ; the consequent
is to the ground as the necessarily preceding is to the necessarily
succeeding in time ; and so on.
4 Kemp Smith's statement (Commentary, p. 358) that 'it implies
that it is only in the noumenal, and not also in the phenomenal, sphere
that substantial existences and genuinely dynamical activities are to
be found' seems to me due to misunderstanding. It is sufficiently
refuted by Kant in A 146-7 -= B 186.
5 A 181 — B 224. There are difficulties here in Kant's text into
which I need not enter, but he is manifestly saying that only schema-
tised categories can be applied to objects.
XL §3] SPECIAL CHARACTER OF THE ANALOGIES 183
it is preeminently true of the Analogies.1 Whether it is a par-
ticularly valuable way of expressing Kant's general doctrine
is another question. It is perhaps not unreasonable to suppose
that the title * Analogies of Experience' was chosen by Kant
primarily because of the first sense which he ascribes to the
word Analogy' in this connexion.
1 Compare Kant's statement at the beginning of the paragraph
(A 1 80 — = B 223). This statement need not cover the whole of the
paragraph, but there is nothing in the argument to suggest restriction
to the Analogies. Kant's doctrine would not apply to the Mathematical
Principles, if the categories must in themselves possess correlates —
see B no — in order to enter into an Analogy; but I see no indication
of this in the argument. I presume that the analogy between category
and schema is more obvious in the categories of relation, partly
because both categories and schemata have correlates, and partly
because there is less likelihood of our identifying the category and the
schema.
CHAPTER XLI
THE FIRST ANALOGY
§ i. The Principle of Permanence
'In all change of appearances substance is permanent, and its
quantum in nature is neither increased nor diminished. '
This is Kant's formula in the second edition. The reference
to the quantum of substance is commonly condemned to-clay ;
but it at least attempts to make Kant's doctrine precise, and
it deserves to be considered on its own merits.
The formula of the first edition makes no reference to the
quantum of substance. 'All appearances contain the permanent
(substance) as the object itself, and the transitory as its mere
determination, that is, as a way in which the object exists.'
The two traditional views of substance are (i) that it is the
ultimate subject of all predicates, and (2) that it is the per-
manent substratum of change. Kant accepts the first view as
involved in the very idea of substance, and suggested by the
categorical form of judgement. When we translate it into
terms of time, substance becomes the permanent subject
of changing predicates, or the permanent substratum of
change. What Kant has now to prove is that there is a per-
manent substratum of change, and only so can the concept
of substance have objective validity.
Kant believes that substance (as a permanent substratum)
belongs only to objects of outer sense; and it is with these
that his proof is really concerned, although he professes to
deal with all changing appearances. Since substance is essenti-
ally spatial, and since the parts of space are outside one another,
Kant holds that there must be many substances, and that
every substance is made up of substances. Hence he rejects
a third traditional view of substance, which defines substance
as the self-sufficient.1
1 This is explicitly stated in Metaphysik, p. 34. He rejects the
definition of Descartes : per substantiam nihil altud intelligere possumus
XLI § i] THE FIRST ANALOGY 185
It must not be forgotten — Kant himself repeats it again
and again — that he is concerned only with substance as appear-
ance (substantia phaenomenon). We have no reason to regard
ultimate reality, or the thing-in-itself, as either spatial or
temporal, either permanent or changing, although it appears
to human beings as a phenomenal world of permanent sub-
stances in space causally interacting with one another. The
fact that in our phenomenal world we recognise, and must
recognise, permanent spatial substances whose changes are not
to be identified with the changes in our sensations ; and even
the fact that we can find the causes of our sensations in the
movements of bodies, and especially of our own bodies — all
this offers not the slightest ground for supposing Kant to have
wavered for a moment from his belief that both the physical
world and our own mental history are nothing more than
an appearance to human minds. Here, as always, his empirical
realism and transcendental idealism are not conflicting ten-
dencies whose nature he fails to understand : they are on the
contrary essential and interdependent parts of his philosophical
system.1 On his view we can have a priori knowledge of per-
manent spatial substances only in so far as the whole physical
world is dependent on human sensibility and thought. Even
if we cannot accept his view, even if we deny that it can be
worked out consistently in detail, we must recognise that
it has at least an initial consistency.
quam rem quae ita existit ut nulla alia re indigeat ad existendum (Princ.
Phil. I, 51). He adds that Spinoza held the same view, and that this
was the source of his error.
Kant himself (in B 407, B 413, and B 417 n.) speaks of substance
(in connexion with the self) as meaning a self-subsistent essence (em
fur sich bestehendes Wescn). But 'self-subsistent' for Kant is not
equivalent to * self-sufficient ' : it means only that which does not
'inhere* as an accident in something else, and is compatible with being
'grounded* in something else.
1 Compare Chapter II § 2 and Chapter XXXI § 10.
1 86 THE ANALOGIES OF EXPERIENCE [XLI §2
§ 2. The Argument of the First Edition
I. Our apprehension of the manifold of appearance is always
successive, and is therefore always changing.1
From this, according to Kant, it follows (i) that by mere
apprehension we could never distinguish objective succession
from objective simultaneity; (2) that if we are to make this
distinction, and indeed if we are to determine objective rela-
tions in time at all,2 our experience3 must have as its ground
or condition something which always is, that is, something abiding
and permanent', and (3) that all objective change and simul-
taneity must be simply so many ways (modes of time4) in
which this permanent exists.5
II. Since simultaneity and succession are the only relations
in time, and since we can determine objective simultaneity and
succession only as ways in which the permanent exists, we
can say that only in the permanent* are time-relations possible.
1 A 182 = 6225.
2 Succession and simultaneity are the only relations in time. See
A 182 =•= 8226.
3 The emendation suggested by Erdmann ('an ihnC for 'an thr')
means that for 'our experience* we must substitute 'the manifold as
an object of experience*. I do not think the emendation is necessary,
and Erdmann himself suggests it only as a doubtful possibility. 'Our
experience* is equivalent to 'our experience so far as it is an experience
of objective temporal relations*.
4 For modes of time, see Chapter XXXIX § 3.
5 Some explanation of this conclusion would have been an advantage.
Even if the permanent is the ground or condition of our experiencing
change (or succession) and simultaneity, and so is the ground or
condition of change and simultaneity, does it follow that change and
simultaneity are ways in which the permanent exists ?
The clause is loosely constructed in German : '. . . something abiding
and permanent, of which all change and coexistence are only so
many ways (modes of time) in which the permanent exists* is Kemp
Smith's translation, which follows the German very closely. The 'of
which' hangs very loosely to the clause as a whole, unless Kant means
'all change and coexistence of which' ; but this would merely assume
that change and coexistence were change and coexistence of the
permanent.
6 The phrase 'in the permanent* seems to mean no more than 'in re-
lation to the permanent*. The equivalent statement below (in A 183 =
B 226) is that 'without this permanent there is no time-relation*.
XLI §2] THE FIRST ANALOGY 187
So far Kant's argument is clearly — what on his principles
it ought to be — an argument from the conditions of experience
to the conditions of objects of experience. We could not
experience any objective time-relations apart from the per-
manent, and therefore there can be no objective time-relations
apart from the permanent.
This conclusion is then restated in other terms. The per-
manent is the substratum of the empirical idea of time itself,1
and it is only by reference to this substratum that time-rela-
tions are possible.
III. Kant's conclusion so far rests, as I have said, on what
he believes to be the condition of experiencing objective time-
relations. He now attempts to reinforce that conclusion by an
argument resting upon the nature of time.
Permanence is in a special sense an expression2 of the nature
of time, for time is the constant correlate* of all existence of
appearances, of all change and all concomitance*
The reasons for this special connexion between permanence
and time would seem to be as follows :
1 This clause — though it professes only to re-state what has already
been said — is difficult. 'Substratum* is not defined — it seems to mean
that by reference to which we distinguish objective simultaneity and
succession, and consequently (according to Kant) that of whose
existence succession and simultaneity are modes; compare A 183
= B 227. Kant no doubt has in mind the traditional doctrine which
emanates from Aristotle. According to Aristotle change implies a
succession of states in a substratum. This substratum is sometimes
called ovalu, and seems to be an element in the doctrine of sub-
stance.
'Time itself is not empirical, and cthe empirical idea of time itself*
seems to mean the empirical time-determinations of objects. This is,
I think, confirmed by the clause which follows. Compare M.A.d.N.
(IV 481) where Kant equates 'empirical space* with the totality of
outer objects.
2 A 183 = B 226, 'ausdruckt*. In B 225 the (permanent) substratum
is said to 'represent* time in general (vorstellt).
3 'das bestandige Korrelatum.' The word 'bestandig* suggests per-
manence. In B 224-5 time is said to be the permanent form of inner
intuition, and it is even said that time abides and does not change.
4 ' Begleitung.' This is equivalent to coexistence or simultaneity.
1 88 THE ANALOGIES OF EXPERIENCE [XLI § 2
(1) Change is not a change of time itself, but of appearances
in time.
(2) Simultaneity is not a simultaneity of time itself,1 for the
parts of time are successive, not simultaneous.2
(3) Although the parts of time come one after another, this
does not entitle us to attribute succession to time itself;
for if we did so we should have to think of another time
in which this succession took place.
All these arguments seem intended to suggest, if not that
time itself is permanent, at any rate that permanence is more
closely connected with time than are succession and simul-
taneity.3 Kant adds a fourth argument connected with dura-
tion4 in time. This argument is of a somewhat different char-
acter. It does not suggest that time itself is permanent, but
rather that apart from the permanent there can be no duration
in time any more than there can be succession or simultaneity.
(4) It is only through the permanent that existence in
different parts of the time-series5 acquires that kind of
quantity which is called 'duration'. If we consider bare
succession in itself, existence is continually ceasing and
coming to be, and has absolutely no quantity at all.6
1 Kant says that simultaneity is not a mode of time itself. See
Chapter XXXIX §3.
2 He might have added for the sake of parallelism that it is not time,
but appearances in time, which are simultaneous.
3 Kant does not ask whether, if time endures or is permanent, we
should require to think of another time in or through which it endures.
4 'Dauer.'
5 The time-series is the series of times (or of parts of time), the
time-order is the order of what is in time. See A 145 = B 184.
8 It has — or is — mere position in an atomic 'now'. The past does
not exist nor does the future. Permanence, in the strict sense, involves
existence through all time, while duration is existence through some
time (A 185 — B 228-9). If a duration is objective, it is in a determinate
relation to all other objective durations, and so presupposes perman-
ence. In the abstract moment there can be no duration (or quantity
of existence), for a moment is not a part, but a limit, of time (see
Ai 69 =6211 and A2o8 =8253). There can, however, be a quantity
or degree of reality m the abstract moment; see A 168 = B 210.
XLI §2] THE FIRST ANALOGY 189
All four arguments are intended to reinforce Kant's original
conclusion1 from the conditions of experience — that without
the permanent no objective time-relations are possible.
IV. Time in itself cannot be perceived.
V. Therefore the permanent must be present in appearances,21
and must be the substratum* of all time-determinations.
It follows (i) that the permanent in appearances is a con-
dition of the possibility of the synthetic unity of appearances
in one objective temporal order;4 and therefore (2) that it is
a condition of experience and so demonstrably necessary.
VI. Therefore in all appearances the permanent is the object
itself f that is, substantia phaenomenon, the ultimate and
unchanging subject to which all changing accidents are attributed
as predicates.
Everything that changes, or can change, belongs only to the
1 Stated in II above in the form 'only in the permanent are time-
relations possible*.
2 Note that this conclusion follows from the fact that time cannot
be perceived. In the earlier stage of the argument — see I above — it
was presumably still an open question whether the permanent required
might not be found in time itself.
3 This again seems to mean more than the 'condition' or 'ground'.
4 Kant says it is the condition of the possibility of the synthetic
unity of all sense-perceptions (where 'sense-perception' is equivalent
to 'appearance'); but there are other synthetic unities and other
conditions (the unity of extensive quantity, the unity of degree, and
so on). The permanent in appearances is not even the only condition
of an objective temporal order, for causality and interaction are so also.
The clause added — that with reference to this permanent all
existence and change in time can be regarded only as a mode of the
existence of what abides and is permanent — adds nothing to what
has been already said, and is loosely expressed Existence (Dasem)
cannot be a mode of existence (E\ntens). Perhaps Kant intended to
write 'simultaneity' (or 'duration').
6 The object was formerly regarded as the necessary synthetic
unity of a group of appearances. Here it is regarded as the permanent
substratum of these appearances. This doctrine is not repeated in the
proof added in the second edition. Strictly speaking, the object is
the substance with its accidents, not the substance in abstraction from
its accidents. The synthetic unity of substance and accident is perhaps
the most fundamental unity which characterises an object.
1 90 THE ANALOGIES OF EXPERIENCE [XLI § 3
way in which this substance or these substances1 exist; that
is, it belongs to the determinations of substance.
§ 3. The Argument of the Second Edition
I. All appearances are in time, and it is only in time as
a substratum2 (or as a permanent form of inner intuition) that
objective3 succession and simultaneity of appearances can
be known.4
II. Therefore time (in which we have to think all objective
succession and simultaneity of appearances) abides and docs
not change; because we can know objective succession and
simultaneity only as determinations of time.5
III. Time itself cannot be perceived.
IV. Therefore there must be found in the objects of sense-
perception (that is, in appearances as appearances of an object)
the permanent6 as a substratum which represents7 time. All
1 Kant ought to have explained how there must be many substances.
The reason is that substances fill space, and that every part of a
substance is a substance, just as every part of space is a space See
Chapter XLII § 7.
2 Here again we should like to know whether 'substratum* means
more than 'condition* or 'ground'. Compare A 30 = B 46. To say that
appearances are simultaneous is to say they are in the same time (or
part of time); and to say they are successive is to say they are in
different times (or parts of time).
3 I have introduced the word 'objective*.
4 B 224. I translate 'represented* (vorgestellf) as 'known*.
6 It is typical of Kant to introduce a statement with a 'therefore*
and follow it up with a 'because*, confusing us with a superabundance
of reasons. The 'because* would seem intended only to repeat the
reason given in I above, but it adds that simultaneity and succession
are determinations of time, presumably on the ground, and in the
sense, that they cannot be apart from time (as their substratum or
condition or ground).
The bold statement that 'time abides and does not change* seems to
go even further than the first edition in ascribing permanence to time.
0 Kant omits to say that this substratum is the permanent until two
sentences later — he supposes we are intelligent enough to infer this
from what has gone before.
7 'represents* (vorstellt) corresponds to 'expresses* (ausdruckt) in
A 183 -= 6226.
XLI § 3] THE FIRST ANALOGY 191
change and simultaneity must be capable of being perceived
or apprehended1 only through the relation of appearances
to this permanent.2
V. The permanent substratum of appearances (or of the
real3) is substance, and appearances (as appearances of objects)
can be thought only as determinations of substance. In other
words, the permanent by reference to which alone can the
objective time-relations of appearances be determined is
substantia phaenomenon (substance in the appearances). It
remains always the same and is the substratum of all change.
VI. Since phenomenal substance cannot change in its
existence, its quantum in nature can neither be increased nor
diminished.4
1 'apprehended', as usual, is to be taken in the technical sense in
which it is connected with sense-perception and involves a synthesis
of the successively given.
2 This clause corresponds roughly to I in the argument of the first
edition.
3 The real is what fills time or the time-content (realttas phaeno-
menon); see A 143 - B 183, A 145 = B 184, A 168 — B 209. It is
here described as 'what belongs to existence', for to exist is to be in
time or to have a determinate position in time. Its duration is the
quantity of its existence, which is to be distinguished from its intensive
quantity (or degree of reality). It can, I think, be identified with the
changing appearances of which substance is the substratum, as is
implied by the statement above, although Kant in the following
sentence speaks of substance itself as the real of appearances, thereby
identifying substantia phaenomenon and reahtas phaenomenon The
real may cover substance as well as the accidents of substance, but it
cannot be substance as opposed to its accidents.
4 It should be noted that although there arc six stages in the argu-
ment of both first and second editions, they do not exactly correspond ;
foi I in the first argument has no corresponding stage in the second
argument, and VI in the second argument has no corresponding
stage in the first argument. The series II, III, IV, V, and VI of the
first argument corresponds very roughly with the series I, II, III,
IV, and V of the second argument. The correspondence is closer in
the last three numbers of these series than in the first two.
CHAPTER XLII
SUBSTANCE
§ i . In what Sense is Apprehension Successive ?
The main differences in Kant's two proofs of substance
are to be found in the earlier stages. The argument of the
second edition starts from the permanence of time as the con-
dition of determining succession and simultaneity: the argu-
ment of the first edition maintains first that the permaneni
is the condition of determining succession and simultaneity,
and then connects permanence with the nature of time. Both
proofs maintain that because time (with such permanence
as it may possess) cannot be perceived, the permanent which
is necessary in order to determine time-relations must be
found in objects or appearances as their substratum or sub-
stance.
Hie main peculiarity1 of the first edition is Kant's assertior
that apprehension is always successive; and it is from thij
that he infers the necessity of a permanent (as the condition o
determining objective succession and simultaneity) before h<
connects this permanent either with the nature of time or wit!
the substratum of appearances.
Our apprehension — that is, the taking up and holding to
gether of the given in sensation — is obviously successive
in the sense that it takes time; but Kant has been thought t<
mean2 that our apprehension is merely successive, or tha
1 In B XXXVII Kant says expressly that he found nothing whicl
required alteration in his proofs , but any argument which is not use*
in the second edition can scarcely be legarded as essential to th
proof
2 This view is expressed most clearly in Ewing, Kant's Treatmct
of Causality, see especially pp. 82 if. and 105 ff. Ewing holds thi
'Kant confused the true statement that our experience is alway
successive with the false statement that our experience is merel
successive*. He takes 'merely successive* to mean that experience ca
in itself give us no glimpse of the coexistent.
XLII § i] SUBSTANCE 193
we can never apprehend different things at the same time.
I am very reluctant to accept such a view, not only because
it is manifestly at variance with common sense, but also because
it seems inconsistent with Kant's most central doctrines. The
mere fact that apprehension is a synthesis of the manifold
means that it is a holding together of different elements in one
moment before the mind, and Kant himself makes it clear that
all analysis presupposes such a synthesis. He does, however,
hold that as contained in one moment — which is of course
a mere abstraction — an idea can be nothing but absolute unity,
and this means at least that it has no extension either in time
or in space.1 He maintains also that we cannot know a line,
however small, without drawing it in thought, a process which
he regards as definitely successive, however short be the time
which it requires.2 He might therefore believe that although
we can in one moment hold together different elements before
our mind, yet in so far as apprehension is reduced theoretically
to a mere taking up (as opposed to a holding together) of the
given, it is a taking up of what is one and indivisible; for
example, that in an abstract moment of time we can 'take up'
only an abstract point of space.
It is difficult to be sure of the precise meaning intended
to be conveyed by such a doctrine, but Kant is quite certainly
dealing with abstractions which are the product of analysis.
He does not believe that any part of an appearance can be given
to us in a moment of time. On the contrary, he maintains that
every part of an appearance is apprehended in a part, and not
in a moment, of time;3 and he argues that every part of an
appearance must be infinitely divisible, since the part of time
in which it is apprehended must be infinitely divisible.
Because it takes some time to apprehend any part of an
appearance, therefore it must be possible to 'go through'
1 A 99. Even in this case he admits that what is apprehended has a
degree, in which plurality is represented by approximation to zero.
See A 168 = 6210.
2 A 162 - B 203. Compare B 154 and Chapter XXXVII § 4.
3 A moment is not a part, but a limit, of time.
VOL. II G
194 THE ANALOGIES OF EXPERIENCE [XLII § i
or 'expose11 successively any part of an appearance, however
small it may be; and an appearance cannot be made up of
simple parts, any more than time can be made up of
moments or space of points.2
Kant must not be supposed to mean that in each moment
of time we apprehend a simple indivisible appearance, and
then join together these simple indivisible appearances into a
complex appearance or sensum.3 He is considering only ideal
limits, and I see little or no ground for believing that he re-
garded apprehension as merely successive in this sense. Such
a view fails to recognise that for Kant an indeterminate quan-
tum or whole can be intuited without successive synthesis.4
In the case of substance I am not sure whether Kant means
more than that the different accidents of a substance must
be successively apprehended;5 and this is manifestly true. We
cannot 'take up' all the accidents of a substance simultaneously.
If we take his statements to mean that apprehension is
merely successive, it can hardly be denied that his doctrine
is false. Even apart from the amount of space occupied by
a momentary sensation, I can at the same time feel a twinge
of pain, hear the barking of a dog a quarter of a mile away,
and see the shining of a star which has been extinguished for
a million years. No doubt all these processes take time, but
they occur together; and a cross-section of them, such as is
present in an atomic now, would contain elements of all three.
It would be impossible to regard such a cross-section as an
absolute unity, if by that is meant a unity which contains
no differences.
The point I wish to emphasise, however, is that this error —
1 To 'go through* (durchgehen) is here equivalent to 'expose' or
'set out* (expomeren). For the widest sense of the 'exposition' of
appearances, see A 416 = B 443.
2 For the whole argument, see Metaphysik, pp. 55-6.
3 To maintain this Kant would have to maintain that time was made
up of moments — a doctrine he consistently denies.
4 See A 426 n. ~— B 454 n.
6 It may be added that so far as anything is a determinate quantum,
its parts must be successively apprehended.
XLII § 2] SUBSTANCE 195
even if we were justified in attributing it to Kant — does not
affect his argument : firstly because there can be no doubt that
many things which we apprehend successively (for example
the sides of a house) are believed to be coexistent, and this
admission is all that Kant requires: and secondly because
we can never determine objective simultaneity merely from the
simultaneity of our sensations. In the example above, although
the sensations are simultaneous, the objective events are not;
for the dog may have barked a little before my pain, and the
star shone ages before the dog was born. Even when the
events perceived are simultaneous, we cannot determine this
by mere sensation apart from thought. Kant is quite right
in saying that by mere sensation or mere apprehension we can
determine neither objective simultaneity nor objective succession .
The special conditions or presuppositions necessary for
determining objective succession are dealt with in the Second
Analogy; those for determining objective simultaneity are
dealt with in the Third Analogy. Kant is at present concerned
with something more general, the ultimate condition of de-
termining any kind of objective time-relation (whether of
succession or of simultaneity). This general condition he
asserts to be the permanent.
§ 2. The Permanent and Time-determination
It is obvious that the position of any appearance in time
cannot be determined merely by reference to the permanent;
for just because the permanent is permanent, because it is the
same at all times,1 there is nothing in it to indicate any difference
in temporal position. Kant himself holds that differences in
temporal position are determined by the relations of appear-
ances to one another (before and after and along with), these
relations being objective when they are necessary, that is,
determined by causal law. What he is arguing at present
1 We shall find later (see § 8 below) that there is a sense in which the
permanent alone can change. I do not think that this affects my point ;
and it may be observed that Kant refers to substance as the unchanging
(das Unwandelbare im Dasein)\ see A 143 = B 183.
ig6 THE ANALOGIES OF EXPERIENCE [XLII § 2
is that apart from the permanent we could never experience
such relations. The permanent is, as it were, the background
against which we are aware of temporal relations.
In everyday experience we are aware of change against
a background of the relatively permanent. To take the simplest
(and according to Kant the most fundamental) case, that of
movement, we are aware that the sun is moving in relation
to objects on the earth.1 Hence the obvious objection may
be raised that for the perception of movement we require
something relatively, not absolutely, permanent; and some
commentators,2 supposing Kant to be concerned with the
question of measuring durations, point out that our measure-
ments depend, not on the permanent or unchanging, but on
the supposedly uniform movements of the heavenly bodies.
The question of how we measure durations seems to me
irrelevant. Kant is asking how there can be any durations for
us to measure, how we can be aware of changes which involve
objective succession and simultaneity; and I see no reason for
attributing to him the view that changes are measured by the
unchanging and not by their relations to one another. Indeed
it would surely be impossible to measure a change by its
relation to the unchanging. The question is simply how we
can perceive change at all.
Kant is perfectly well aware that objects on the earth are
themselves moving;3 and his statement about the movement
of the sun 4 is meant only as a pictorial and popular illustration
of his doctrine, from which he passes to the assertion that the
permanent of which he speaks can be found only in matter.
Another illustration is given in his lectures on Metaphysics,5
where he says that a sailor could never be aware of the ship's
motion, if the sea were moving along with it, unless there were
something permanent, as for example an island, in relation
1 See B 277-8. 2 E.g. Paulsen, Immanuel Kant, p. 182.
3 In a similar context Kant points out expressly that we can have
no experience of absolute rest or absolute motion. See M.A.d N.
i. Hauptstutk (IV 487-8), where the point is worked out in detail,
and compare 4. Hauptstucky Allgemeine Anmerkung fur Phanome-
nologie (IV 559). 4 B 277-8. 6 p. 37.
XLII §2] SUBSTANCE 197
to which the ship's motion could be observed. He there states
expressly that this is to be taken only as a crude comparison.
It is, however, much easier to be sure of what he does not
mean than of what he does mean. The permanent of which
he speaks is the quantity of matter, and he certainly believes
— as I imagine was believed generally at the time — that apart
from the conservation of matter physics is impossible.1 But
it is not enough to say that the permanent in this sense is
a necessary presupposition of physics. Kant is arguing that
it is a necessary presupposition of our experience of change;
yet no one could maintain that we are directly aware of a
constant amount of matter in all our perception of change.
What Kant seems to hold is that our perception of change
presupposes something permanent, although only by experience
can we discover what that something permanent is.2 The
relatively permanent as against which we do perceive change
is at first taken to be the absolutely permanent, but it fails
to withstand scientific criticism. With the advance of know-
ledge we are compelled to substitute something more satis-
factory, such as mass or energy. But unless we presuppose
something absolutely permanent, the unity of experience
would be impossible.3
On this point at least — whatever be his justification for it —
Kant is perfectly clear. The coming into being of some sub-
stances and the passing away of others wrould destroy the one
condition of the empirical unity of time.4 It would mean that
1 See Metaphysik, p. 34.
2 Just as our perception of an event presupposes a cause, although
only by experience can we determine what that cause is.
3 Similarly experience always presupposes causality, though our
empirical determination of actual causes may be imperfect.
4 A 1 88 — B 231-2. This I take to be the unity of the time in
which the world is actually experienced. The same point is made
also, even more forcibly in A 186 = B 229. If new substances were
to come into being — and the same principle holds if existent substances
were to disappear — the unity of experience, the unity of time, and the
unity of change would be gone. Kant's doctrine is fundamentally
opposed to the Cartesian doctrine that all conservation is creation,
that in every moment the world is created afresh.
i98 THE ANALOGIES OF EXPERIENCE [XLII § 2
appearances were related to two different and unconnected
times in which existence flowed as it were in parallel streams l
— which is nonsense. But there is only one time in which all
different times must be placed, not as coexistent, but as succes-
sive.2 This argument is the one which becomes predominant
in the second edition, and we are, I think, entitled to regard
it as the primary ground of Kant's theory. Indeed, since all the
Principles are supposed to rest on the nature of time, the proof
of permanence must find its basis in the nature of time.
On the other hand, it is important to observe, both here and
throughout the Analogies, that if Kant follows his theory
consistently, he cannot argue directly from the nature of time
(or space) to the nature of what is in time (or space). He must
on the contrary argue indirectly, that is, he must argue from
the relation of time (or space) to possible experience,3 and so
must endeavour to establish the conditions of experience.4
We may put this point in a different way. The time with
which Kant is concerned, since it is a condition of experience,
is the one time in which all objective time-determinations are.
All objective time-determinations, whether of succession or
simultaneity, must be found in an object, that is, must be
constituted by referring appearances to an object in which they
are related ; and only so can they be distinguished from merely
subjective or imaginary time-relations. Since time itself cannot
be perceived, experience requires a permanent object and
ultimately one permanent substratum for the whole objective
and phenomenal world.5
1 'neben emander', side by side.
2 A 188-9 = 6231-2. Kant is, I think, assuming that since absolute
time cannot be perceived, there can be for us one time only if there is
one permanent substance (or set of substances) in time.
3 Compare A 184 -= B 227-8, and A 736-7 = B 764-5. If he fails
to do this, his proof is 'dogmatic' and to be rejected.
4 Naturally enough, Kant does not make this point explicit in
every sentence, but we must not attribute to him a direct or dogmatic
argument when he leaves it to us to fill in the necessary qualifications.
6 This argument, stated here in a summary manner, is to be dis-
tinguished from a dogmatic argument which simply asserts that change
is a succession in the states of a substratum.
XLII § 3] SUBSTANCE 199
§ 3. The Permanence of Time
We get into new difficulties when we attempt to argue from
the permanence of time. It is no easier to regard time as per-
manent than to regard it as successive — if we suppose time
to endure, must there not be another time through which
it endures ? Nevertheless Kant is right in maintaining that the
time in which events occur must be a unity. We must be able
to determine the position of all events in relation to one another
in one and the same time, and this means that we must be able
to hold successive parts of time before us in one time. Kant's
ascription of permanence to time seems to mean no more than
this. Furthermore, we cannot regard existence as an indivisible
point between a non-existent past and a non-existent future.1
Existence must have quantity or duration in time, if experience
is to be possible; but once we admit any duration at all, it
seems difficult to deny a continuous and permanent duration.2
Kant, as I have pointed out, believed that permanent sub-
stances are to be found only in space.3 No permanent object
is given to us in inner sense, and for this reason he rejects
all attempts to prove that the soul is a substance. It would
therefore seem more satisfactory to rest the proof of substance
on the nature of space. Space is permanent amid all the changes
in time; and permanent substance, on Kant's view, might
be regarded as necessary to 'represent' or 'express' the perma-
nence of a space which, like time, cannot be perceived.4 Some-
thing like this view is expressed in the Metaphysische Anfangs-
grunde der Naturwissenschaft? and Kant's notes on his own
1 Dr. Broad even goes so far as to maintain that the past is 'real*.
See Scientific Thought, p. 66.
2 I suppose the modern doctrine avoids this by taking events as
ultimate, but I think Kant would want to carry further the analysis of
an event.
3 This view is already present in the first edition, e.g. in A 349-50.
4 The space and time which cannot be perceived are the absolute
space and time in which all things are, not the relative spaces and
times which we are immediately aware of through sensation. Compare
M.A.d.N. (IV 481).
6 Compare e.g. (IV 503) and § 7 below.
200 THE ANALOGIES OF EXPERIENCE [XLII § 3
copy of the first edition of the Kritik I show that at one time
he intended to re- write the argument in terms of space (or of
space and time). Such re-writing could not be confined to the
First Analogy — it obviously demands, for instance, a re-writing
of the chapter on the schematism of the categories. Perhaps
for this reason Kant changed his mind, and made the proof
of the second edition rest, even more than that of the first,
on the permanence of time. Nevertheless he indicates that the
proof ought to bring in space as the permanent in time; for
he takes our breath away by a later assertion that space alone
is permanently determined, while time, and therefore every-
thing in inner sense, is in constant flux !2
To bring in space would make the proof of substance more
complicated, but I think also more plausible. We must be able
to hold time together as a unity, if we are to be aware of space
as permanent through time3 — to state this is to state a necessary
condition of human experience. And Kant's argument might
be that since we can perceive neither absolute space nor abso-
lute time, there must be a permanent in the spatial objects
of experience to 'represent' or 'express' the permanence
of space in time.
It may be thought that on idealist principles we require
no more for Kant's purpose than a permanent knowing self.
This might perhaps explain our knowledge of the succession
of our own ideas, though I doubt whether it could explain our
knowledge of the world of spatial objects enduring through
an infinite time. But for Kant the history of the individual
mind is only a succession of appearances among other known
successions, and we could not be aware even of our own mental
history except against a background of the permanent in
space.4 There is nothing permanent in the empirical self
1 See Erdmann, Nachtrage LXXVII-LXXXIV, especially LXXX.
'Here the proof must be so expressed that it applies only to substances
as phenomena of outer sense. Hence it must be derived from space
which (with its determinations) is at every time.'
2 B 291 ; contrast A 143 — B 183 and B 224-5.
8 Or to experience objects in a space which must be the same at
all times. 4 See B 275 ff.
XLII § 4] SUBSTANCE 201
as it is known through inner sense ; and to suppose that we can
pass from the unity of apperception to the knowledge that
the soul is a permanent substance — this, according to Kant,
is nothing but a paralogism of reason. The permanent which
is the condition of our experience is to be found in objects
of outer sense and in them alone.1
§ 4. Substratum and Substance
Kant's argument amounts to this — that since time (or
space) is permanent, there must be something permanent
given in experience to represent or express an unperceivable
time (or space). The argument from time by itself has the
disadvantage that we can decide only empirically whether the
given permanent is to be found in objects of inner or outer
sense. If we argued, as I have suggested, from the permanence
of space in time,2 we might perhaps reasonably infer that the
permanent is to be found only in objects of outer sense, which
occupy space and last through time.
Even if we admit the validity of this argument for the
permanent, it may be objected that the permanent need not
be the substratum of appearances: all that we require is a
permanent appearance among the changing appearances. If
Kant means more than this — and surely he does mean more
than this — what is his justification for saying that the per-
manent must be in objects or appearances as their substratum ?
This seems to me the most difficult point in the whole
of Kant's argument. In the first edition he asserts straight
away that if we can determine objective succession and simul-
taneity only by relation to the permanent, succession and
simultaneity must be ways in which the permanent exists,
and that the permanent must be the substratum of the empirical
1 See the Paralogisms of Pure Reason, A 341 = B 399 ff., and also
the Refutation of Idealism.
2 This seems to me the correct presupposition of Kant's argument.
By appealing to the permanence of space we do not do away with the
reference to time, nor do we eliminate the necessity for holding
successive times together in the unity of one time.
VOL. II G*
202 THE ANALOGIES OF EXPERIENCE [XLII § 4
idea of time.1 In the second edition he takes time as the sub-
stratum of succession and simultaneity,2 and he seems to imply
that the permanent, as representing or expressing time, must
therefore be the substratum of successive and simultaneous
appearances.3 It is for this reason that he calls it substance,
and asserts that the real (that is, the given appearances) can
be thought only as its determinations.
In all this one thing at least is clear. Kant is not arguing
from the pure category (or the form of categorical judgement)
that the permanent must be the subject of all predicates and
therefore the substratum of all change. He is arguing, on the
contrary, that because the permanent is the substratum of all
change, therefore it is (in the world of phenomena) the ulti-
mate subject of all predicates.4 If this interpretation is sound,
his argument for a permanent substratum of change is inde-
pendent of the derivation of the categories from the forms
of judgement, although he doubtless thinks that when sub-
stance is described as the ultimate subject of predicates,
something is added to the view that it is the permanent sub-
stratum of change.
About this problem it is very easy to talk nonsense, but Kant
seems to believe that in order to represent the unity of time
(or the permanence of space in time) we require more than the
continuous ceasing to be and coming into existence of a quali-
tatively identical appearance. We require something which
neither comes into existence nor ceases to be. Coming into
existence and ceasing to be, or in one wrord change, is nothing
other than a way in which the permanent exists, and the
permanent is not merely one among many appearances, but
is the substratum of all appearances.
1 A 182-3 = B 22 5-6.
2 B 224. Substratum in this sense is equated with the permanent
form (or condition) of inner intuition ; compare also A 30 -- B 46.
3 It should, however, be observed that simultaneity and succession
are not related to time as accidents are to a substance; for they are
not 'modes of time itself.
4 That is to say, he is arguing, as we should expect, from the schema
to the category.
XLII § 4] SUBSTANCE 203
This view is confirmed by the general account given of
substance. Kant distinguishes sharply between a substance and
its accidents. The latter are only ways in which substance
exists,1 or ways in which the existence of a substance is posi-
tively determined.2 We do indeed distinguish the existence
of the accidents as inherence from the existence of the sub-
stance (which is subsistence)'? but this is only a method — and
a rather misleading method — of asserting that the accidents are
the ways in which substance exists. Kant says it is inevitable
that if we distinguish inherence and subsistence, we shall come
to think of the substance as existing apart from its accidents,
and the accidents as existing apart from the substance. The
whole history of the doctrine of substance bears out the truth
of this assertion, and he rightly rejects such a view as turning
a logical distinction into a real separation.4 He is always clear
that we know a substance only through its accidents, just
as it is the condition of human knowledge that we know a
subject only through its predicates.5
If a substance is known only through its accidents, it cannot
be merely one appearance among others and distinguished
from them solely by the fact that it is unchanging or perma-
nent. Such permanence, I take it, would in any case be for Kant
1 A 186 =r. 6229.
2 A 187 = B 230. Even negations are determinations of substance —
they express the not-being of something in substance, not the not-
being of substance itself. See A 186 = B 229. 3 A 186 = B 230.
4 He seems even to deny that we can rightly speak of a relation
between substance and accident; and for this reason he maintains
that the category of substance and accident is placed under the head
of relation, not because it itself is a concept of relation, but because
it is the condition of relations — that is, of time-relations, namely
succession and simultaneity.
6 See Metaphysiki p. 33. In this place he approves the view, which
he attributes to Locke, that substance is a support (Trager) of accidents,
and asserts that when we think of a substance as existing apart from
its accidents, we think of something quite unknown. He calls this
'the substantial' (das Substanxiale) and identifies it with 'something in
general' (etwas uberhaupt) or, in other words, with the transcendental
object (when that is regarded as other than the unity of its appearances).
The same view is present in A 414 — 6441.
204 THE ANALOGIES OF EXPERIENCE [XLII § 5
only the continuous ceasing to he and coming into existence
of a qualitatively identical appearance; and this would not
be sufficient for his theory. Whatever be the precise meaning
of 'substratum', and whatever be the adequacy of the Critical
proof, the view that substance is the permanent substratum
of all appearances must be regarded as an essential part of
his doctrine.
§ 5. Can Substance be Perceived?
If substance is the permanent substratum of appearances
and is known only through its accidents, we are faced with
a further difficulty. How can we know that substance possesses
a permanence which its accidents do not? Is the permanence
of substance something which cannot be perceived, although
it has to be presupposed as a condition of our experience
of objective change? Such a doctrine would be very peculiar;
for the reason why the permanent had to be presupposed
as the substratum of appearances was that time itself cannot
be perceived. If the permanent equally cannot be perceived,
what are we to make of Kant's argument ?
It seems clear enough that on Kant's view we must be able
in some sense to perceive, not only substance, but also the
permanence of substance ; the problem is to determine exactly
what that sense is. The permanence of substance is presupposed
by experience, and so is known a priori] but we must be able
to find the permanent in actual experience and to discover
examples of it by ordinary observation.1
That permanence can in some sense be observed is stated
or implied by Kant in several passages. For example, he
asserts explicitly that the permanence of matter as appearance
can be observed.2 We can apparently seek for permanence
1 The same doctrine holds of causality.
2 A 366 This is implied also in A 350. Kant also implies that we can
find by outer sense a permanent appearance (or intuition) in space:
see A 364 and B 412. We must not, however, take this to mean that
substance is only one (permanent) appearance among many other
(changing) appearances.
XLII § 5] SUBSTANCE 205
by a comparison of sense-perceptions, though this is not the
usual method for determining the presence of substance, nor
could it be carried out with sufficient completeness : no amount
of observation can establish the strict universality which
belongs to an a priori concept.1
We are given little help for the detailed working out of this
problem, but manifestly it has to be considered from the
point of view of common sense and of science as well as from
the point of view of philosophy.
It is always difficult to describe the point of view of common
sense or ordinary experience; for the plain man does not
make his presuppositions explicit to himself, but simply takes
certain things for granted. We all observe the motion of the sun
in relation to the unmoving earth, the motion of the ship
in relation to the unmoving island, and so on. More funda-
mentally, we all take it for granted that a thing remains the
same while its qualities change, and even that the physical
world is abiding or permanent amid its changes.
What is taken to be permanent may vary at different times
and for different purposes, although permanence is always
assumed and also to some extent observed. But it seems not
unreasonable to assert that what is taken to be permanent
is in general what fills space,2 and above all what may be
described as the solid.3 Observed qualities are taken to be
qualities of a solid which fills space, and even to occupy an area
which is identical with the surface of the solid.4 The perma-
nence of the solid is partly taken for granted and partly revealed
in its observed qualities. We all assume that a chair remains
1 Compare A 205 — B 250-1. The example of the weight of smoke
in A 185 = B 228 at least suggests that we could find empirical con-
firmation for our a priori presupposition.
2 'To fill space* is 'emen Raum erfitllen\ A mathematical triangle
may be thought to occupy space (einnehmen), but not to fill it. See
M.A.d.N. 2. Hauptstuck (IV 497).
3 I do not of course wish to suggest that for common sense there is
nothing permanent in water, fire, or air; but the solid is the most
typical case.
4 Compare Price, Perception, p. 143. This view cannot be maintained
on reflexion.
206 THE ANALOGIES OF EXPERIENCE [XLII § 5
the same when we are out of the room, and that on our return
we see the same chair and not another chair with precisely
identical qualities. We do so even if we find that the chair has
changed ; for example, if it is in a different position or has been
broken.
We get into difficulties only when we begin to ask what
it is that is permanent ; for so many of the observed qualities
manifestly are not. We discover, for example, that there is no
permanence of position: our geocentric theory of astronomy
must be given up in favour of one that is heliocentric, and
ultimately in favour of one that is relativistic. We discover also
that our solid bodies are lacking in the permanence which
we at first ascribe to them: even their most fundamental
qualities change, and we try to find permanence in something
more ultimate, in the elements of which they are composed,
in atoms, in mass or energy, and so on. This is the work of
science, but the principles at work seem to be still those which
were at work in our ordinary experience. Always the permanent
seems to be presupposed, and its presence is at least partially
confirmed by observation. Further knowledge produces fresh
dissatisfaction, and our view of what is permanent has to be
altered. We may even be tempted to ascribe permanence to
'a supposed I-know-not-what', which is a 'support' of acci-
dents;1 and this is not very far from abandoning the idea of
permanent substance altogether.
On Kant's view we must necessarily employ, whether
consciously or unconsciously, the concept of permanent
substance in space; for otherwise we shall destroy the unity
of time and the unity of experience, and we shall be incapable
of making any distinction between objective change and a
subjective succession of ideas. Permanent substance in space
he appears to identify with mass — the matter of the time;
but we must distinguish his general philosophical principle
from its special application at a particular stage in the develop-
ment of science. There would be nothing inconsistent with his
general principle, if mass should turn out to be unsatisfactory,
1 Compare Locke, Essay, Book II, Chap. XXIII, sect. 15.
XLII § 6] SUBSTANCE 207
and if we were compelled to put something else, for example,
energy, in its place.
On this interpretation what is present alike in common
sense, in science, and in the Critical Philosophy is the pre-
supposition that there must be a permanent in space, and that
this permanent is essentially what fills space: its presence
in space is thought to be confirmed, at all the different levels,
by actual empirical experience.
How do we know this permanent which fills space? We
know it, as we know everything else, by the co-operation of
thought and intuition. In all experience we combine or syn-
thetise given appearances in time and space in accordance with
certain a priori concepts, and we regard these appearances, thus
necessarily combined, as appearances of a permanent spatial
object.1 The permanence of what fills space is always pre-
supposed; but the character of what fills space is revealed, and
its permanence verified, most conspicuously in our observations
of impenetrability or resistance — not only impenetrability to
our own bodies, but also impenetrability to other bodies.
These observations give us our original unscientific conception
of solidity. They also give us, especially in conjunction with
observations of weight, the conception of matter (which Kant
himself accepts) as that which fills space by its powers of
repulsion and attraction, and is identified in a special sense
with 'the real'.
§ 6. The Quantum of Substance
In the Kntik of Pure Reason Kant is not entitled to take into
account empirical principles derived from observation.2 All he
can hope to prove is that in the real which fills space3 and time
there must be a permanent substratum of change. Any attempt
1 Causality is presupposed as well as substance, but this must be
considered later.
2 Compare the opposition between 'Transcendental Philosophy
and 'the universal science of nature' in A 171 ~ 6213.
3 The argument as stated by Kant cannot be said to justify us in
ascribing this importance to space, but I can see no other way of
giving a satisfactory account of his doctrine.
208 THE ANALOGIES OF EXPERIENCE [XLII § 6
to discover the empirical character of this permanent sub-
stratum, or to identify it with matter or mass or energy as
kno\\n to physical science — any such attempt belongs to
another enquiry, which may be called Rational Physiology.1
On the other hand if we eliminate all reference to physical
matter, his doctrine may appear to be empty and unimportant.
Is it possible for us to determine a priori any assignable char-
acteristic of the permanent which is the substratum of change ?
Kant appears to think that it is possible to do so, and in this
way to avoid any appearance of vagueness ; for in the second
edition he puts fon\ard a more precise and definite statement
of his meaning.2 He asserts that the quantum of substance
in nature can neither be increased nor diminished; and he
regards this as following directly from the fact that substance,
as the permanent substratum of all change, cannot itself change
in existence.3
It is far from easy to estimate the value of such a contention.
We do well to exhibit caution in accepting what may appear
to be facile claims to a priori knowledge, and such caution
is fully in accordance with the spirit of Kant himself.4 Most
commentators are inclined to dismiss this more concrete
assertion as an unhappy addition to Kant's general doctrine;
and they may be right in so doing. Certainly his statement
is much too summary, and in the absence of any further elucida-
tion or expansion it is perhaps hazardous to offer any explana-
tion or defence.
Nevertheless I have come to feel some doubt about the
usual way of interpreting this passage, and I am no longer
so sure that Kant is making a hurried and unjustifiable leap
1 Compare A 845-6 ---- B 873-4 and A 848 = B 876.
2 B 225 This is also expressed in the very formula of the Analogy
itself in B 224.
3 It is difficult to be sure of the significance to be attached to
'existence' in this connexion. Substance must exist at all times — sec
A 185 = B 228 — and so presumably must have at all times a constant
and abiding character, however much its accidents may change. This
constant character, so far as it can be known a priori, can only be its
quantum. 4 Compare A 175 = B 217.
XLII §7] SUBSTANCE 209
to the doctrine of the conservation of mass as accepted by the
science of his time. No doubt he found in this the empirical
embodiment of what he claimed to be a priori knowledge;1
but his alleged a priori knowledge ought to be of a character
so general that different embodiments might be found for
it as science continues its progress by its own empirical methods.
I can sec nothing in Kant's statement which justifies us
in refusing to interpret it in the most general way possible
so that it might apply to any empirical reality, whether mass
or energy or anything else, which science may discover to be
permanent in space. What he claims is that there must be a
permanent which fills space, and which must be permanent
in respect of its quantity. I have no wish to be dogmatic on
this question ; but I am inclined to think that if we can know
a priori that the real in space is permanent, we can know this
only in respect of that in the real of which alone we have
a piiori knowledge, and there is nothing \vhatever in the real
of which we have a priori knowledge except its quantity.2
If such be the presupposition of Kant's argument, I do not
say that his argument is sound; for there are far too many
pitfalls in the \vay. But I think \\e can affirm that his argument
is not to be summarily dismissed, and even that without some
addition of this kind his general doctrine \vould be so vague
as to be almost useless.
§ 7. Material Substance
If \\e are to understand Kant's theory we must look at it
in its concrete form, even although this involves an empirical
side which, strictly speaking, has no place in the Kntik of Pure
Reason. He identifies substance with matter as known to the
science of his time, and finds in the contemporary doctrine
of the conservation of matter the empirical confirmation
of his more general principle that the quantum of substance
in nature can neither be increased nor diminished.
1 This is evident even in the first edition ; see A 185 = B 228.
2 Compare A 176 = B 218. The quantity of the real as such is
intensive.
210 THE ANALOGIES OF EXPERIENCE [XLII §7
This is shown by his account of the philosopher who was
asked the weight of smoke.1 The answer given was that the
weight of smoke could be determined by subtracting the
weight of the ashes from the original weight of the fuel which
had been burned.2 If, however, we wish to follow Kant's theory
in detail we must go to the Metaphysiche Anfangsgrunde der
Naturwissenschaft, a work which attempts to combine the
principles of the Critical Philosophy with a bare minimum
of material derived from empirical observation.3 It is con-
cerned only with objects of outer sense and in particular with
the matter of which they are composed.
In this work material substance is described as that in space
which is movable in itself — that is, in separation from every-
thing else which exists outside it in space.4
It must be remembered that Kant's account of matter
presupposes the truth of all the Principles of the Under-
standing and especially of the three Analogies. When he
proves matter to be substance, he starts from substance, not
as meaning the permanent,5 but as meaning the ultimate
subject of existence — the addition of the words 'of existence'
1 A 185 = 6228. For the origin of
/^/oc (Vol. II, p. 203, of Tcubner edition).
2 On the margin of his copy of the Kntik Kant added 'How did he
know this? Not from experience*. See Nachtrage LXXXV.
3 This work was published in 1786 just before the publication of
the second edition of the Kntik. There Kant deals with matter under
the heads of quantity, quality, relation, and modality — these four heads
giving us respectively (i) phoronomy (the pure theory of motion),
(2) dynamics, (3) mechanics, and (4) phenomenology. He starts from
the empirical fact that the fundamental determination of any object
of outer sense must be motion ; for it is by motion alone that outer
sense can be affected (IV 476). Matter is described under the four
heads as follows* (i) matter is the movable in space; (2) matter is the
movable so far as it fills space ; (3) matter is the movable so far as, qua
movable, it possesses moving force ; and (4) matter is the movable so
far as, qua movable, it can be an object of experience. See M.A.d.N.
(IV 480, 496, 536, 554).
4 M.A.d.N. (IV 502).
8 Perhaps the reason for this is that the doctrine of the conservation
of matter is to be proved later.
XLII § 7] SUBSTANCE 2 1 1
is unusual1 — which is never a predicate. 'Matter is the subject
of everything which can be reckoned to the existence of things
in space; for apart from matter no subject could be thought
except space itself. The concept of space, however, is not the
concept of any existent, but is merely the concept of the
necessary conditions of the external relations of possible
objects of outer sense. Therefore matter, as the movable in
space, is substance in space'.2
Kant then argues that all the parts of material substance,
so far as they are themselves subjects, and not merely predi-
cates of other matters, must themselves be substances. The
parts are, however, subjects, if they are themselves movable3
and are consequently something existing in space independently
of their combination with other adjacent parts of material
substance.4 Therefore the movability of matter, or of any part
of it, is a proof that the movable, and every movable part
of it, is substance.5
To speak more generally — Kant's view is that since material
substance is spread out in space, its parts must be outside one
another. These parts, since they can be moved, or separated
from the whole of which they are parts, must themselves
be substances.6
Kant clearly regards the scientific idea of matter as develop-
ing from the commonsense idea of solidity or impenetrability
which is revealed to us by the sense of touch.7 Matter is the
movable which fills space, and it does so, not in the sense
in which a mathematical triangle may be thought to occupy8
1 Kant wishes to refer to a real, and not merely a logical, subject.
Sec B 129.
2 M.A.d.N. 2. Hauptstuck (IV 503). Compare the argument I have
suggested in § 3 above.
3 'wenn siefiir sich beweghch . . . smd.'
4 fausser threr Vcrbmdung mil under en Nebenteilen.'
5 M.A.d.N. 2. Hauptstuck (IV 503).
6 M.A.dN. 3. Hauptstuck (IV 542). This explains how Kant can
pass from Substance' to 'substances' in A 184 = B 227.
7 M.A.d.N. 2. Hauptstuck (IV 510).
8 'ewnehmen.' To fill space is 'einen Raum erfullen'. See M.A.d.N.
2. Hauptstuck (IV 497).
212 THE ANALOGIES OF EXPERIENCE [XLII §7
space, but by resisting the penetration of other movables.1
To penetrate into space is a motion — in the initial moment
it may be called a tendency to penetrate— and to resist this
motion is to cause its diminution or reduction to rest. Resist-
ance— for reasons into which I need not enter — is therefore
to be regarded as itself a cause of motion, and a cause of motion
is called a moving force.2 Hence matter fills space through
moving force,3 and the fundamental moving forces by which
it does so are those of repulsion and attraction.4
The quantity of matter is the aggregate5 of the movable
in a determinate space. So far as all its parts are considered
as working (moving) together in the same direction, it is called
'mass'. A mass of determinate shape is called a 'body' (in the
mechanical sense).6 The quantity of matter is measured
through the quantity of motion at a given velocity.7 The
quantity of motion of a body (that of a point consists only
in a degree of velocity) at the same velocity is measured through
the quantity of the matter moved. These two statements
do not constitute a vicious circle; one explains the meaning
of a concept, the other its application to experience. The
quantity of the movable in space is the quantity of matter ; but
the quantity of matter (the aggregate of the movable) shows
itself in experience only through the quantity of motion at an
equal velocity (for example, through equilibrium).8
I mention these details — which I do not profess to under-
stand, and which are perhaps themselves not wholly intelligible
apart from the whole argument from which they have been
extracted — in order to show the background for Kant's view
1 M.A.d.N. 2. Hauptstuck, Erkl. i (IV 496).
2 'bewegende Kraft.'
3 This presupposes the doctrine of the Second Analogy.
4 M.A.d.N. 2. Hauptstuck (IV 497 ff.). This is simply an empirical
fact.
6 'die Menge*. This is a whole whose parts are outside one another.
See A 163 — B 204 and compare M.A.d.N. 3. Hauptstuck (IV 539).
6 M.A.d.N. 3. Hauptstuck, Erkl. 2 (IV 537).
7 M.A.d.N. 3. Hauptstuck, Lehrsatz i (IV 537). I omit the proof of
this. 8 M.A.d.N. 3. Hauptstuck (IV 540).
XLII§8] SUBSTANCE 213
that the necessary permanence of substance is realised in the
conservation of matter. The quantity of matter is, according
to Kant, the quantity of substance in the movable, and is not
the quantity (or degree) of a quality of substance (such as
repulsion or attraction).1 The quantity of substance is the mere
aggregate of the movable, the movable being what constitutes
matter; for it is only this aggregate of the moved which, with
the same velocity, can give a difference in the quantity of
motion. For reasons into which again I do not enter, the
quantity of substance in matter can be estimated only mechan-
ically (that is, through the quantity of the motion belonging
to the matter), and not dynamically (that is, through the
quantity of the originally moving forces.)2
§ 8. The Conservation of Matter
From this Kant goes on to establish the three laws of mech-
anics, the first of which is especially germane to the First
Analogy.3 '//* all changes of corporeal nature the quantity of
matter in the whole remains the same, unmcreased and undi-
Kant's proof presupposes it to have been proved in the
Kntik that amid all the changes of phenomenal nature sub-
stance is permanent, which he here takes to mean that no
substance can come into being or pass away. Here, as he says,
1 M.A.d.N. 3 Hmiptstuck (IV 540). This shows clearly that the
permanent is not for Kant one appearance among others, although it
* shows itself in experience'.
2 M.A.d.N. 3 Hauptstuck (IV 541). The quantity of the originally
moving forces is a degree.
J The second law is that all change of matter has an outer cause —
every body endures in its state of rest or motion, in the same direction
and with the same velocity, if it is not compelled through an outer
cause to abandon this state. See M.A d.N. (IV 543).
The third law is that in all imparting of motion action and reaction
are always equal. See M.A.d.N. (IV 544).
The second and third laws are intended to stand to the Second and
Third Analogies, as the first law stands to the First Analogy.
4 M.A.d.N. 3. Hauptstucky Lehrsatz 2 (IV 541).
214 THE ANALOGIES OF EXPERIENCE [XLII §8
he has to show only what substance in matter is. The proof
runs as follows.
In all matter the movable in space is the ultimate subject1
of all the accidents which inhere in matter ; and the aggregate
of this movable, whose parts are outside one another, is the
quantity of substance. Therefore the quantity of matter, as
regards its substance, is simply the aggregate of the substances
of which it consists. Therefore the quantity of matter cannot
be increased or diminished, unless a new substance comes
into being or passes out of being. But amid all change of matter
substance never comes into being or passes out of being.
Therefore the quantity of matter can neither be increased nor
diminished, but remains always the same in the whole; that
is, it endures somewhere in the world in the same quantity,
although this or that matter can be increased or diminished
through addition or subtraction of its parts.2
This proof (which concerns substance only as an object of
outer sense) rests upon the view that the quantity of an object
in space must consist of parts outside one another ; that these
parts, so far as they are real (that is, movable), must necessarily
be substances; and that consequently the quantity of spatial
substance cannot be increased or diminished without the creation
or extinction of substance, which is impossible.3
1 He ought, I think, to say * substance*.
2 M.A.d.N. 2. Hauptstuck, Lehrsatz 2, Beweis (IV 541-2). Pnchard
(Kant's Theory of Knowledge, p. 273) maintains, following Cook Wilson,
that Kant's doctrine implies that there may be creation and extinction
of substances. I cannot see the justification for this view, if a substance
is made up of substances, and its parts can move independently. For
Kant constant quantity is a consequence of the permanence of sub-
stances, not an equivalent expression for it.
3 This argument, Kant believes, would not hold if we supposed
the soul, an object of inner sense, to be a substance ; for such a sub-
stance could have a quantity (that is, an intensive quantity) which did
not consist of parts outside one another, and since its parts would not
therefore be substances, it could increase or diminish without trans-
gressing the principle of the permanence of substance. Kant uses this
doctrine in order to refute attempts to prove the immortality of the
soul on the ground that the soul is a simple substance. Compare
B4i3ff.
XLII§9] SUBSTANCE 215
§ 9. The Empirical Criterion of Substance
I set forth this proof, not in order to defend its validity,
but to show where Kant finds in experience the permanent
whose necessity he believes he has proved. The doctrine of
substance, like that of causality, is confirmed by empirical
observation, and receives concrete meaning only in experience.
Its necessity can never be proved by experience, but must be
proved, if at all, by reference to the conditions of possible
experience (particularly the unity of time and space).
Kant himself points out that to establish the permanence
of any substance by comparing our different sense-perceptions
would be a very inadequate method.1 We do not use observed
permanence as our empirical criterion of substance. A better
and easier empirical criterion of substance is action.2 This
is mentioned by Kant, not in the First Analogy, but in the
Second, because it presupposes the truth of causality.
Causality leads to the concept of action, and action to the
concept of force, and thereby to the concept of substance.3
Kant excuses himself from working this out in detail as inappro-
priate to a mere Kritik of pure reason, but he asks himself
how we can make an inference from action to the permanence
of what acts.4
This question can, Kant believes, be easily answered by his
1 A 205 ~ B 251.
2 'Handlung.' A 204 = B 249; A 205 = B 250.
3 A 204 = B 249. Causality is the quality of a substance, in so far
as substance is regarded as the cause of accidents. Action (which can
be ascribed only to substances) is the determination of the force of a
substance as a cause of a certain accident, and it must have a real
effect (unlike power or Vermogen, by which we represent the possibility
of force). 'Force* (Kraft) is used for the relation (respectus) of substance
to the existence of accidents, in so far as substance contains the ground
of these accidents. We know forces only through our observation of
changes, and it is the duty of science to reduce forces to as few funda-
mental forces (Grundkrafte) as possible.
I take these definitions from Metaphysik, pp. 34-5, but it must be
remembered that these lectures are printed from students' notes, and
their accuracy (from internal evidence) is not always to be relied upon.
4 A 205 = B 250.
2i6 THE ANALOGIES OF EXPERIENCE [XLII §9
Critical method. Action means1 the relation2 of the subject
of causality to its effect. Every effect consists in an event, and
therefore in the transitory;3 hence the ultimate subject of the
event or the effect is the permanent which is the substratum
of everything that changes. The reason alleged for this is that
— according to the principle of causality — actions are always
the first grounds of all change4 (or exchange) of appearances, and
cannot therefore lie in a subject which itself changes5 in the
sense in which appearances change ; for then it would be neces-
sary to have other actions and another subject which determined
this change.6
This argument is not clear without an explanation of what
is meant by the 'subject of causality' and its relation to the
permanent substratum of change. Kant, however, affirms as
his conclusion that the first subject of the causality of all
coming into being and passing away (in the field of appear-
ances) cannot itself come into being or pass away.7 Hence the
presence of action gives a sure ground for asserting the presence
of empirical necessity8 and permanence in existence, and there-
1 'bedeutet.'
2 If this relation is identified (Metaphyiik, p. 34) with force, action
(as a determination of force) ought to be a determination of that
relation, not that relation itself.
3 The transitory 'signifies' (bezeichnet) time considered as successive,
just as the permanent in appearances 'expresses' or 'represents' time
considered as permanent.
4 The word here is ' WechseV, which implies an exchange of states of
a substance. See § 10 below. 6 'wechselt.'
6 ' Wechsel.' Kant's argument in certain respects bears a resemblance
to the argument that motion piesupposes a prime mover which is not
itself moved. This argument was used by St. Thomas as a proof of
the existence of God (see Sum Theol 1,11,3, and compare Sum. c. Gen.
XIII), and appears to be of the type rejected by Kant m the Anti-
nomies. No doubt there are differences in the two cases, but I
feel so uncertain of the present argument that I prefer to make no
comment.
7 A 205 = B 251. This statement is equivalent to the statement
that the first subject of causality does not admit of change in the sense
of exchange (Wechsel).
8 'Empirical necessity' would seem to be the necessity which is to
be found in the phenomenal world of experience.
XLII§io] SUBSTANCE 217
fore the presence of substance as an appearance (substantia
phaenomenon).1
§ 10. The Concept of Change
The concept of change has to be interpreted2 in the light of
the doctrine that succession can be determined only in relation
to the permanent.3 Coming into being and passing away are
not to be taken as changes of what comes into being and
passes away. A change is a way of existing4 which follows upon
another way of the same thing's existing. That is to say there
is an exchange, or substitution,5 of one state6 of a thing for
another state of that thing, but the thing itself must remain the
same thing. We cannot say that a thing has changed, unless
it remains the same thing; and we can put this paradoxically
by saying that it is only the permanent, or substance, which
changes, while the transitory, or the accidents, do not change,
but rather are exchanged, for one ceases to be and another
takes its place.7
1 A 206 - B25i.
2 A 187 = B 230. The correction or interpretation (Beruhtigung) —
not the 'justification' (Berechtigung) as Pilchard translates it — of the
concept of change rests upon this doctrine of permanence. Prichard
maintains (Kant's Theory of Knowledge, p. 274) that Kant's method
here is a dogmatic argument which proves the necessity of a permanent
substratum by an analysis of the nature of change. I do not sec how
the passage can he so interpreted in view of its context, for Kant is
here explaining how change is to be understood in the light of the
doctrine that has been established. His previous argument does not
rest on a definition of change, but on the contention that there can
be no experience of objective succession unless objective succession is
taken to be a change in or of the permanent. If the argument rested on
a definition of change, it would be open to Lord Balfour's objection
that we may very well be content with 'alternation' in place of 'change' ;
see A Defence of Philosophic Doubt, p. 114.
3 The permanent is only one of the conditions of determining
succession, but it is a necessary condition.
4 'ewe Art zu existieren.* 6 'Wechsel.'
6 'Zustand.' This word has a temporal significance. See Metaphysik,
PP- 34~5- A timeless object has no states.
7 This point is difficult to put clearly owing to the ambiguity of
words. Kemp Smith uses the word 'alteration' for what I call 'change',
2i8 THE ANALOGIES OF EXPERIENCE [XLII § n
In the light of this1 we can say that when we perceive a
change, we perceive a change in a permanent substance, and
never an absolute coming into being or passing away. In our
empirical knowledge it is always the permanent which makes
possible the idea of a transition from one state to another,
or from not-being to being ; and these states are always recog-
nised as being exchanged for one another in the permanent.
This is, I think, empirically true; what we perceive — or seem
to perceive — is a thing changing colour, not one colour and then
another. Kant reinforces this statement by insisting that since
we cannot perceive an empty time, we cannot see a coming
to be except by reference to what was before; and he argues
that if we attach what comes to be to what was before— as
we must — we are obliged to regard what was before as enduring
up to the coming to be, and what comes to be can be regarded
only as a determination of what was before, that is, of the
permanent. The same is equally true as regards passing away,
for we cannot perceive an empty time after such a passing
away.2
§ ii. Science and Experience
Kant believes — if I may attempt to summarise the results
of this difficult discussion — that his doctrine of permanent
substance is a necessary presupposition, not only of Newtonian
physics, but of ordinary everyday experience. At first sight
this seems difficult to accept, but perhaps the scientific notion
of substance, like the scientific notion of causality, is the result
of clarifying a concept which is assumed without question by
common sense. The world which is revealed to us in experience
and 'change' for what I call 'exchange*. The German words
are 'Veranderung* and 'WechseV. Watson translates them as 'change*
and 'alternation1, which seems to me better than Kemp Smith's
terminology.
1 A i88 = B23i.
2 All this confirms the view that Kant is not arguing from a definition
of change, or from an analysis of the concept of change, but from the
conditions of our experiencing an objective temporal order or
succession.
XLII§u] SUBSTANCE 219
certainly seems very different from the succession of unrelated
impressions and ideas to which it is reduced by the analysis of
Hume. What we seem to perceive is not a colour, but a coloured
surface or a coloured body ; and when we are aware of a change
of colour, we seem to be aware not merely of one colour and
then another colour, but of a permanent body which changes in
colour.1
No doubt such bodies are regarded by common sense as
only relatively permanent, and the common-sense concept of
body is extremely crude in comparison with that of science.
Nevertheless the solid bodies which for common sense possess
the changing qualities revealed to our senses are essentially
what fills space;2 and science in determining more precisely,
the character of what fills space, not only refines — and perhaps
even refines away — the concept of body, but gives a new and
precise meaning to the permanence which bodies are supposed
to possess.
If Kant could be said to have proved that the permanence
of what fills space is a necessary condition of our experience
of succession in time, he would have given an answer to Hume;
and the importance of his principle would be enormously
increased if he were justified in deducing as a consequence that
the quantum of substance in nature can neither be increased
nor diminished. Further than this, as Kant recognises, it
is impossible to go without calling in the aid of empirical facts ;
it belongs to science alone to determine the accidents of sub-
stance, as it belongs to science alone to determine the cause of
any given effect.
1 Most changes in the spatial world we regard as changes of bodies,
and perhaps this might be extended to all changes, although there is
clearly need of a separate discussion for such changes as are observed
in a flash of lightning or in a bird's song.
2 In all experience, as we combine the given appearances in one
space and time by means of the transcendental synthesis of imagina-
tion, we combine our given sensa as accidents or qualities of what is
supposed to fill space ; and there is much to be said for the view that
such acts of combination are a priori, that is, they do not depend on the
particular character of the given sensa.
220 THE ANALOGIES OF EXPERIENCE [XLII § n
Kant's science is now superseded, and we need attach no
importance to the detailed theories which he accepted. What
we have to consider is his central doctrine — that if science is
to be science, and if experience is to be experience, it must
necessarily employ the concept of substance and accident as
well as the concept of cause and effect.1 I confess that in the
present condition of science it is difficult for one who is not a
scientist — and perhaps impossible for one who is— -to share
Kant's belief; but I think it not unreasonable to ask whether
these concepts are being definitely abandoned in favour of
others, or whether they are being modified and corrected with
the advance of knowledge. That Kant's conclusions are not yet
wholly superseded is shown by a statement of Emile Meyerson,
himself not the least distinguished among modern exponents
of the philosophy of science, in which he asserts of the attitude
of the most advanced physicists that it 'confirme nettement la
supposition que la science, la raison scientifiquey aspire profondement
d concevoir un reel de substances en tant que substrat et explication
des phenomenes changeants. Tout pas accompli dans la direction
opposee apparait au savant comme un sacrifice, un renoncemenf?
If language so Kantian can be used of the fundamental concepts
of modern science, it is still worth enquiring into the reasons
by which the Critical Philosophy attempted to establish the
necessity of these concepts.
1 I think we must take this to imply, not only the permanence of
substance, but its permanence in regard to quantity; and this means
that the quantum of the real which fills space cannot be increased or
diminished. If we reject this addition, Kant's doctrine loses much of
its importance.
2 Quoted in Mind, N.S. Vol. XLI, No. 163, July 1932, p. 382.
CHAPTER XLIII
THE SECOND ANALOGY
§ i. The Principle of Causality
In the second edition the Principle established by the Second
Analogy is called cthe principle of temporal succession in
accordance with the law of causality'. In the first edition it
is called 'the principle of production',1 where production
seems to be equivalent to 'causation*.
The formula of the second edition is as follows: All
changes* take place in conformity with the law of the connexion?
of cause and effect*
The law of cause and effect has for long appeared to be
one of the most fundamental, if not indeed the most funda-
mental, of all the presuppositions accepted alike by science and
by ordinary experience ; and although its universality even in
the physical world appears to be questioned to-day by physicists,
as it has in the past been questioned by theologians, neverthe-
less to set it aside altogether, without putting something in
its place,5 would deprive us of the main clue by which we have
1 'Erzeuguiig.' This word, I think, like the English word 'production',
implies force or activity in the cause.
2 'Veranderungen * This has been explained in A 187 — B 230 as
involving the exchange (or succession) of the determinations of a
permanent substance.
3 'Verknupfung.' Connexion, or nexus, involves a synthesis of
heterogeneous elements which necessarily belong to one another.
See B 201 n.
4 B 232. In the first edition the formula is: Everything that happens
(that is, begins to be) presupposes something upon which it folloivs in
accordance with a rule. See A 189. 'To happen' is to be an objective
event.
5 It is not always easy to draw a sharp distinction between inter-
preting an old concept in a more satisfactory way and putting a new
one in its place. We must in any case hold to-day that the concept of
causality requires remterprctation, or at the very least that the mean-
ing of the concept cannot be taken as obvious and in need of no further
analysis.
222 THE ANALOGIES OF EXPERIENCE [XLIII § i
sought to understand the nature of the world. Hence it would
be difficult to exaggerate the importance of a valid proof of
causality, which quite certainly can never be given us by
ordinary inductive methods, since in such methods causality
(or something akin to causality) is already presupposed. It
wTould also be difficult to exaggerate the importance which
Kant's proof has in the system of the Critical Philosophy;
for it is here, more than anywhere else, that we must find the
answer to Hume, and it is here that the doctrine of the Trans-
cendental Deduction attains its most characteristic and most
fundamental application.1
In such a case we are entitled to demand that the argument
offered us should be water-tight. There ought to be no doubt
about its interpretation, and it ought to be capable of with-
standing a cool and sceptical scrutiny such as Hume brought to
bear on everything which claimed to be a priori knowledge.
Unfortunately there is a real difficulty in understanding
some of Kant's statements, and a still greater difficulty in
understanding the relation of his statements to one another.
To unsympathetic critics it may easily seem that he is one of
those philosophers who conceal the weakness of their argument
under a cloud of words. I believe, on the contrary, that his
obscurity is due to the fact that he is struggling with new and
difficult thoughts. I believe also that, even if he is in error,
there is much in his view which is worthy of serious considera-
tion.
One point is perfectly clear. Kant is arguing that if we are to
distinguish the objective succession of events in the phenomenal
world from the subjective succession of our ideas, we must
regard the former succession as necessarily determined, that
is to say, as governed by the law of cause and effect. This con-
tention he does not claim to be self-evident. It depends on
1 This claim may be made also for the Third Analogy (as combining
in itself the First and Second Analogies), but the Third Analogy
seems in some ways little m6re than an application or extension of the
principles already established, and the number of arguments brought
forward in the Second Analogy shows that for Kant the real crux of
his doctrine is to be found here.
XLIII § i] THE SECOND ANALOGY 223
Critical doctrines which have already been established; and
what we want to know is the precise nature of the Critical
doctrines presupposed and their precise relation to the con-
tention which we have now to consider.
It might be thought that objectivity has already been shown
to involve necessity, and that consequently objective succession
must be necessary succession. But in that case Kant's elaborate
proof would be superfluous. All that Kant claims to have shown
is that appearances, to be appearances of an object, must be
united in the synthetic unity of apperception, or must have
that necessary synthetic unity without which they cannot be
thought by one mind.1 This necessary synthetic unity must
indeed for Kant be such that it can be thought in all the forms
of judgement; for the forms of judgement are the forms of
synthesis without which thought is impossible, and there are
no objects apart from thought. But Kant is not arguing that
because we must be able to judge any object under the form
'if A, then BJ, therefore every object must be governed by the
law of cause and effect.2 On the contrary, the hypothetical form
of judgement is for him an empty form awaiting an object ;
and what we now have to prove is that all objects given to us
under the forms of space and time must have a characteristic
which enables them to be judged by the hypothetical form of
judgement. That characteristic is necessary succession, and the
proof of necessary succession must be a proof independent of
the form of judgement.
Kant is certainly presupposing that space and time are forms
of sensibility, and that appearances given under the forms of
space and time are therefore not things-in-themselves, but
appearances of things-in-themselves to human minds. There
can be no reasonable doubt that he regards this presupposition
as essential to his argument. He also believes all objective com-
1 I have already pointed out in Chapter XXX § 3 that this contention
remains extremely vague unless we can describe this synthetic unity
in detail.
2 Such an argument would be manifestly invalid, since the hypo-
thetical form of judgement involves no reference to time.
224 THE ANALOGIES OF EXPERIENCE [XLIII §2
hination and connexion of appearances to be determined by a
transcendental synthesis of imagination working through
the medium of time.1 What he has to show is that if we are to
experience objective changes in one common homogeneous time
whose parts succeed one another, there must be a succession
of appearances which is necessary, and so is governed by the
law of cause and effect.
§ 2 . The Six Proofs of Causality
Kant shows his sense of the importance of the present
argument by a multiplication of proofs \\hich recalls the method
of the Transcendental Deduction. We have, as usual, a proof
added in the second edition, \\hile in the first edition \\e have
what are commonly regarded as five successive proofs.2 Thus
\\e have:
Proof I B 232-4 (t\\o paragraphs).
Proof II A 189-94 — ^ 234~39 (four paragraphs).
Proof III A 194-5 — B 239-40 (two paragraphs). This is
followed by a third paragraph of a more general character
(A 195-6 — B 240-1), which cannot be considered as belonging
specially to Proof III.
Proof IV A 196-9 — B 241-4 (three paragraphs).
Proof V A 199-201 -= B 244-6 (three paragraphs).
Proof VI A 201-2 -- B 246-7 (one paragraph).
This multiplicity of proofs has given rise to the theory that
they \\ere composed at different times and represent different
levels of Kant's thought. As such theories of origin are, in my
opinion, of no help for the understanding of the argument, I
1 No doubt he believes also that this transcendental synthesis of the
imagination is itself determined by the pure categories, and in par-
ticular by the pure category of ground and consequent , but I do not
think this is one of the premises of his argument. On the contrary,
this doctrine is fully established in regard to ground and consequent
only when it has been proved that all objective succession is necessary
succession.
2 This division I take from Adickes in his edition of the Kritik. It ia
accepted by Kemp Smith.
XLIII § 3] THE SECOND ANALOGY 225
propose to ignore them. It should, however, be noted that
these proofs are not to be regarded merely as different versions
of the same proof added arbitrarily to one another. If we con-
sider the first edition by itself we have at least some appearance
of development. Proof II (the first in the first edition) develops
the argument as a whole ; Proof III is an indirect proof stating
the impossible consequences which follow if the principle of
causality is denied ; Proof IV at least professes — if it does not
altogether carry out its professions — to appeal to actual experi-
ence for confirmation; Proof V brings out and elaborates the
dependence of the argument on the nature of time ; while Proof
VI is intended to be a summary, and a much-needed summary,
of the main points or 'moments' of the argument. I can see no
reason wrhy Kant — whose method of writing is very different
from that of Professor Moore or Professor Prichard — should
not have composed this series of arguments in the order in
which they are printed, and Proof IV is the only one which
in my opinion can reasonably be regarded as superfluous.1
§3. The First Proof
The proof added in the second edition2 begins with an
introduction which is clearly intended to suggest that the
Second Analogy rests on the First Analogy as a necessary
presupposition. This is not made explicit in the proofs them-
selves; but Kant presumably held that only a belief in per-
manent substances filling space entitled him to assume, as he
does, a contrast between the simultaneous characteristics of
a house and the successive characteristics of a moving ship.
The introduction is a 'reminder'3 of what we have already
1 It may be observed that this multiplication of proofs is not only
known to have been a feature of Kant's teaching : it is also explicitly
present, though not to the same extent, in such an early work as the
Nova Dilucidatw, see Sectio III (I 410-11).
2 B 232-4. In the case of the Second Analogy I deal first with the
proof given in the second edition because its importance might fail
to be appreciated, if it were considered as the last of six proofs. As
the terms employed have been already defined, this course does not
suffer from the usual disadvantages. Compare Chapter XXXVII § i.
8 B 233, * Vorerinnerung*.
VOL. II H
226 THE ANALOGIES OF EXPERIENCE [XLIII § 3
learnt1 — that succession (or exchange) of appearances is only
a 'change* of permanent substances, that is, a successive
being and not-being of the determinations of a substance
which does not itself either come into being or pass away,
but whose existence is positively determined in different
ways at different times.2
Kant's proof runs as follows :
I. I perceive that appearances follow one another; and
this means that at different times I perceive different states
of the same thing or things.3 Hence in sense-perception of
this kind I am connecting4 two different sense-perceptions
or appearances5 in time.
II. Connexion (or nexus) is a species of combination or
synthesis necessary for knowledge of objects. It is never the
work of mere sense or intuition, but is the product of a syn-
thetic powrer of imagination* which determines inner sense
in regard to its time-relations.7
1 In A 187-8 = B 230-1. See Chapter XLII § 10.
2 Kant's argument may seem 'dogmatic* in this passage, because he
says that the concept of change presupposes one and the same subject
as existing with two opposite determinations, and therefore as endur-
ing I think, however, that this analysis of the concept of change is
for Kant a consequence of establishing the necessity of permanent
substance, and not a premise from which such a necessity is proved.
3 B 233. The reference to 'things* shows that Kant considers himself
now entitled to assume more than Hume admitted. Hume admitted
only consciousness of a succession of appearances. Kant believes
himself to have proved that we are justified in ascribing successive
states to a permanent substance or substances.
The 'opposition* attributed to states of the same thing I take to be
manifested in difference.
* 'verknupfe.' This is used in the technical sense to indicate 'con-
nexion* or 'nexus'. See B 201 n.
6 I take 'sense-perceptions* to be here equivalent to 'appearances*.
6 Here as so often sense-perception is connected (if not identified)
with the synthesis of apprehension, which is the work of imagination.
7 This last clause might seem to imply that the connexion so far
is subjective. Inner sense is determined so far as imagination succes-
sively brings different appearances before the mind. Kant may,
however, have in mind an objective connexion. In that case he goes
on to explain that it involves more than imagination.
XLIII § 3] THE SECOND ANALOGY 227
III. Imagination uncontrolled by thought can combine
appearances in different ways, either B after A or A after B.
As far as mere imagination is concerned, although we are
aware that we are imaginatively putting appearances in a
particular temporal order, we cannot be aware that the appear-
ances are states of an object and occur in that order independently
of our imagination. Hence sense-perception, so far as it is
a synthesis of the given by means of mere imagination, does
not determine the objective temporal relation of successive
appearances.1
Whatever be the difficulties in this assertion, Kant is clearly
right, if he is saying that neither by mere sense nor by mere
imagination, nor by any combination of the two, can we
determine the objective order of events.
Kant's reason for this assertion is the doctrine which lies
at the root of all the Analogies — that time itself cannot be
perceived. If time itself could be perceived, we could, he
believes, determine in relation to it the order of appearances
in the ob;ect itself, and this process of determining would be
1 There is a whole series of subjective orders distinct from the
order which we believe to be objective. Thus the subjective order of
our sensing* is different from the objective order; for what we sense
successively we may believe to be simultaneous The subjective order
of our imaginings may also be different from the objective order, when
what we imagine is real events — I can imagine the death of Caesar
after imagining the battle of Actium. Again I can imagine an order of
fictitious events, and even this order (while still a subjective order
dependent on my imagination alone) may be different from the order
of my imaginings , for I may choose to imagine first a fictitious event
and then the fictitious events which led up to it. Even in imagining
real events I can imagine them to take place in an order different from
their attual order, and I can do this without asserting that imaginary
order to be real. For example I can imagine America to have declared
war on Germany when the Lusitama was sunk, and can try to estimate
the probable consequences. Of course if I imagine that America
actually did declare war on Germany when the Lusitama was sunk,
that is not mere imagination but erroneous thinking. Even in the case
when I imagine real events, there is an element of thought present in
the recognition that the events are real; and there is also an element
of thought present, if I recognise that the order in which they are
imagined to be is not their actual or objective order.
228 THE ANALOGIES OF EXPERIENCE [XLIII § 3
akin to empirical perception. The death of Julius Caesar would,
I suppose, be actually given to perception with the mark upon
it of a particular moment on the Ides of March, 6.0.44, an^ a^
subsequent efforts to recall his death in imagination would
necessarily recall that particular mark as an inseparable part
of the whole event recalled.1 Because this is not so, we are
compelled in experience to determine the objective temporal
order of events by their necessary connexion with one another.
IV. This last point is the point which Kant duly proceeds
to make. If we are to know the objective relation2 of appear-
ances to one another in time, we must not only imagine, but
think, the temporal relation of the appearances (that is, of the
successive states of substance), and we must do so in a particular
way — our thought of it must be such that 'thereby* it is deter-
mined as necessary which of the appearances must be placed
(or posited*) before and which after9.5
1 We should, I suppose, know that the successive appearances of a
house were objectively simultaneous, because each appearance would
have the mark of the whole time through which it endured. But
perhaps it is a mistake to render too precise an alternative which is
admittedly impossible.
2 B 234. Kant says 'If we are to know the objective relation of
appearances as determined' , but this seems to be equivalent to know-
ing it, or knowing it as objective. For sense-perception without thought
this objective relation is undetermined or unknown (as objective);
for thought it is known (as objective). 'Determined' here cannot
mean 'necessarily determined'. In Metaphysik, p. 23, Kant says that
'to determine' is of two opposites to posit (setzeri) one, and this may
be relevant, since by 'positing' we must understand the absolute
positing of thought, not the arbitrary and subjective positing of
imagination. 3 'dadurch.'
4 'gesetzt'y 'placed* or 'posited*. This word is especially prominent
in the second edition. Actuality is absolute position, so that the object
is posited (gesetzt) in itself, and not relatively to my understanding
(Metaphystk, pp. 27-8; compare A 598 = B 626 and also B 142).
Existence is also said to be positio absoluta (Metaphysik, p. 25).
6 More simply — if we are to know that AB is an objective succession,
we must not only sense A and then B and combine them in that order
in imagination : we must also think that B necessarily follows A. Such
thinking may of course be 'obscure': perhaps we should say that we
(consciously or unconsciously) 'assume* or 'presuppose* that B
necessarily follows A.
XLIII § 3] THE SECOND ANALOGY 229
It is on this statement that the whole of Kant's argument
turns. What comes before it is, I suggest, clearly sound. What
follows merely renders explicit the consequences of this
assertion; for a temporal succession which is determined as
necessary is a succession determined in accordance with the
law of cause and effect.
V. The thought or concept involved is therefore a concept
of necessary synthetic unity ^ and consequently a pure concept
of the understanding,2 not a concept derived from sense-
perception by the ordinary method of abstraction. The pure
concept in question is called, with unusual elaborateness,
the concept of the relation of cause and effect, which relation
is such that the cause determines the effect as its consequence
or sequel in time* This means that the later event could not
precede the earlier event,5 as it can for imagination uncontrolled
by thought. It means also that if the earlier event occurs, it
must be possible to perceive the later immediately thereafter ;
whereas if two events are merely imagined as successive, the
perception of the first event does not imply that the later event
can also be perceived immediately thereafter — or indeed at all.6
1 It is a concept of a particular kind of necessary synthetic unity,
the necessary unity (or causal nexus) of appearances whose succession
is an objective succession.
2 It will be remembered — see Chapter XXXIX § 6 — that in B 219
Kant argued from the a priori connexion imposed by the concept to
necessity. Here he argues from the necessity of the connexion to the
a priori character of the concept.
3 Kant believes that all necessary, and indeed all objective, succession
is causally determined, but not that the earlier event is necessarily the
cause of the later. Night, for example, is not the cause of day.
4 The reference to temporal sequence distinguishes the schematised
category of cause and effect from the pure category of ground and
consequent.
6 This is naturally subject to the proviso that Bi (the effect of Ai)
can precede A2 (the cause of 62).
6 I think that this is Kant's meaning — not that if two events are
merely imagined as successive, the second event may be something
which need not be perceivable at all (as when I imagine that a par-
ticular incantation of Circe might cause men to turn into swine). But
the statement is obscure.
230 THE ANALOGIES OF EXPERIENCE [XLIII §4
VI. Hence it is only because we subject1 the succession of
appearances (and so all 'change'2) to the law of causality that
experience (as empirical knowledge of appearances and their
objective succession) is possible. Since the conditions of the
possibility of experience are necessarily the condition of the
possibility of phenomenal objects,3 phenomenal objects, or
objects of experience,4 are necessarily subject to the laws of
cause and effect.
§ 4. The Object and its Temporal Relations
The first proof in the first edition5 also begins with an intro-
duction. This introduction reaffirms Kant's general account
of the nature of an object and prepares the way for the special
case of objective succession.6
One great difficulty in following Kant's argument is the
ambiguity of his terms. Thus in the argument of the second
edition 'appearance' was used primarily for the different states
of a substance, states which succeed one another in the object.7
In the present argument 'appearance' is used for a whole
1 'unterwerfen.' I do not think Kant means that we first have a
subjective succession of appearances, and then make it objective by
bringing it under the law of cause and effect. Rather in being aware
of an objective succession we are necessarily considering it as deter-
mined by the law of cause and effect. Kant may, however, be arguing
from the necessity in the order of apprehension to necessity in the
order of events in the object. See § 5 IV below.
2 It must be remembered that 'change* is succession (or exchange)
of the states of a substance. Kant is here talking of objective change or
succession.
3 If the objects we know were things-in-themselves, we could never
know, according to Kant, that they were governed by causal law.
4 Kant says 'appearances themselves as objects of experience'.
He may mean 'appearances so far as we know them to be successive
states of objects'. 5 A 189-94 =. B 234-9.
6 For the general account see A 104 ff. and B 137, and compare also
A 197 = B 242 ff. Kant uses the phrase 'transcendental object* in
A 191 = B 236, a phrase not used in the additions made in the second
edition, but I believe the general doctrine of the object to be the same
in both editions. See Chapters XX § 2, XXII §§ 1-2, and LV § 3.
7B233.
XLIII §4] THE SECOND ANALOGY 231
object, such as a house.1 It is not easy to be sure whether this
usage is maintained consistently throughout: in some places
it may seem more natural to take 'appearance* to be a part or
state of the object. Let us, however, say broadly that the appear-
ance is the whole object, and that its parts or states are 'the
manifold of the appearance'. We can then say that the appre-
hension of the manifold of the appearance is always successive ;
and this is equivalent to saying that our ideas of the parts
follow one another.2
I need not consider again the precise sense in which Kant
regards apprehension as always successive.3 If Kant's view
were that we never directly apprehend even the subjectively
coexistent or simultaneous, he would be wrong, and his
argument would so far be weakened. There can, however, be
no doubt that we commonly regard as coexistent what has been
successively apprehended, for example, the different parts of
a house ; and this is a sufficient basis for the argument. We must
remember that the whole appearance and its parts may alike
be described as 'ideas': they are not things-in-themselves.
The whole appearance, it may be said, is made up of parts
which are successively apprehended; and it is thus a sum or
aggregate of ideas,4 which, so far as our apprehension is
concerned, may be described as following one another.
The question then arises whether these ideas (or parts)
follow one another in the object (or the total appearance).
In order to answer it we must consider what we mean by
'object'.
Every idea, so far as we are aware of it, may be called an
object ; but this clearly is not the sense required here. We want
to know the meaning of 'object', when we speak of our ideas,
1 A 190 = B 236. In A 192 = B 237 it is used for a moving ship.
2 A 189 = B 234.
3 See Chapter XLII § i. If by the manifold of (or in) the appearance
Kant means the parts of such an object as a house — and this is the
example he himself gives m A 190 — 6235 and A 192 = - B 237-8 — his
statement is true in the sense that we could never perceive all the
parts of a house simultaneously.
4 Compare A 191 = B 236.
232 THE ANALOGIES OF EXPERIENCE [XLIII § 4
not as objects, but as 'designating* or 'symbolising'1 an
object.2
If we take our ideas to be objects merely in the sense that we
are aware of them, then, Kant says, they do not differ from
apprehension (which is the 'taking up* of the given into the
synthesis of imagination).3 I believe he means by this that they
do not differ as regards their time-relations* The time of an
idea qud idea present to consciousness is the time of its appre-
hension; and since our apprehendings are successive, we can
say that our ideas are always produced successively in the mind.
This means that the manifold of appearances5 is always produced
successively in the mind as it is taken up by our acts of appre-
hension.
Kant asserts that if appearances were things-in-themselves,
we could never decide from the succession of our ideas how
the manifold (that is, the parts) of these appearances is
combined in the object. The reason he gives is that we have
to deal only with our ideas and the character of things-in-
themselves is quite outside our sphere of knowledge.6 But
obviously if appearances were things-in-themselves — and
such is the hypothesis he is considering — this would not
be the case.
The argument is badly expressed ; but I take Kant to mean
1 'bezeichnen* ; A 190 = B 235. Kant here seems to mean that our
idea (for example, a seen colour) is taken as characterising the total
object (for example, a house).
2 In this passage (A 189-190 — B 234-5) Kant seems to use 'appear-
ances*, not for the total object, but for the parts or ideas of which
it is made up. This might perhaps be questioned; for in A 190-1
= B 236 the whole appearance is described as an idea whose trans-
cendental object is unknown. For the sake of clearness I have avoided
the use of the word 'appearance* here.
3 This is the usual technical sense of 'apprehension*.
4 Compare A 194 = B 239. I cannot believe that Kant means to
identify the manifold apprehended with the act of apprehending it;
and the 'differences* of which he speaks in the Second Analogy are
to be understood as differences in temporal position.
6 I take Kant to mean that, for example, the parts of a house are
produced successively in the mind.
6 A 190 = 6235.
XLIII §4] THE SECOND ANALOGY 233
that if we regarded an appearance,1 for example, a house, as a
thing-in-itself, then we could never pass from the succession
of our ideas (in which the parts of the house are given one
after another) to knowledge of the way in which these parts
were combined in the house itself.2 All we have given us is
the succession of our ideas. If by means of imagination we
combined these ideas (or what is given in them) in one and the
same time and regarded them as coexistent, we could never
know that this combination represented anything in the
thing-in-itself. For we know nothing of things-in-themselves
except that they are supposed to 'affect' us through our ideas.3
If we grant this, we are brought face to face with the Critical
problem. We are assuming that appearances, such as houses,4
are not things-in-themselves. We are also assuming that nothing
is given to us except our ideas : the whole house is a given idea
in the sense that it is given to us in parts (or ideas) which are
always successive.5 Can we then explain how the parts (or the
manifold) of the appearance have a temporal combination—
for example, as coexisting — in the appearance itself? On Critical
1 If we take Appearance' here to mean the parts of the whole object,
the argument runs on the same lines. We could never know from these
successively given parts how they were really combined in the object.
2 Strictly speaking, we should not know that there was anything
which could be called a 'house': we should only know that certain
given ideas succeeded one another.
3 If we take this as the proper interpretation of Kant's argument,
we may doubt whether it is intended to stand on its own feet: the
language used seems to imply that Critical principles are already pre-
supposed. If time is a form of our sensibility, we can never be
justified in ascribing temporal relations to things as they are in
themselves. Kant hopes to show later that objective succession and
coexistence could never be known except as necessary succession
and coexistence, and he believes that if objects were thmgs-in-
themselves we could have no knowledge of necessity.
4 A 190 = B 235. Here again it is quite easy to restate the problem,
if we take appearances to be the successively given parts of a whole
object, and not the whole object itself; but I prefer to suppose that
Kant is using 'appearance' in the latter sense, as he does m what
immediately follows.
5 Note that mAi9i=B236 the whole appearance (of a house) is
said to be given and to be an aggregate of ideas.
VOL. II H*
334 THE ANALOGIES OF EXPERIENCE [XLIII §4
principles a house is an appearance, or object, which is neither
a thing-in-itself not a succession of ideas in us. How on such
a basis can we justify our belief that although the parts of the
house are apprehended successively they are nevertheless
coexistent in the object? As Kant says, 'How can the manifold
be combined in the appearance itself, when the appearance is
nothing in itself?'1
Kant himself emphasises the difficulty of this question for
the Critical Philosophy.2 From the point of view of ordinary
experience or of science a house is quite properly regarded as
a thing-in-itself.3 From the Transcendental point of view it
is only an appearance, that is, an idea whose transcendental
object (here clearly equal to the thing-in-itself) is unknown.4
Yet we are trying to make a distinction between the succession
of ideas (in which the parts of the object are given) and the
given appearance as a whole. We are regarding the whole
given appearance as the object — the phenomenal object —
of these ideas in spite of the fact that it is only a sum or aggre-
gate of these ideas. And we are supposing that our concept of
'house', which is presumably extracted by analysis from the
successive ideas of our apprehension,5 must be in agreement
with this object, if we are to have truth. How can this be
possible ?
At this stage Kant offers us his general solution of the problem.
He stresses the fact that the agreement of our concept with the
object is empirical truth ;6 and he implies that if we can state the
conditions under which alone a concept can agree with its object,
that is, if we can state the formal conditions of empirical
1 A 191 = 6236. That is, when the appearance is not a thing-in-
itself at all.
2 Prichard (Kant's Theory of Knowledge, pp. 280 ff.) argues that this
difficulty is insuperable.
3 Compare A 45-6 = B 63. 4 A 190-1 = B 236.
6 It can be so extracted only because our ideas have been combined
in accordance with the categories; m particular because they are
regarded as states of a substance, states whose relative position in time
is determined by causal law.
6 Compare A 58 = B 82 ff., A 157-8 = B 196-7, A 237 = B 296,
A 451 = B 479, and Log. EM. VII (IX 50-1).
XLIII § 4] THE SECOND ANALOGY 235
truth,1 then we can answer the question, 'How can the manifold
be combined in the appearance itself?'
The formal conditions of empirical truth must be formal
conditions of experience (and so of objects).2 Kant, however,
has in mind, not the Mathematical Principles (which are con-
cerned with intuition as such), but the Dynamical Principles,
and in particular the Analogies ; for these are concerned with
the existence of objects, and are necessary only under the
conditions of empirical thinking in an experience.3 When we
speak of 'the manifold as it is combined in the appearance
(or in the object) itself,' we mean the manifold as it is combined
in accordance with the Analogies, and not as it is combined
arbitrarily in imagination or as it is given to us successively
in apprehension. The object can be distinguished from the
ideas successively given in apprehension, because (although
it is itself only an appearance, and indeed a complex of ideas)
'it stands under a rule which distinguishes it from every other
apprehension and makes a particular kind of combination in
the manifold necessary.'4 The 'rule' under which the object
stands is most naturally taken to mean one of the Analogies.5
Kant adds 'That in the appearance which contains the condition
of this necessary rule of apprehension is the object'.
In this passage there are many difficulties of interpretation.
Kant's argument is quite general; and if he means the 'rule'
to be 'a formal condition of empirical truth' (as I think he must),
then the rule cannot be confined to the Second Analogy.6
1 We are not asking, c Under what conditions does this concept of
house agree with this house?' — that depends on the details thought
in the concept and given in sensation. We are asking * Under what
conditions is it possible for any concept to agree with any object?'
— or perhaps better 'How on Critical presuppositions is it possible
that there can be any object with which our concept may agree?'
2 Compare A 202 = B 247 and A 62-3 = B 87.
3 A 160 — B 199. * A 191 — B 236.
5 The fact that Kant speaks of a 'rule', and not of a 'law' or 'principle',
does not exclude the Analogies ; see for example A 177-8 = B 220 and
A 1 80 = B222.
6 Still less could it be a particular causal law except in the sense
that to stand under the general law of causality is always to stand under
a particular law.
236 THE ANALOGIES OF EXPERIENCE [XLIII § 4
The 'rule' might equally well be the Third Analogy: indeed
the only case which Kant has so far considered is the case of
objective coexistence, which is governed by the Third Analogy.1
Nevertheless for the sake of simplicity we need consider only
the case of objective succession, in which case the rule would be
the Second Analogy.2
The Second Analogy may certainly be described as a rule
which makes a particular kind of combination in the manifold
necessary. But can we say that 'it distinguishes an appearance
from every other apprehension'?3 Above all can we describe
it as 'a rule of apprehension'? We shall find similar puzzles
in what follows.4 At present I think we need only say that
whatever we may make of Kant's terminology, the applicability
of the law of cause and effect does, on his view, mark out an
objective succession from a merely subjective succession,
and does render it necessary that our apprehension should
follow a certain order.5
There are special difficulties in the final statement : 'That in
the appearance which contains the condition of this necessary
rule of apprehension is the object.'6 We may compare with
this the statement that the object is regarded as 'that which
1 It is true that the proof of the Third Analogy does not make use
of the term 'rule', hut we must remember that the schema of com-
munion is the coexistence of the determinations of different substances
'in accordance with a universal rule'; see A 144 = B 183-4. Compare
also A 217 — B 264.
2 Compare the parallel passage in A 202 = B 247. The schema of
causality, it may also be recalled, is the succession of the manifold so
far as that succession is subjected to a rule; see A 144 = B 183.
3 We should expect him to say either (i) that it distinguishes an
appearance as object from every other idea apprehended or (2) that it
distinguishes the apprehension of an appearance as object from every
other kind of apprehension. It is hard to be sure whether Kant's
language, when he thus seems to equate apprehension and its object
(or content), is due to carelessness or not ; there seems to be a kind of
method in it, but without further justification or explanation it is a
source of confusion. Compare the difficult assertion already noted
(A 190 = B 235) that our ideas as objects of consciousness are not
different from apprehension. 4 See especially A 193-4 = B 238-9.
6 So far it might be called loosely 'a rule of apprehension',
6 A 191 = 6236.
XLIII § 4] THE SECOND ANALOGY 237
prevents our cognitions from being haphazard or arbitrary;'1
and again that 'all appearances, in so far as through them
objects are to be given to us, must stand under a priori rules
of synthetic unity'.2 I have already argued3 that Kant in these
passages does not suggest that necessary synthetic unity (which
is the essential characteristic of a phenomenal object) is due to
the transcendental object regarded as a thing-in-itself. Similarly
heae there is no ground for thinking that he is speaking of the
transcendental object.4 1 take it that in this passage, as elsewhere,
he is identifying the object with the necessary synthetic unity
of the manifold.5 This necessary synthetic unity contains in
particular a necessary synthetic unity of time-determinations6
or, more simply, a necessary time-order7 ; and it is this necessary
time-order in the appearance which is the condition of a neces-
sary rule of apprehension,8 notably in the case of objective
succession.9
1 See A 104.
2 See A 1 10. Compare B 137, 'Object is that in the concept of which
the manifold of a given intuition is united'; and also A 158 = B 197.
3 See Chapter XXII §2.
4 It would be strange indeed to speak of the transcendental object
as 'in the appearance', if by the transcendental object is meant the
thing-m-itself.
5 Strictly speaking, the object is the manifold so far as that manifold
possesses necessary synthetic unity.
6 Compare A 177-8 = B 220, where the necessary synthetic unity
in time-relations (or time-determinations) is clearly the unity of the
time-order.
7 In A 145 = B 184-5 the schemata of relation are concerned with
the time-order in regard to all possible objects.
8 Here Kant is concerned with the rule as a rule of apprehension,
and he finds its condition in the object, although he spoke previously of
the appearance as an object in so far as it (and not the apprehension)
stood under the rule. Difficulty again arises from the fact that the rule
governing the appearance and the rule of apprehension seem to be both
distinguished and identified.
9 The case of objective coexistence is more complicated. If we
consider only objective succession, Kant's doctrine is expressed more
clearly in A 193 = B 238, where he says that objective succession
consists in the order of the manifold of appearance, an order in
accordance with which one apprehension follows another in con-
formity with a rule.
238 THE ANALOGIES OF EXPERIENCE [XLIII § 5
If we take the 'rules' of which Kant speaks to be the Analo-
gies, he appears to regard them both as rules governing objects
and also as necessitating thereby the order of our apprehensions.1
The phrase 'condition of a rule* is puzzling wherever it occurs,
but on this interpretation it may not unreasonably be taken to
mean a transcendental schema.2 It is natural enough to speak
of an object as 'containing' the transcendental schemata;3
and the schemata of relation as a whole are concerned with
the necessary time-order,4 which I have assumed to be what
Kant describes here as the condition of a rule.5 It is in any case
the transcendental schemata of relation which Kant must show
to be present in objects, if he is to prove the truth of the Analo-
gies.6 Indeed he has to show that an object exists as an object
only so far as there are present in it the transcendental schemata
of relation. His immediate task is to show that succession in
the object must be necessary succession.
§5. The Second Proof
I. We are now in a position to get on with our task and to
consider the special case of objective succession.7 Kant insists
that we could not perceive an objective event or change without
1 In the latter sense he appears to describe them as rules of
apprehension.
2 It should be noted that Kant speaks of the categories as containing
the condition or conditions of a priori rules; see A 132 -- B 171,
A 135 = B 174, and also A 140 = B 179. In these contexts the 'con-
ditions of a rule* seem to be the transcendental schemata; and this
suggests that we should at least ask ourselves whether the phrase can
have the same meaning here.
3 This seems to be implied in A 139 = B 178, where Kant says
that time is contained in every empirical representation of the manifold.
The whole passage should be consulted.
4 See A 145 = B 184. The 'time-order* is the objective and necessary
order of the manifold in time. Where the Second Analogy is the rule,
the condition is the schema of 'necessary succession'; and necessary
succession in the object is the condition of necessary succession in our
apprehension.
6 The phrase occurs also in A 193 = B 238-9, where it is a source of
new difficulties.
6 Compare A 181 = B 223-4. 7 A 191-4 = B 236-9.
XLIII § 5] THE SECOND ANALOGY 239
perceiving something else immediately before it ; for we can no
more perceive something happening after an empty time than
we can perceive empty time itself. But in perceiving the front
and back of a house our apprehension is just as successive as
it is when we perceive an objective change, so that the mere
successiveness of our apprehension does not prove the succes-
siveness of what is apprehended.1
II. There is, however, another point to be noted. Suppose
that we are aware of an objective succession, that is, of an event
a followed by an event /?. Let our sense-perception of a be
called a and our sense-perception of /? be called b. Then if the
succession is objective, that is, if a is followed by /? in the objective
world, a must precede and cannot follow b, and b must succeed
and cannot precede a. If a ship is moving down stream,2 we cannot
first see it lower down and then see it higher up, whereas in
the case of a house (where there is no such objective
succession) we can see first the front and then the back or vice
versa.3
It is absolutely vital not to misunderstand this crucial
statement. Kant is not arguing from the observed irreversibility
of my sense-perceptions to an objective succession. He is on
the contrary arguing from an assumed objective succession to
the irreversibility of my sense-perceptions. He is not saying
that I find I cannot reverse the order of my sense-perceptions,
1 In this passage Kant speaks of distinguishing one synthesis of
apprehension (or sense-perception) from others, as I think he ought
to have done above, instead of speaking about distinguishing an object
from other apprehensions.
2 It should be noted that the earlier position of the ship is not the
cause of the later. Kant's doctrine is that every objective succession
must be causally determined, not that it must be a sequence of cause
and effect.
3 No doubt the order of the appearances of the house to me is
determined by the movements of my body, but it is not determined
by any change in the object, that is, in the house. If I make my mental
history an object to myself, the successive appearances of the house
are actual objective events, and as such they are as much determined
as any other objective events.
240 THE ANALOGIES OF EXPERIENCE [XLIII § 5
and then conclude I must be dealing with an objective succes-
sion. Such a statement, even if it were true — and I think it is
false1 — could never justify us in affirming any kind of necessity ;
we could only say that we had hitherto found our sense-
perceptions to occur in a particular order and no other. Kant
starts with the assumption that we are aware of an objective
succession, and asserts that, if so, our sense-perceptions must
occur in a particular order. The order in the succession of
sense-perceptions is in this case determined by the order of
events.2 There is a rule governing our apprehension, a rule
which is always to be found when we are perceiving objective
events, and it makes the order of our successive sense-percep-
tions (in the apprehension of these successive events) a necessary
order.3
III. In this case4 therefore— that is, in the case where we
are ex hypothesi perceiving an objective succession — we must
derive the subjective succession in our apprehension from the
1 Unless we already assume that we are perceiving objects, and
indeed that the objects perceived are substances. I think Professor
Pnchard is right (Kant's Theory of Knowledge, p. 294) in saying that
we do not begin by knowing a subjective succession and then pass to
a knowledge of objective succession either by finding that the sub-
jective succession is irreversible or in any other way. Indeed is there
any meaning in talking about the irreversibihty (or for that matter the
reversibility) of a subjective succession, unless we are already pre-
supposing the existence of an objective world in time ? In a subjective
succession considered solely by itself we could say only that our ideas
had occurred in the order in which they had occurred.
2 Compare A 192 = B 237: 'The order in which the sense-percep-
tions succeed one another in apprehension is in this instance determined,
and to this order apprehension is bound/
8 A 193 = B 238. In the above paragraph I am not denying that
on Kant's view the irreversibihty of our sense-perceptions may
entitle us to assert objective succession, if we already assume that we
are perceiving objects whose states must be either successive or
coexistent: I deny only that such an observed irreversibihty can by
itself give us necessity. The necessity which Kant attributes to the
subjective order of our sense-perceptions is not known by observation,
but is a consequence of its * derivation' from an objective order. And
indeed for Kant necessity can never be known by mere observation.
4 'in unserem Fall.'
XLIII § 5] THE SECOND ANALOGY 241
objective succession of appearances* If the subjective succession
is not derived from an objective succession,2 it is arbitrary and
undetermined,3 and does not enable us to distinguish one
appearance from another as regards the time of its occurrence
in the objective world. In short it proves nothing about the
temporal connexion of the manifold in the object.4
IV. The objective succession of appearances is then said
— and this seems to be a mere expansion of what has been said
before — to consist in that order of the manifold of the appear-
ance according to which5 the apprehension of the preceding
1 The appearances in question are events or changes in the pheno-
menal world. In this much-quoted sentence Kant, as so often, confuses
his readers by beginning with a 'therefore' and following it up with a
* because*.
2 Kant's own expressions are very abbreviated, but I take 'jene sonst*
to mean 'the subjective succession when it is not derived from an
objective succession* and 'jene alleiny to mean practically the same.
3 Kant may be here repeating what he has already said about the
house, that where there is not a series of objective events or changes,
there is nothing to make our apprehension begin at one point rather
than at another in its synthesis of the manifold. His statement that
in such a case the subjective order is 'wholly arbitrary' and 'wholly
undetermined' seems to be exaggerated. It is perhaps possible for him
to mean that when we set aside all considerations about objective
succession (or coexistence), when in short we consider the subjective
order of our sense-perceptions in complete abstraction from any kind
of objective order, the subjective order is undetermined and arbitrary
in the sense that it is a given order for which we can see no reason and
in which we can find no necessity. Such a statement I believe to
be true.
4 The difficulty of this is that it is an indication, if not a proof, of
the coexistence of the manifold. Hence there is something to be said
for the alternative interpretation suggested in note 3 above, since the
subjective order, considered in abstraction from the objective, is
always (according to Kant) successive and does prove nothing about
the temporal connexion of the manifold in the object.
6 'according to which' surely implies that the subjective succession
is derived from, or determined by, the objective succession. The
passage may be compared with that in A 191 = B 236, where Kant
speaks of 'that in the appearance which contains the condition of the
necessary rule of apprehension'. Kant seems to me to regard the
subjective and objective successions as, so far, distinct, not, as Pro-
fessor Pnchard suggests (Kant's Theory of Knowledge > p. 289), as
identical. The identification, I think, comes later.
242 THE ANALOGIES OF EXPERIENCE [XLIII § 5
event follows the apprehension of the succeeding event in
accordance with a rule.1 Here the rule is clearly what Kant
calls a rule of apprehension — a rule that (in virtue of the objec-
tive succession a/?) sense-perception a must be followed by
sense-perception b. And Kant goes on to say that it is only
because of this rule2 that I am entitled to say of the appearance,
or object, itself (and not merely of my apprehension) that there
is in it a succession. He even adds that to assert a succession in
the object is the same thing as to say3 that I cannot arrange my
apprehension otherwise than in just this succession.
The interpretation of this is a matter of the greatest difficulty.
Kant is not, I think, merely repeating what he has already
said — that when I am aware of an event a followed by an
event ]8, the sense-perception a must be followed by the
sense-perception b, and that such a necessary succession
of sense-perceptions must always be present whenever there is
awareness of an objective succession. He is passing beyond
what is, on the face of it, an affirmation of common sense to
its interpretation on Critical principles. If the event a and the
event /? were things-in-themselves, it is manifest that wre could
never pass from the common-sense assertion that, in perceiv-
ing the objective succession ajS, sense-perception a must be
followed by sense-perception b to the quite different assertion
that the objective succession ajS is itself causally determined.
Kant appears to be arguing that since the event a and the
event j3 are, on Critical principles, only the content of sense-
perceptions a and b, the attribution of necessary succession to
a and b (on the ground of the objectivity of the succession aj3)
is ipso facto an attribution of necessary succession to a and /?;
1 This, for Kant, is the same as 'necessarily follows*.
2 'dadurch.' The following sentence, I think, supports this inter-
pretation, but it is possible that 'dadurch* should be translated more
loosely as equivalent to *m this way*, that is, 'where there is an order
in the manifold which necessitates a succession of apprehensions in
accordance with a rule*.
3 'so viel bedeutet als.y It is in this sentence, I think, that we get the
identification of the objective order with the necessary subjective
order, an identification which Professor Prichard maintains has already
been made. See note 5 on previous page.
XLIII § 5] THE SECOND ANALOGY 243
and the necessary succession is in both cases identified with
succession in accordance with a rule.
This contention seems to me to be the crux of Kant's argu-
ment.
V. My interpretation seems to be confirmed by what fol-
lows. In accordance with such a rule (which hitherto has been
spoken of as a rule of apprehension) there must therefore be
present in what precedes an event the condition of a rule1
in accordance with which2' this event always and necessarily
follows, so that, the first event having been given, I must
always be able to go on and apprehend or perceive the second
event.3 This process cannot be reversed, for when the second
event is given I cannot go back and apprehend the first event.4
1 Kant seems to mean here that in the total state of affairs which
precedes the event there must be present something upon which the
event must follow. He does not mean that the cause of the lower
position of the ship is its previous position higher up the stream.
The presence of this Something* is 'the condition of a rule*.
In A 191 — 6236 'the condition of a rule* seemed to be the trans-
cendental schema, and it may appear that the present use of the
phrase is entirely different; but it should be noted that the trans-
cendental schema of causality is described, not only as succession in
accordance with a rule, but also as 'the real upon which, whenever
posited, something else always follows* (A 144 — B 183). This is the
condition of the applicability of the category or law or rule of cause
and effect. It is thereby of course also the condition of the applicability
of a particular causal law — the general law is manifested only in
particular applications.
* 'Which*, I take it, refers to 'rule*.
3 I have introduced this last clause, because its introduction seems
to be assumed by the following sentence, which says that I cannot
'conversely* go back from the event and determine (by apprehension)
what precedes it.
4 This statement seems obvious enough, but Kant thinks it necessary
to support it with a reason. 'For no appearance goes back from the
succeeding point of time to the preceding, although it must be related
to some preceding point of time\ on the other hand, the advance (of
appearances presumably) from a given time to the determinate suc-
ceeding time is necessary*. This contrast of the determinate succeeding
time with the indeterminate preceding time seems to rest on the fact
that the succeeding time is given with its content in perception,
whereas the preceding time can (unless we remember what happened
244 THE ANALOGIES OF EXPERIENCE [XLIII § 5
Hence because an event is essentially something which follows
upon something else,1 I must necessarily relate it, when
perceived, to something else in general2 which precedes it
and upon which it follows in accordance with a rule, that is,
necessarily. In this way the event, as the conditioned in time,
gives a sure indication that there is some preceding condition
or cause. The preceding condition or cause does not merely
indicate that there is some event which must follow as effect;
it actually determines* the event (in the sense, I take it, that it
must necessarily be followed by an effect which, if we knew
what to look for, we could actually perceive).4
Kant's insistence that we cannot go on to perceive the cause
which we presuppose whenever we are aware of an objective
event — a point which seems almost too obvious to state — is
presumably due to the fact that for him all events are in the last
resort ideas or appearances to human minds. He has to insist
that nevertheless we can and do place or * posit' unperceived
(and now unperceivable) events in a time which is past.
in it) be imagined only in abstraction, for we cannot 'construct* its
content by our knowledge of the general law of cause and effect.
All this bears a certain external resemblance to what I have called
the Fifth Proof of causality. See below, Chapter XL IV § 4.
1 Literally 'since there certainly is something which follows'.
2 I do not know what its cause is, but I do know it must have some
cause. Hence the phrase 'something else in general', which perhaps
also indicates that what precedes is an object.
3 For the word 'determines* (bestimmt) see also A 199=6 244 and
Chapter XLIV § 4.
4 Provided our senses were adapted to it. See A 226 = B 273.
CHAPTER XL IV
THE SECOND ANALOGY (continued)
§ i. The Third Proof
The third proof1 is commonly described as the indirect2
proof, but it might be regarded as a mere appendix to the
previous proof.
Kant starts with the hypothesis that what the previous
argument has proved is untrue. Suppose that a perceived
event is not preceded by something on which it must follow
in accordance with a rule. In that case all succession of sense-
perceptions would be merely subjective — through the sub-
jective succession of sense-perceptions in apprehension it
would not be 'objectively determined* which of these sense-
perceptions must precede and which succeed.3 To say this is
to say that we should have a mere play of ideas4 unrelated to
any object. More precisely, our sense-perceptions could not
distinguish the objective time-relations of one appearance
from those of another — the time of every appearance would
simply be the time of its apprehension.
The reason given for these assertions is Kant's fundamental
1 A 194 — B 239 fF. (two paragraphs).
2 It must be remembered that every Critical proof is in a sense
indirect. The Principles of the Undei standing are not established
directly from concepts, but indirectly from the relation of these
concepts to possible experience. See A 737 = B 765 and compare
Log. Einl IX (IX 71). The method of the third proof, if it is an
independent proof, is reductio ad absurdum.
3 A 194 = B 239. Note that it appears to be the succession of our
sense-perceptions which is objectively determined only if events are
governed by causal law. Compare the statement in A 193 = B 238
that the subjective succession of our apprehension is undetermined
unless it is derived from the objective succession of appearances.
Compare also what I take to be the statement mA2Oi ^ 1*246 that
'in apprehension there is an order of successive synthesis which an
object determines'; and again (in A 191 = B 236) 'that in the appear-
ance which contains the condition of this necessary rule of apprehension
is the object*.
4 Compare A 101, A 201 = B 247, and also § 5, below.
246 THE ANALOGIES OF EXPERIENCE [XLIV § i
doctrine that whether we apprehend the successive or the
coexistent, our apprehension considered in itself is always
successive: in his own phrase 'the succession in apprehension
is always of the same kind'.1 I take this to imply that, so far as
mere apprehension is concerned, the appearance given to us
is nothing but a succession of ideas. If so, 'there is nothing in
the appearance which determines the succession in appre-
hension2 in such a way that thereby a certain succession as
objective is rendered necessary'.3
This last statement appears to be expressed more clearly
when Kant says that 'the mere succession in my apprehension,
if it is not determined through a rule in relation to something
that precedes, does not entitle us to assert any succession in
the object'.4 Whatever be the obscurity in this statement,
Kant is clearly not asserting that by examining the subjective
succession of our apprehensions, we can sometimes find in it
irreversibility and infer therefrom an objective succession.
He is, on the contrary, maintaining that from the subjective
succession of our apprehensions, taken by itself, we could
never pass to objective succession.
It is more difficult to be certain about the positive doctrine
1 A 194 = B 239. This way of stating the doctrine again opens up
the question whether there may not be apprehension of the coexistent
over a limited area. If it were so, this might help to explain how we
come to regard as coexistent what is successively apprehended: for
the content of our successive apprehensions may partly overlap.
2 The German is simply 'it' (sie\ which I take to mean 'the suc-
cession in apprehension*. Grammatically 'it* might refer to 'the
appearance*.
3 A 194 = B 239-40. I have translated literally, but most of the
commentators regard the text as corrupt. If 'as objective* could mean
'as objectively determined', it would give good sense ; for the subjective
succession is rendered necessary if it is objectively determined. Or
again, if Kant is identifying the succession in the appearance (or object)
with the succession in apprehension, a succession which is objective
is a necessary succession in our apprehension. On the other hand the
explanatory passage which follows suggests that Kant meant to say
'thereby a certain succession is rendered necessary and so objective*.
4 A 195 == B 240. Note that here the rule which governs the
succession of events is supposed to determine the succession in my
apprehension.
XLIV § i] THE SECOND ANALOGY 247
asserted. Kant appears to hold that unless we believe something
in the appearance to make the succession of our apprehensions
a necessary succession, we cannot speak of an objective succes-
sion. This seems to me obviously true. The peculiarity of his
doctrine is the view that the succession in the appearance (or
in the object) must itself therefore be a necessary succession.
This, I think, follows for him from the fact that the object is
only an appearance, and not a thing-in-itself.1
Kant sums up his conclusion thus : * When we experience an
objective event,2 we always presuppose it to be preceded by
something on which it follows in accordance with a rule'.3 Apart
from this presupposition we could not speak of a succession in the
objective world, but only of a succession in our apprehension.
Because Kant is an empirical realist, he believes that an
objective succession may be directly present to my successive
apprehensions. Because he is a transcendental idealist, he
believes that such an objective succession, though not confined
to my apprehension, is nothing apart from a possible human
experience.4 When we perceive an objective succession, the
objective succession of appearances is identical with the sub-
jective succession of my ideas ; and the necessity which marks
the subjective succession in such a case must mark also the
objective succession. If we distinguish the two successions, the
necessity in the objective succession may be said to be the source
of the necessity in the subjective one. If we take it that there is
only one succession, we consider that succession to be a neces-
sary succession, and only so do we regard it as objective.5
The main difficulty, as throughout the Second Analogy,
is that Kant speaks at times as if there were only one succession
and at other times as if there were two. The succession of events
1 Compare Chapter XLIII § 5, IV.
2 Literally 'when we experience that something happens*.
8 A 195 = B 240.
4 There is something which is its ground in thmgs-m- themselves,
but that ground is beyond our knowledge.
5 Kant says, not too happily, 'I make my subjective succession (in
apprehension) objective* in virtue of the rule which governs events;
see A 195 = B 240.
248 THE ANALOGIES OF EXPERIENCE [XLIV § 2
is a much wider series than the succession of my sense-percep-
tions, and there may be a succession of my sense-perceptions
when there is no succession of events.1 It is only when I per-
ceive an objective succession that the two series so far coincide.
It may be asked why I should decide in some cases and not
in others that the succession in my apprehension is necessary
and consequently objective. We should never be justified in
doing so if we considered the succession in my apprehension
merely in itself. Kant is assuming that we are regarding the
colours, shapes, sizes, and so on (which we perceive and which
are consequently called our ideas or our sense-perceptions)
as states of permanent substances in space.2 Once that is assumed
it is easy to discover whether our sense-perceptions are in a
necessary succession or not, whether, for example, we can see
the positions of a ship in the reverse order or not. Only thus
can we decide whether the succession is in the ship as well as
in our apprehension. Kant is not inferring objectivity in
general from an observed necessity in the succession of sense-
perceptions taken to be merely subjective — such a transition
would be quite impossible, as he himself asserts. He is assuming
objectivity, as we all must, from the start. Only on the presup-
position of objectivity (or of permanent substances in space)
can we find that necessity in the succession of our sense-per-
ceptions which entitles us to assert objectivity in the succession
or to attribute succession to the object.
§ 2. Origin of the Concept of Causality
At this stage Kant interposes a reply to those who maintain
that the concept of causality is acquired by observing the repe-
tition of similar series of events.3 His answer is firstly that a
concept so acquired could never have universality and necessity ;
and secondly that this view makes the common mistake of
1 When I perceive successively the coexistent. 2 Compare B 232-3.
3 A 195-6 = B 240-1. This view contradicts Kant's theory, not
only because it derives the concept of causality from experience, but
primarily because it supposes we could be aware of objective events
without having a concept of causality, however obscure. Kant is
concerned here, not so much with Hume (who derives the concept
XLIV § 3] THE SECOND ANALOGY 249
supposing that the process by which a concept becomes 'clear'1
to our consciousness is the source (or origin) of the concept
itself. The concept of causality cannot acquire logical clarity
except as a result of experience, but it is at work in experience
from the first.2
§ 3. The Fourth Proof
The fourth proof3 professes to appeal for confirmation to
experience. Our task is to show4 that we never, even in experience,
ascribe succession to an object except when there is a rule which
compels us to observe this order of sense-perceptions — here
equivalent to appearances — rather than another.5 But although
Kant makes some attempt to restrict himself to analysis of the
facts, the general line of the argument can hardly be said to differ
in any important way from the argument of the first proof.
He even begins by repeating his introductory account of
from awareness of a succession of ideas or impressions) as with the
popular views which have 'always* been held.
When Kant speaks of an 'event* (BegebenJieit) or of 'what happens'
(was da geschieht), he means an objective event or happening. See
especially A 198 = B 243.
1 For 'clear* and 'obscure* ideas see Chapter XIX § 8.
2 Similarly all thinking presupposes the law of non-contradiction
from the first, but that law acquires 'logical clarity* only when we
begin to think about thinking, that is, when we study logic.
3Ai96 = B24ifT. (three paragraphs).
4 Kant says to show €im Beispiele\ which Kemp Smith translates
'in the case under consideration*. I take this to mean 'the case where
we experience an objective succession* ; for Kant does not here offer
any concrete examples of what we are considering. Compare 'in
unserem Fair in A 193 — B 238; but the phrase seems peculiar, and
perhaps suggests that an example was at one time supplied and
subsequently removed.
5 Kant adds that it is precisely this necessitation which 'first of all*
makes possible the idea of a succession in the object. If we interpret
this 'first of all* in a temporal sense, we must take Kant to hold that
we are first of all aware of a merely subjective succession, then —
Heaven knows how — we become aware of its necessity, and finally
we infer an objective succession. The absurdity of this doctrine has
been sufficiently exposed by Professor Prichard, but I do not believe
it should be attributed to Kant if any other interpretation is possible.
In this passage I take the 'rule* to be the Second Analogy considered
as determining the order of our apprehensions inasmuch as it deter-
mines the order of events apprehended.
25o THE ANALOGIES OF EXPERIENCE [XLIV § 3
what is meant by 'object'.1 He insists that our ideas are only
modifications or determinations of the mind occurring in a
particular temporal order, and that they cannot possess refer-
ence to an object (or objective significance) merely by being
related to another idea which is regarded as in a special sense
an idea of the object ;2 for this idea would be just as subjective
as the ideas which referred to it. He then states the Critical
doctrine. The relation of ideas to an object merely imposes upon
them a particular kind of necessary combination, and so sub-
jects them to a rule or law.3 And conversely it is only the
necessity in the temporal order of our ideas which gives them a
relation to an object.4
Kant then proceeds to deal explicitly with the case of objective
succession. Since our apprehension is always successive,
succession in our apprehension does not by itself establish
succession in the object apprehended.5 But as soon as6 I per-
ceive, or rather presuppose,7 that in the succession of my
apprehensions an idea follows in accordance with a rule from
1 See A 189-91 = B 234-6 and Chapter XLIII § 4.
2 The text is obscure and perhaps corrupt, but Kant seems to
affirm that when we say ideas are ideas of an object, we do not mean
that the object to which they refer is only a particular idea 'object*
to be found among the other ideas. When we say 'the object is hard,
white, and sweet*, we are not referring these ideas to the idea of
'object', but to the object itself.
3 Kant is presumably here thinking of the law of causality, although
what he says is true of all the Analogies, which are concerned with
the existence of objects and not merely with the character of the
intuitions through which objects are given. Compare A 1 60 - - B 199
and A 179 = B 222.
4 These two statements together ought to make it clear that when
Kant talks of objectivity making necessity, and necessity giving
objectivity, he does not intend to imply that we have first necessity
and then objectivity, or vice versa. This combination seems to me
very important, because otherwise the second sentence, like so many
others, could be taken to imply that there is a process from subjective
ideas to a world of objects. This encourages me to deny the same
implication when it seems to be present in similar sentences taken
by themselves. 5 A 198 -- B 243.
6 This must not be taken to imply that I am first aware of a necessary
succession in what is subjective, and then infer an objective succession.
7 The second expression would appear to be a correction of the first.
XLIV§3] THE SECOND ANALOGY 251
the state1 which precedes it, I am aware of an event or objective
happening ; that is to say, I know2 an object which I am com-
pelled to place or 'posit' in a determinate position in time,
a position which it must be given in view of the preceding
state.3 This is unhappily expressed, because it may seem to
suggest that there is a psychological process by which we pass
from awareness of the subjective to knowledge of the objective.
I believe on the contrary that Kant is really trying to analyse
the act of perception into its elements, as becomes clearer in
what follows.
When I perceive an event, my perception contains or involves
a judgement4 that something precedes the event (for we cannot
know that anything is an event unless we know that there
was a preceding time in which it did not exist, and we cannot
perceive a preceding time unless it is filled). This would,
I think, be generally admitted; but Kant goes farther, and
asserts that the event can acquire5 a determinate or objective
position in time only if we presuppose that there is in the
state6 which precedes it something upon which it always
1 I use Kant's word 'state* (Zustand). This 'state* must be in some
sense an idea, like the idea which follows it, but Kant believes it may
also be a state of affairs. 'In accordance with a rule* always implies
necessity.
2 'erkenne.' Kemp Smith translates 'apprehend*, but I think it is
better to distinguish 'apprehension' from 'knowledge', since apprehen-
sion is only one factor in knowledge.
3 Here again we have the same word 'state', which may be a state
of mind or a state of affairs — it seems to me that Kant is leaving its
character vague — but the objectivity now ascribed to what follows
must belong equally to what precedes.
4 Kant says literally 'in this idea there is contained that something
precedes* (so ist in dieser Vorstellung ersthch enthalten: dass etwas
vorhergehe). From this it would seem he means that the perception not
only implies a fact, but also contains a judgement, though this judge-
ment may be 'obscure* at any rate as regards the details judged. In
A20i -= 62 46 the perception is said to contain knowledge (Erkenntnis)
of an event. But perhaps I am reading too much into the word 'idea*.
6 The word Kant uses is 'acquire* (bekommeri), but I do not think
he means that the event first of all has no such position and subse-
quently acquires it.
6 Here again 'state* is evidently used to cover the whole state of
affairs of which the cause is a part.
252 THE ANALOGIES OF EXPERIENCE [XLIV § 3
follows in accordance with a rule.1 Here again we have Kant's
central contention that objective succession must be necessary
succession, or succession in accordance with a rule.
This point is elaborated by the assertion of what Kant
describes as consequences.2 Firstly I cannot reverse the series,
that is, I cannot place or 'posit* the events in the reverse order ;3
and secondly if the preceding state is posited,4 this determinate
event necessarily and inevitably follows.
Finally Kant sums up his position.5 There is in our ideas6
an order in which the present7 (so far as it is an event8)
refers to some preceding state as its indeterminate correlate,
while the correlate stands to the event in a determining relation
(the relation of cause to effect) and necessarily connects9 the
event with itself in the time-series.10
I cannot think that this proof adds anything to what has
already been stated. Its language is unfortunate, so far as it
suggests in places that Kant is describing a process of passing
1 I think this already implies necessity; and when Kant says that
necessary succession follows from this, he is not making an inference,
but restating his contention in other terms.
2 'woraus sic/i denn ergibt.'
3 Note that in this case irreversibility very definitely follows from
objectivity, and not objectivity from irreversibility.
4 The word 'posited' here clearly implies existence — to exist is to
have a position in time. 6 A 198-9 =-- B 244.
6 Here the causal order is expressly stated to be an order in our
ideasy an order in which they are 'posited*.
7 das GegenwartigeS This must be an appearance, and so far an idea.
8 I take this to be the meaning of 'sofern es geworderf ('so far as it
has come to be').
9 The usual technical sense of 'connects' (verknupft).
10 This difference in the relations of effect to cause and cause to
effect was elaborated in A 193-4 — B 238-9. Compare Chapter XLIII
§ 5, V. The cause determines the effect, but the effect does not determine
the cause. This means for Kant that when we perceive the cause we
can go on to perceive the effect, but not vice versa. I can find no
evidence that this use of the word 'determines* is also intended to
express the common -sense view (so hard to analyse) that the cause
'produces' the effect, and does not merely precede it. Kant's list of
what he calls the 'predicables' — see A 82 = B 108 — and other passages
suggest that he regarded causality as more than mere necessary
succession.
XLIV §4] THE SECOND ANALOGY 253
from awareness of the subjective to knowledge of the objective.
The grounds for its central contention — that objective succes-
sion must be necessary succession — are, I think, stated less
clearly than in the second proof. What appears to me to be
manifest — and I regard it as an essential part of the Critical
Philosophy — is that for Kant objective events are only appear-
ances to human minds, and may even be described as ideas.
The difficulty of his exposition lies in the fact that these ideas
are regarded as being in a subjective succession so far as they
are successively apprehended, and in an objective succession
so far as they are posited, or given a position by thought, in
one homogeneous time. When we are actually perceiving
events, these two successions are asserted to coincide, and it is
not always certain which of the two successions Kant has in
mind.
§ 4. The Fifth Proof.
The fifth proof1 is commonly regarded as totally different
from all the others.2 It is an argument from the nature of time,
and it might be put in the form that there must be necessary
succession in appearances in order to represent in experience
the necessary succession of the parts of time3 — just as there
must be a permanent substratum of appearances in order to
represent or express the unity of the one time of which all
times are parts.4 This argument closely resembles the argument
for permanent substance, and it rests, as all Kant's proofs
do, on the supposition that time itself cannot be perceived.
1 A 199-201 = B 244-6 (three paragraphs).
2 It seems to me just possible that Kant may have regarded it as an
elaboration of what is obscurely hinted at in A 194 = B 239 at the end
of the second proof. There he points out that the passage of appearances
in time is always in one direction, and this follows upon the distinction
made between the relation of effect to cause and the relation of cause
to effect. The present proof follows immediately upon the same dis-
tinction, but it deals explicitly with the direction of the passage of
time as well as with the direction of the passage of appearances in time.
3 Compare A 205 = B 250 where the transitory is said to designate
or symbolise (bezeichnet) time, as regards its succession.
4 See B 225 and A 183 = B 226.
254 THE ANALOGIES OF EXPERIENCE [XLIV § 4
The preceding time necessarily determines the succeeding
time — in the sense that I cannot get to the succeeding time except
through the preceding.1 This is regarded by Kant as a necessary
law of our sensibility, because time is only a form of our sensi-
bility. He holds that for this reason it is also an indispensable
law of our empirical knowledge* of the time-series that appear-
ances in past time determine all existence in succeeding time,
and that subsequent appearances, as events? take place only
so far as their existence is determined4 by previous events.
The ultimate ground for this contention is that only by reference
to appearances can we know5 empirically this continuity6 in
the sequence7 of times. B
Kant goes on to insist once more on the presence of under-
1 This seems also to be the sense in which the cause 'determines*
the effect. Compare Kant's definition of continuity m A 209 = B 254.
2 The word is ' Vorstellung* (idea), but this must here mean know-
ledge. The knowledge is empirical, because we distinguish different
times only by the events in them.
3 The phrase 'as events' seems to imply that we may have subjective
appearances (the images of imagination) which are not events in the
objective world. As events in our mental history they also are deter-
mined by past events.
4 This determining of the existence of events is regarded as equiva-
lent to 'fixing' it (fcstsetzeri) in accordance with a rule. The word
'festsetzen* is commonly used for fixing a time — making, in the
American phrase, a 'date' — and suggests that 'to determine' is 'to
posit' or 'to give a definite position' in time.
5 Here again I think it essential to note that Kant is speaking of
'knowledge* (which involves understanding) and not of apprehension
(which does not).
6 It is important to observe that Kant uses the word 'continuity*
for this 'determination' of later by earlier time. This 'continuity' is
'transferred* to appearances, for Kant speaks of the 'continuous*
sequence in the series of possible sense-perceptions (A 200 -= B 245).
Continuity is discussed later in A 207 = B 253 fF , and at the end of
the discussion (A 210-11 — B 256) Kant seems to reassert something
like the fifth proof. 7 'Zusammenfiang.'
8 Dr. Ewmg (Kant's Treatment of Causality, pp. 74-6) seems to me
to ignore this point, and to treat Kant's argument as if it were a
dogmatic argument from the nature of time to the nature of what is
in time. He also suggests that a period of time considered as pure time
is as much determined by the succeeding as by the preceding period.
This Kant would deny to be the case in the sense in which he uses
the word 'determine*. Compare A 412 = B 439.
XLIV § 4] THE SECOND ANALOGY 255
standing in such empirical knowledge. It is understanding
which makes experience possible, for apart from understanding
we cannot know objects at all; and the analysis by which it
makes our ideas of objects distinct'1 presupposes the transcen-
dental synthesis — also at least partly the work of understanding
— by which alone we can have such ideas to analyse.2 In the
particular case we are considering — the case of objective suc-
cession— understanding is said to transfer3 the time-order
to appearances and their existence.4 It does so by adjudging
to each a temporal position determined a priori in relation to
previous appearances, and to do this is to judge each appearance
to be an effect. Unless appearances had such a temporal posi-
tion determined a priori, they would not accord with time itself,
since all the parts of time have such a position determined
a priori? The necessity for this activity of the understanding
— an activity which involves an a priori synthesis of appear-
ances— is due to the fact that we cannot determine the temporal
position of appearances by reference to absolute time (for
absolute time cannot be perceived) but only by their relations
to one another.
This argument is difficult and liable to misunderstanding.6
If we assume — in spite of modern physics — that time must
1 See Chapter XIX § 8.
2 Compare A 103-4 and also A 77-8 = B 103. 3 'ubertragt.'
4 I take it that understanding does so in the sense of ascribing to
appearances, as events, a position relative to one another in one
homogeneous time. This seems to be implied by the clause which
follows.
6 This looks like a dogmatic argument from the nature of time to
the nature of what is in time, but in the light of the context we must
take Kant to mean that under the condition stated they would not
accord with time in our experience.
6 The remainder of the argument (A 200-1 = B 245-6) only
elaborates in difficult language what has been already said. Kant, it
should be noted, explicitly says that to regard an appearance as having
a determinate position in time is to regard it as an object : only so can
it be said to 'exist1. He also speaks of the principle of causality as 'the
principle of sufficient reason*. This seems to me mere carelessness,
and I cannot believe that at the time he wrote the argument he
identified the principle of causality with that of sufficient reason.
256 THE ANALOGIES OF EXPERIENCE [XLIV §4
have a direction, we are entitled to say that if we are to be
empirically aware of a succession of times, we must be aware
of a succession of events in time ; and that an event which is
past in relation to another event cannot also be present or future
in relation to the same event.1 It may seem that Kant is con-
fusing the assertion that there must be a succession of events
with the quite different assertion that there must be a necessary
succession of events, that is, a succession determined by causal
law. Nevertheless I doubt whether he is guilty of so elementary
a fallacy. He seems to be arguing, not merely from the fact
that wre must be empirically aware of the succession of parts of
time, but from some special characteristic of that succession.
This characteristic he describes by saying that we can get to a
part of time only by going through the previous parts, and he
identifies it with continuity. The continuity of time means that
no part of it is the smallest possible part, and that in order to
get from any point of time to any subsequent point we must pass
through a part of time which is infinitely divisible.2 Kant
maintains that if we are to experience time as continuous,
we must experience change as continuous, and he seems to
regard this continuity of change as implying (if not as being
identical with) causation.3 If so, his argument cannot be con-
sidered apart from his account of the continuity of change.4
The whole subject is full of pitfalls, but it seems to me that
we are far too apt to take time, and the continuity of time, for
granted, and to ignore the question about what this must imply
in regard to our perception of events.5 If we do ignore this
question, are we not assuming that we can perceive absolute
1 This is all that Dr. Ewing (Kant's Treatment of Causality, p. 74)
will allow to be a legitimate inference. It is, I think, only another way
of saying that there must be a succession of events. Dr. Ewing, it
should be added, recognises also the possibility of arguing from the
continuity of time to the necessity of a causal connexion in objects of
experience, but he does not recognise, as I think he ought, that this
contention is an essential part of Kant's argument.
2 See A 209 = B 254.
8 Compare Alexander, Space, Time, and Deity (Vol. I, pp. 279 ff.).
•See A 207 == B253ff.
6 Compare Laird, Hume's Philosophy of Human Nature, p. 109.
XLIV § 5] THE SECOND ANALOGY 257
time, which, as Kant says, is impossible? The brevity of his
exposition, and the uncertainty which I at least feel in regard to
its precise meaning, are grounds for suspending judgement
about the validity of the argument ; but I am far from accepting
the view that we have here an elementary fallacy, and not a
serious problem which requires to be faced.
§ 5. The Sixth Proof
The sixth proof1 is only a summary. It states what Kant
regards as the 'moments' of an argument which is certainly in
need of simplification. I will attempt to separate the 'moments'
from one another, although it is not altogether easy to do so.
I. In all empirical knowledge there is a synthesis of the
manifold by means of imagination, and this synthesis is always
successive; that is to say, our ideas (whether their content is
judged to be successive or coexistent) are always successive.
II. The succession of ideas has in imagination no deter-
minate order — it is not necessary that one idea should precede
and another follow.
We should expect Kant to be still talking about imagination
as it is present in empirical knowledge generally. In that case
the succession of ideas, if we consider it in its subjective
aspect only, has simply the order which it has, and we can
see no necessity in it.2 But Kant goes on to say that the series
of successive ideas can be taken either backwards or forwards.
This is what he has hitherto asserted to occur when we are
apprehending the objectively coexistent.3 Since this seems
irrelevant here, he may be talking about a free play of the
imagination, which can put ideas in any order we please. If
B246 (one paragraph).
2 Compare the statement that the subjective succession by itself is
arbitrary and undetermined (A 193 = B 238). For the ambiguities of
this see Chapter XLIII § 5, III.
3 See, for example, A 192-3 = B 237-8. Such reversibility is not
universal, but is confined to a special case.
VOL. II I
258 THE ANALOGIES OF EXPERIENCE [XLIV § 5
so, this is a new point in the first edition, though it appears
to be made in the argument added in the second edition.1
Fortunately the ambiguities of Kant's statement do not
here affect seriously the nature of the argument.2 It is otherwise
when we come to the ambiguities of the following 'moment'.
III. If the synthesis is a synthesis of apprehension (that is,
a synthesis of the manifold of a given appearance), then the
order is determined in the object.
Here, although Kant does not make his meaning clear,3
he is considering only the case where what is apprehended
is an 'event*. When this is so, the object determines the order
in which ideas are taken up or apprehended.4 Kant himself
puts this more precisely when he says that 'in apprehension5
there is an order of successive synthesis which an object deter-
mines'.6 In accordance with this order, he adds, something must
necessarily precede, and when this 'something' is posited? the
other (that is, the event) must necessarily follow*
Here again I can only suppose Kant's argument to be that
when we apprehend an objective succession, the succession of
ideas in our apprehension is necessary; and since we are
1 B 233. For the ambiguities of this see Chapter XLIII § 3, III.
2 Imagination (whether considered as 'taking up* the manifold
successively or as combining the manifold in imaginary successions)
does not by itself determine the objective order of events.
3 Unless indeed the phrase 'given appear ance' is intended to indicate
that the appearance in question is an 'event' (Begebeiihett).
4 Compare A 193 — B 238 where the subjective succession is said
to be derived from the objective. Compare also the statement about
the object in A 191 = B 236.
6 'dann.* This might conceivably refer to 'object'.
6 Grammatically the sentence may also be translated as 'which
determines an object'. Kemp Smith translates it thus, and we can
find a parallel in B 218 when experience is said to determine an object
through sense-perceptions. I think either statement would fit the
argument. Compare 'objectively determined' in A 194 = B 239 and
the corresponding footnote in § i of the present Chapter. It is, as
usual, difficult to be ceitain whether Kant is identifying or distinguish-
ing the subjective and objective successions.
7 'Posited* as usual implies position in time and so existence.
8 Compare A 193 = B 238-9, A 195 = B 240, A 198 — B 243.
XLIV § 5] THE SECOND ANALOGY 259
concerned not with things-in-themselves, but with appearances
as possible sense-perceptions, the necessary succession of our
ideas is ipso facto a necessary succession in the object.1 If so,
objective succession is necessary succession, and this is what
Kant has to prove.
If I am right, this 'moment' contains the crux of Kant's
argument. What follows is only explanatory: it brings out his
view that apprehension or perception — if it is to be perception
of an event or an objective succession — involves judgement.
IV. If my perception2 is to contain knowledge of an objective
event,3 it4 must be an empirical judgement. We must think
that the succession5 is determined;6 that is, that the event pre-
supposes another appearance in time, upon which it follows
necessarily, or in accordance with a rule.
V. On the other hand, if I did posit7 the preceding event,
and the subsequent event did not follow,8 1 should be compelled
to regard as a mere subjective play of my imagination what I
had hitherto taken to be an event in the objective world.9 If
1 Compare Chapter XLIII § 5, IV.
2 * Wahrnehmung1 or 'sense-perception'. As we have so often seen,
sense-perception and apprehension are always closely connected by
Kant, and sometimes even identified.
3 This is what Kant ought to have said above, when he said 'if the
synthesis is a synthesis of apprehension*.
4 Grammatically this must apply to 'perception*. If it could apply
to 'knowledge', we should avoid the loose statement that sense-
perception is judgement.
6 'die Folge.' This perhaps might mean, not 'the succession', but
'the event which succeeds*. This would fit in better with Kant's
grammatical construction. If we take Kant to mean 'succession', he
must now mean the objective succession.
6 Compare B 234 for a similar insistence on the necessity for thought.
7 Here again 'posit* very clearly implies thought of the existence or
occurrence of what is 'posited* at a determinate time.
8 Kant says 'did not follow necessarily', but 'necessarily* adds
nothing to the statement. In this place, as in A 193 = B 239, Kant
clearly implies that if the event follows, it can be perceived.
9 This statement should be compared with the third proof
(A 194 -= B 239). It suggests that the third proof is intended only as
a 'moment* in the second proof.
260 THE ANALOGIES OF EXPERIENCE [XLIV § 5
I regarded it as somehow objective, I should call it a dream,
that is, an event in my mental history.
This statement obviously requires qualification — I might
for example come instead to the conclusion that I had been
mistaken about the cause. Nevertheless Kant seems to me to
be correct in saying that we distinguish appearances in dreams
and fancy from events in the objective world by the fact that
they do not accord with a world which is governed throughout
by causal law.1
VI. The relation of cause and effect2 is thus the condition
of the objective validity of our empirical judgements3 in rela-
tion to the series of sense-perceptions, and consequently is
the condition of the empirical truth of these judgements, and
therefore the condition of experience.
This may seem an unnecessarily elaborate way of saying
that the principle of cause and effect is the condition of our
knowledge or experience of objective succession. The reference
to empirical truth shows, however, that Kant is referring us
back to his general solution of the problem of objectivity (or
of the existence of objects).4
1 Compare A 451 = B 479, and also Laird, Hume's Philosophy of
Human Nature, p. 115.
2 This is elaborately described as 'the relation of appearances (as
possible sense-perceptions) in accordance with which what follows
(the event) has its existence determined necessarily and according to
a rule by something which precedes*. It is important to observe that
appearances are described explicitly as 'possible sense-perceptions'.
Kant clearly regards all events as possible sense-perceptions, not as
things-in-themselves, nor again as actual sense-perceptions: he is in
short a transcendental idealist. Needless to add, he is not saying that
in every succession known to be objective, the earlier event is the
cause of the later ; nor is he saying that we cannot know a succession
to be objective until we know its cause. He is saying that when we
know or assume any succession to be objective, we presuppose that
each objective event has, in the total state of affairs which precedes it,
'something* which determines it or is its cause. As this presupposition
need not be 'clear* to ourselves, we may say more simply that objective
succession implies necessary succession.
3 This looks back to 'moment* IV.
4 See A 191 = B 236 and compare Chapter XLIII § 4. See also
A 1 60 = B 199 at the end.
XLIV § 5] THE SECOND ANALOGY 261
VII. All succession or change in objects of experience must
therefore be governed by causal law.1
It is very evident that the whole argument turns on what
I have marked as 'moment1 III. It is also evident that Kant
was careless in writing his summary; for he seems to bring in
one point which has not previously been raised, and he ignores
another point of importance, namely, the doctrine that absolute
time cannot be perceived. There is no reference to the argument
of Proof V.
1 On the principle that the necessary conditions of experience are
necessary conditions of objects of experience. See A in and A 158
= B 197-
CHAPTER XLV
THE ARGUMENT FOR CAUSALITY
§ i . Kant's Presuppositions
If we are to understand Kant's argument, we must first
of all be clear as to the presuppositions which he believed to be
necessary. These seem to be as follows: (i) an object is a set
of appearances (which may also be called ideas or possible
sense-perceptions) bound together by necessity or possessing
necessary synthetic unity ; (2) the successiveness of our appre-
hensions is not by itself sufficient to justify the assertion that
there is succession in the object;1 (3) absolute time cannot
be perceived; and (4) we possess knowledge of objective
successions.
The first of these presuppositions is the outcome of Kant's
discussion in the Aesthetic and in the Transcendental Deduction ;
and we must assume it for the purposes of the argument. The
other three seem legitimate assumptions on any philosophical
theory.2
Kant himself in the second edition3 stresses a further pre-
supposition— that all successions (and he is thinking primarily
of objective successions) are a successive being and not-being
of the determinations of permanent substances.4 I believe
that this presupposition is as essential to the arguments of the
first edition as it is to the argument added in the second edition.
1 I adopt this form of statement as sufficient for the purposes of
Kant's argument.
2 The fourth assumption may be denied by philosophers of the
school of Berkeley and Hume, but even they cannot deny that we
seem to possess knowledge of objective successions. An analysis which
is compatible with what experience seems to reveal is (so far) pre-
ferable to one which is not. 3 B 232-3.
4 It may be objected that this is inconsistent with the first pre-
supposition given above; but we have to remember that for Kant, if
given appearances or ideas are to constitute an object, one of the ways
in which they must necessarily be bound together is as states of a
permanent substance in space.
XLV § 2] THE ARGUMENT FOR CAUSALITY 263
Indeed it is only because we take given appearances (or ideas)
to be states of permanent substances that we can speak of their
order in our apprehension either as necessary or as reversible
and irreversible. If we fail to recognise this as essential to the
argument, we are almost bound to fall into the error of supposing
that Kant is trying to explain how we can pass from knowledge
of necessity in the subjective order of our apprehension to
knowledge of objects. Kant's view is, on the contrary, that we
can discover necessity in the subjective order only if we already
assume that there are permanent objects or substances of which
given appearances are states. And this view seems to me
obviously correct.
In addition to these fundamental assumptions, there appear
to be two minor ones: (i) when we arbitrarily imagine events
in a particular order, we are not entitled to affirm that the
events are in that order ; and (2) when we know that a succession
is objective, thought must be involved as well as sense and
imagination. On these points Kant's doctrine is, I suggest,
absolutely sound.
§ 2. Kant's Argument
Kant's main argument seems to reduce itself to the assertion
that, granted these assumptions, the experience of objective
succession must be experience of necessary succession; and
contrariwise, if the successions we experience were not governed
by necessity, there would be no experience of objective suc-
cession, nothing but a blind play of ideas which we could not
consider to be experience at all.
This may seem to be mere assertion and unworthy of the
name of argument. The impatient reader may be tempted to
reply that if the Critical doctrine be accepted, it is indeed
impossible to understand how we can have knowledge of
objective succession; and that Kant, without any pretence at
argument, merely asserts objective succession to be necessary
because, on his presuppositions, he cannot think of anything
else which could reasonably be put forward as a ground for
regarding a succession as objective. The difficulty in which
264 THE ANALOGIES OF EXPERIENCE [XLVj 2
he finds himself, it may be said, is obvious, but we have no
reason to accept his baseless assertion of necessity as the only
possible way to escape from it. A simpler solution is the denial
of his fundamental presupposition, namely, that an object is a
set of appearances to the human mind and not a thing-in-itself .
This cavalier method would not go far to solve the real
difficulty to which Kant has called attention — that when we
apprehend appearances successively, we sometimes affirm
objective succession and at other times we affirm objective
coexistence ; nor would it help us towards a proof of causality,
if such a proof be possible. And although I think it is true that
Kant's argument is simply an assertion, in the sense that it is
an appeal to what he calls 'judgement', I do not believe that
the assertion is made for no other reason than the impossibility
of finding any other solution.
As I understand Kant's argument, he is offering us an
analysis of what is necessarily involved in experience, and
particularly in experience of objective succession. Whenever
we perceive an objective succession in which event j3 follows
event a, our perception b must follow our perception a. But
since, on Critical principles, the events a and ft are only
appearances to us, and are in this case identical with the per-
ceptions a and 6, this means that where our experience is of
objective succession, event j3 must follow event a.1 The suc-
sion of perceptions and the succession of events are in this case
not two successions, but only one. I can see no other way of
interpreting the argument.
Now it seems true to say that when we perceive an objective
succession, our perceptions must come in a certain order and
no other. The central question is whether the recognition of
this is legitimate on Kant's view of objects, or whether it rests
on the supposition that objects are things -in-themselves. If
we adopt the second alternative, we must regard his whole
argument as an elementary fallacy — we must say that he first
of all affirms necessity in the succession of our perceptions
1 This need not mean that a is the cause of /?, but only that (i must
follow upon a in accordance with causal law.
XLV § 3] THE ARGUMENT FOR CAUSALITY 265
on the ground that our perceptions are distinct from, and deter-
mined by, objective events ; and that he then goes on to infer
necessity in the succession of objective events on the ground
that when we perceive an objective succession, there is no
distinction between our perceptions and objective events. If
on the other hand he is entitled to hold both that when we per-
ceive events, these events are identical with our perceptions,
and that when we perceive events, our perceptions must come
in a certain order and no other, then, it seems to me, he is
entitled to his conclusion.
Kant's argument here, it should be noted, bears a resemblance
to the more general argument of the Transcendental Deduction :
it is in fact a special application of that argument. There he
asserted1 that when we have knowledge of an object, necessity
is always implied — the object is regarded as that which prevents
our cognitions from being arbitrary or which imposes upon
our cognitions a necessary synthetic unity. He then argued
that we are concerned only with our own ideas, and that the
concept of the object is simply the concept of the necessary
synthetic unity of ideas, a unity which is really imposed by the
nature of the mind. A study of the Transcendental Deduction
will, I think, confirm my interpretation of the present argument.
§3. Objective and Subjective Succession
Such an argument is not to be lightly or easily accepted ; but
we ought to ask whether the distrust which, as it seems to me,
it inevitably arouses is based on reason or is due to the diffi-
culty of the human mind in adjusting itself to a revolutionary
hypothesis. Even if the doctrine seems to verge on madness,
there is at least a method in the madness. If the interpretation
I have put forward be accepted, we can understand how the
whole argument hangs together — why, for example, Kant finds
it necessary to insist that an object is only a complex of ideas ;
why he asserts that the presence of succession in the object
means only that I cannot arrange my apprehension otherwise
than in this succession;2 why he appears to identify what he
1 See especially A 104-5. 2A 193 — B 23 8.
VOL. II I*
266 THE ANALOGIES OF EXPERIENCE [XLV § 3
calls 'the rule of apprehension' with the causal law of the objec-
tive succession; and why, having once made his point, he is
content to assert, as if it were something quite obvious, that
an objective succession must be a necessary succession.1
In any case it seems to me beyond question that for Kant
when we perceive an objective succession, the objective suc-
cession is identical with the subjective succession of our
ideas, and the same ideas or appearances are successive both
as ideas in my mind and as states of the object known.2 To
some this may seem sufficient ground for rejecting his whole
theory, but we must ask ourselves whether such a theory
is self-contradictory or impossible.
It is clearly impossible for any believer in representative
idealism ; and representative idealism, though the least defensible
of philosophies, seems to be the natural assumption of the human
mind. But Kant is not a representative idealist, except in so
far as he believes that the phenomenal world is only an appear-
ance to us of unknown things-in-themselves. As regards the
phenomenal world he is an empirical realist, and his whole
philosophy is a rejection of representative idealism. If the
phenomenal world is only an appearance to human minds,
why should it be impossible that a succession of states in a
phenomenal object3 should also be a succession of ideas in my
mind ?
No doubt even in that case what is apprehended cannot be
identified with my act of apprehending, but I do not think
Kant maintains that it is.4 If an idea is a content apprehended,
1 He does so even in the argument added in the second edition,
although this is placed before his more detailed exposition.
2 In this I agree with Professor Pnchard, Kant's Theory of Know-
ledge, p. 281.
3 It must not be forgotten that Kant believes himself to have proved
that a phenomenal object is a permanent substance with changing
attributes, although it is only an appearance to human minds of an
ultimate reality which we have no reason to regard as either permanent
or changing.
4 In A 1 90 = B 235 Kant does say that an idea differs not at all
from my act of apprehension ; but I believe from the context he means
only that it does not differ from my act of apprehension as regards its
time-relations.
XLV § 3] THE ARGUMENT FOR CAUSALITY 267
it can surely be both an event in my mental history and an
event in the objective world. An idea in a dream may, as a
content, differ in no way from a content apprehended in waking
life. We regard it as an event in a mental history, but we refuse
to regard it as an event in the objective world ; and our reason
for so refusing is that it does not fit into the necessary succession
of contents which for us constitutes the objective world. The
fact that the content apprehended in waking life fits into the
necessary succession which we regard as objective does not
imply that such a content is not also an event in our mental
history. Kant's theory may be mistaken, but I do not see
that it is self-contradictory. Indeed some such theory seems
to be necessary, if we hold that in waking life what we are
aware of is objective reality, and not merely an idea which
represents objective reality.
I do not think we can avoid this by saying that the events
in my mental history are mere apprehendings. An event in my
mental history is a whole in which the apprehending and the
apprehended are combined. And I do not think that this
doctrine means the absolute identity of the subjective and the
objective. Starting from the contents successively apprehended
in waking life we construct in imagination, and in accordance
with the categories, a whole world of possible contents or
appearances (or what Kant calls possible sense-perceptions),
and these appearances we regard as states or determinations
of permanent substances, which fill time and space. We dis-
tinguish the order of events in the world so constructed from
the order of our actual perceptions and our actual thinkings ;
and we distinguish this world and its events from the events
which appear to us in dreams or are invented arbitrarily by
our fancy. The order of events and the order of perceptions
are identical only in the case where we are directly perceiving
events.
It is on the identification of the two successions in this
particular case that Kant's main argument for causality rests.
It would be ludicrous to suppose that events were things-in
themselves, and to argue that because the succession of our
a68 THE ANALOGIES OF EXPERIENCE [XLV § 4
perceptions is necessary when we perceive events, therefore
the succession of the events is determined by causal law.
And whether Kant is right or wrong, his argument is, as he
says, a Critical proof which seeks to establish the conditions
of our experience of objective succession, and it is not a dogmatic
proof from an analysis of the concept of event.1
§ 4. The Conditions of Experience
An analysis of the conditions of experience is to be sharply
distinguished from a treatise on the methods of induction.
Kant believes that experience is essentially and always an
experience of objective succession,2 and he is arguing that it
must therefore be an experience of necessary succession. His
argument is of a purely general character intended to establish
the principle of causality. It is no part of his business to describe
in detail the methods by which we decide whether a succession
is objective, and still less to describe the methods by which we
determine the precise cause of a particular event.3 The criti-
cisms brought against him for failing to do this seem to me
irrelevant. A proof of causality would in itself be an important
contribution to philosophy, and it is absurd to blame anyone
1 Pnchard (Kant's Theory of Knowledge, p. 300) maintains that such
a dogmatic proof is possible, and that there can be no other.
2 Even where we perceive an objective coexistence (as in perceiving
the different parts of a house) what we perceive is, I suggest, recognised
as an object whose characteristics remain the same amid change.
Kant indeed seems to hold that change is merely an empirical fact
whose necessity cannot be inferred from the fact that the world is in
time ; but it is hard to see how apart from change of some sort we
could be aware of time, and Kant himself speaks of the transitory as
'symbolising' the successiveness of time. Without such 'symbolising* I
do not think we could be aware of time or of its successiveness. See
A 205 — B 250 and compare A 452 n. = B 480 n.
3 When Kant says m A 203 = B 249 that temporal succession is the
only empirical criterion of the effect, he obviously means that this is
the only empirical criterion by which we can distinguish effect from
cause, when we already know that two phenomena are causally con-
nected. It is most unreasonable to separate this statement from its
context, and then to blame Kant for the inadequacy of his theory of
induction.
XLV § 4] THE ARGUMENT FOR CAUSALITY 269
because he deals with his own problem and does not deal with
ours.
The modern interest in inductive methods has led to an
altogether disproportionate interest in Kant's statement that
when we perceive objective events the order of our sense-
perceptions is irreversible.1 It is far too commonly supposed
that Kant is trying to infer objectivity, or even causality,
from the irreversibility of our sense-perceptions. Yet it is
surely obvious that we could not know the succession of our
perceptions to be irreversible, unless we knew that we were
perceiving an object and indeed a substance; we could only
know that our perceptions came to us in the order in which
they came. What Kant himself maintains is that when we
perceive an objective event, our sense-perceptions must be
irreversible — not that when we find our sense-perceptions to be
irreversible, we infer that we are perceiving objective events.
The word 'irreversibility' is not even used by Kant himself.
It is only our shorthand method of describing that necessity
which he finds in the succession of our perceptions when we
are aware of objective events.
It should be noted that when we assume what we are perceiv-
ing to be a real object, we can by experiment2 discover whether
or not it is possible to receive sense-perceptions (or appearances)
in the reverse order; and from this we can determine whether
the successively given appearances are coexistent or successive
in the object. If, for example, we find that we are unable to get
certain sense-perceptions (or appearances) in the reverse order,
we conclude that a particular succession in our apprehension
is also a succession in the object. But this manifestly presup-
poses from the beginning that we are perceiving an object;
and indeed we have no right to assert that the order of our sense-
perceptions is a necessary order, unless we are assuming that
1A 1 92 — 623 7. Professor Loewenberg, for example (University of
California Publications in Philosophy, Vol. 15, p. 9) takes Kant's
formula for causality to be 'irreversible succession', although he adds,
very rightly, that Kant's full meaning of causality cannot be expressed
by this formula.
2 For example, in the cases of a house and of a moving ship.
270 THE ANALOGIES OF EXPERIENCE [XLV §4
what we perceive is a succession in the object.1 We can never
reach necessity by observation, and least of all by observation
of the order of our own ideas as such; and even if we could,
we could never be justified in inferring objectivity from a merely
subjective necessity.
I cannot see why Kant should be expected to describe in
detail the empirical methods by which we learn to distinguish
an objective succession from an imaginary succession or from
a set of coexistent appearances successively apprehended.
Such a study lies presumably in the field of empirical psychology,
and Kant is free to accept any reasonable account that psycho-
logy may offer. There is, for example, no reason why he should
deny that in asserting the existence of real objects we depend
very largely upon what Hume describes as the firmness or
solidity or force or vivacity or steadiness of our ideas. All he
maintains is that where objectivity is asserted, there necessity
is presupposed ; and that where we are convinced that appear-
ances to us will not fit into the world as a system governed by
causal laws, there we deny the objectivity of the appearances.
This is obvious in the case of hallucinations, mirages, and
even dreams, which may lack nothing in vivacity or force
or steadiness.2
Again it is no real objection to Kant's doctrine to say that on
his theory night must be the cause of day.3 He has nowhere
asserted that when we experience successive events, the first
must be the cause of the second. He has asserted only that such
a succession must be causally determined, and that in the total
state of affairs preceding any event there is to be found some-
thing, 'some as yet indeterminate correlate',4 which is the cause
1 Compare Pnchard, Kant's Theory of Knowledge, pp. 288-9.
2 Compare A 45 1 =. B 479.
A The denial of this is explained by Dr. Montz Schhck (University
of California Publications in Philosophy , Vol. 15, p 102). 'Day' and
'night', he points out, are really not names for 'events' in the sense
in which this word is used in science. 'And as soon as we analyse
day and night into the scries of natural events for which these names
stand, we find that the sequence of these events must be regarded as a
very good example of "causal connection".' 4 A 199 = B 244.
XLV § 5] THE ARGUMENT FOR CAUSALITY 271
of that event. Nor has he asserted that in order to know that
an event is objective, we must first of all know its cause. His
doctrine is, on the contrary, that when we judge an event to be
objective, our judgment presupposes that the event is governed
by the general law of causality, and therefore that its cause
is to be found in some previous event. The determination of
the cause is a matter for science alone, and the discussion of
the methods by which science determines the cause is a matter
for Inductive, and not for Transcendental, Logic. Kant's
doctrine on all these matters seems to me to be sound. The only
question is whether he has succeeded in proving that necessary
succession is a condition of experience.
§ 5. The Process to Experience
It may be thought that some of the objections have been
too lightly dismissed ; for if Kant is describing the process by
which we pass from awareness of a succession of ideas to know-
ledge of the objectively successive and objectively coexistent,
he is surely obliged to give some account both of the methods
by which we do so and of the reasons by which these methods
can be justified.
My answer to this criticism, which raises a question of
fundamental importance for the interpretation of the Kritik,
is that Kant is not attempting to describe any process of this
kind. What he is doing is to determine the necessary conditions
or presuppositions of all experience; and this task is, as he
himself states,1 entirely different from the task of describing
how experience develops or comes to be. I do not deny that
sometimes language is used which may seem to describe a
process of development, but allowance must be made for the
difficulty of avoiding such language in an abstract analysis.
And I refuse to believe that Kant is attempting to describe
how experience develops, not only on the ground that he him-
self denies this whenever the question is raised, but on the more
1 See especially Prol. § 2ia (IV 304): 'Ilier nicht von der Entstehen
der Erfahrung die Rede set, sondern von dem, was in thr hegt\ Compare
also Chapters III § 3, VI § 7, and XVI § 5
272 THE ANALOGIES OF EXPERIENCE [XLV § 5
fundamental ground that such an interpretation makes Kant's
argument so \\eak that it is hardly too much to describe it as
nonsense, while my interpretation, I submit, makes it sense.1
It is, in the first place, impossible to believe that there is a
development from awareness of the subjective to knowledge of
the objective.2 We can recognise the subjective only when we
distinguish it from the objective (this is Kant's own view);
for 'subjective* and 'objective* are correlative terms which
mean nothing except in relation to one another. And if we
started with awareness of something merely subjective, it
would, so far as I can see, be impossible to pass to knowledge
of the objective.
In any case — and this is my second point — Kant's argument
for causality does not offer us even a plausible account of such
a transition. First of all, according to this interpretation, we
are aware of a subjective succession, which in some inex-
plicable manner we recognise to be subjective. Then we
become aware in a still more inexplicable manner (for we
cannot have empirical knowledge of necessity) that a particu-
lar subjective succession is necessary or irreversible. Finally
we conclude — on what grounds and by what right? — that we
are aware of an objective succession.3 The harshest criticisms
1 This is the central matter on which my interpretation differs
consistently from Professor PnchartTs penetrating analysis in Kant's
Theory of Knoivledge. He interprets Kant as explaining how experience
of the objective comes to be, and I entirely accept his criticisms of the
view he ascribes to Kant, but I do not believe that what he is here
attacking is Kant's view.
2 We may of course be in doubt whether a particular appearance
is subjective or objective and we may resolve that doubt; but this
process occurs when we have already distinguished the objective
world from the subjective succession of our ideas. There must also
be a process in infancy (perhaps repeated whenever we awake from
sleep) whereby we pass from an awareness in which the subjective
and objective are not distinguished to a knowledge in which they are.
It may be possible for psychology to describe such a process, but this
has nothing to do with Transcendental Logic.
3 The further conclusion that the objective succession must there-
fore be a necessary succession merely adds a crowning absurdity to
this absurd series.
XLV § 6] THE ARGUMENT FOR CAUSALITY 273
of Kant's doctrine would be altogether too kind, if this were the
proper interpretation of his argument ; but such an interpreta-
tion (and I cannot see one that is more plausible, if Kant
is describing a process from subjectivity to objectivity) seems
to me to refute itself.
§ 6. Causality and Time
I have attempted to make clear what I regard as the inner
core of Kant's argument — the contention that if we accept
the Critical presuppositions, objective succession must be
necessary succession. There is, however, a danger that in so
doing we may fail to recognise the importance of the part
which time plays in the argument. Kant's doctrine of time
forms a strand which runs through his whole discussion,
although it finds its clearest, and in some ways its most
difficult, expression in the special argument which deals with
the continuity and irreversibility of time.1
We must remember that for Kant an object may be said
to exist, and so to be a real or actual object, only if it has a
determinate position in one common homogeneous time
(and space). The same doctrine applies to the special case of
succession, or change, in the object, the case to be considered
in the Second Analogy. If a succession is objective, then the
changes which take place in objects (changes which may be
called simply 'events') must have a determinate position in
one common homogeneous time (and space). Kant's argument
all through is that time itself (or absolute time) cannot be
perceived, and therefore events can have a determinate
position in time only from their relation to one another. This
determinate position cannot be given to mere apprehension,
since apprehension may be successive where there is no succes-
sion of events. On this he bases his doctrine that when we
experience a succession of events as objective, we presume
that the succession is necessary — the position of events
relatively to one another can be determined in one common
homogeneous time only if it is presupposed that they follow
1 A 199 = B 244 ff. See Chapter XLIV § 4.
274 THE ANALOGIES OF EXPERIENCE [XLV § 6
one another in accordance with a universal rule. Unless they
do so, the whole distinction between objective succession and
a succession which is merely subjective or imaginary must
disappear. We are no longer in a position to make an appeal
to things-in-themselves as a way of avoiding this conclusion,
and it is doubtful whether they would be any help to us
even if we could.
This line of argument — whether it be sound or unsound —
is certainly fundamental to Kant, and it is borne out by his
general account of the Analogies.1 All three Analogies are
concerned with necessary connexion in time; the Second
Analogy is concerned with that rule of necessary connexion
which relates to succession as one of the three modes of
time.2
We may even say that the Analogies, and in particular
the Second Analogy, express the rules of necessary connexion
in time in general? they are derived, not from given sensations,
but from the nature of time as such and the necessary unity
of apperception. We must not indeed imagine Kant to treat
time as a thing-in-itself , a kind of receptacle which determines
everything in it in certain ways. Such a view, apart from its
inherent absurdity, would not help us in any way ; for time itself
cannot be perceived.4 Kant's view on the contrary is that given
appearances must conform to certain rules, if we are to be
aware of objects in one time, and so to have empirical knowledge
of time itself.
It is only a step from this doctrine to the special argument
which rests on the continuity and irreversibility of time:5
this special argument does little more than bring out details
which have not been made explicit. I need not enter into its
difficulties again; but it is all-important to recognise that
Kant is concerned with the conditions of experiencing events
in one common homogeneous time, which is here, as elsewhere,
regarded as continuous and irreversible. We could not, according
1 Sec B 218-19 and A 176-7 ff. 2 A 177-8 = B 219-20.
3 Compare B 219. 4 Compare A 452 n. = B 480 n.
6 A 199 — B 244 ff. Compare Chapter XLIV § 4.
XLV § 7] THE ARGUMENT FOR CAUSALITY 275
to Kant, experience events in such a time,1 we could not even
have empirical knowledge of the continuity of time,2 unless
appearances conformed to causal law.
The general principle of this contention is already familiar
to us from the Transcendental Deduction. The reason why
the causal law prevails, and must prevail, throughout the
objective world as known to us is that this world consists only
of appearances, and that the human mind (for which alone
this world exists) must 'posit' appearances in one common
homogeneous time: to do so is to subject appearances to the
universal law of causality ; for without this the unity of time,
and so the unity of apperception, would disappear, and there
could be no experience and no objective world.3
However little we may like Kant's doctrine, there seems to
me no reason to doubt that this is what his doctrine is.
§ 7. Particular Causal Laws
It cannot be too often repeated that for Kant what the mind
thus imposes upon objects is the universal law of necessary
succession or causation. Particular causal laws can be known
only as a result of experience.4 All such laws are only particular
determinations of the one universal law which is imposed
by the human mind ; but they are not themselves imposed by
the mind, nor can they be known a priori. Their particularity
belongs to the matter of experience, not to its form. As such
it must be due to things-in-themselves and not to the knowing
mind.5
This doctrine taken in its widest scope — the doctrine,
namely, that the universal form of all objects is imposed
by the mind on a matter given by things-in-themselves — seems
to be a possible hypothesis involving no internal contradiction.
There may be special difficulties as regards causation,6 but
these difficulties do not affect the general principle.
1 A 199-200 ~ B 244-5. 2 A *99 = B 244.
3 See especially the conclusion of the Transcendental Deduction in
both editions. This type of argument is used in all the Analogies.
4 Compare A 126, A 127-8, B 165, A 159 -- B 198, and A 216 ~
B 263. 5 Compare Chapter VI § 8. 6 See § 8 below.
276 THE ANALOGIES OF EXPERIENCE [XLV § 7
Although particular causal laws cannot be known a priori,
Kant always assumes, as we all do, that it is possible for us to
discover particular causal laws. He assumes, that is to say,
that we can separate out particular chains of cause and effect
which will be found to repeat themselves. This is seen most
clearly in his continual insistence that given the cause the effect
must always and necessarily follow. It is, I think, seen even in
the frequent assertion that the effect must follow 'in accordance
with a rule'; for a 'rule' seems to imply regularity and repe-
tition. I believe Kant recognises the whole state of affairs
which precedes any event to be the condition of the occurrence
of that event ; but he appears to assume that there is always one
event, or series of events, which can be described as in a special
sense the cause of any given effect.1
So far as I can see, such assumptions are not a consequence
of the principle of causality, nor have they been justified by
any argument.2 It is theoretically possible that in a universe
governed throughout by causal law there might be no repeti-
tions. Kant himself recognises in another connexion that,
in spite of the formal and universal laws by which nature must
be governed, the given matter might be such that in nature no
similarities could be found;3 and clearly if we could find no
similarities in nature, we could equally find no repetitions.4
This is not the place to examine Kant's solution of this
problem, which concerns, not the categories, but the Ideas
of Reason.5 I doubt whether he faced its implications as regards
1 In Metaphysik, p. 42, he says explicitly that an event has many
concausae, but of many coordinate concausae one is the principal cause,
and the others are secondary. This doctrine is clearly implied m his
account of the continuity of change and of causation ; see for example
A 2io-i - B 256.
2 For a different view, see Evving, Kant's Treatment of Causality,
p. 102. If there is any proof of the separability of particular causal
series, it must, I think, lie in the fact that causal events, like substances,
are spread out in space, and that the transition from cause to effect
is continuous. 3 See A 653-4 = B 681-2.
4 I do not think Kant faced this problem sufficiently till he wrote
the Kntik of Judgement] see especially Erste Einlettung V.
5 See especially A 657-8 .= B 685-6.
XLV § 7] THE ARGUMENT FOR CAUSALITY 277
causality; but if we follow the general line of his thought, we
may, I think, say that it is in the nature of human reason to
isolate, so far as it can, relatively separate chains of causes and
effects, and always to seek a further cause beyond the proximate
cause which has been found. The possibility of doing so depends
on the repetition of similar causal series in nature; and this
repetition in turn depends, not upon the nature of the human
mind, but upon the nature of things-in-themselves or, if we
prefer it, on the grace of God. I imagine that in this case, as
in the case of teleology, our reason bids us to examine nature
as if it were the creation of an all-wise spirit and were adapted
to the needs of human understanding.1
It may be said that unless there were repetitions of similar
series in nature, we could never make the concept of cause and
effect 'clear' to ourselves;2 and indeed, if Kant's argument
is sound, we could never become aware of objective succession,
and so we could never have anything which could be described
as human experience. May not such repetition be regarded as a
necessary condition of experience, and is not such repetition
therefore established by precisely that method of argument
by which Kant seeks to establish the universal law of causality
itself?
The answer to this question is most emphatically in the
negative. We can indeed determine empirically certain con-
ditions which are necessary to experience, and among these
conditions is, I think, a certain amount of regularity or repetition
in nature, and perhaps even the repetition of chains ot causes
and effects. But we cannot say a priori that these conditions
must be fulfilled. As I understand Kant, in the case of the
universal law of causality (as in the case of all Principles of
the Understanding) if we grant the unity of apperception
and time as a form of our sensibility, the application of the
law to all events whatsoever in the phenomenal world follows
as an inevitable consequence.3 He is not saying that unless the
phenomenal world conforms to the law of causality, we could
1 Compare A 686 = B 714 ff. 2 See A 196 — B 241.
3 Compare A 216 = B 263 and A 217 = B 264.
278 THE ANALOGIES OF EXPERIENCE [XLV § 8
have no experience of it. He is saying that there could be no
phenomenal world unless it so conformed.
I would add that in this discussion Kant makes no mention
of other kinds of causality, such as the possibility of free actions
or final causes: these questions have to be dealt with later.
But so far as I can see, the admission of such possibilities later
demands no modification or qualification of his present doctrine
which is concerned only with mechanical (or efficient) causation.
If a succession is to be objective, it must conform to the universal
law of cause and effect as here explained, although in particular
cases it may conform also to further laws with which we are
not here concerned.1
§ 8. The Transcendental Synthesis of Imagination
I have attempted to set forth the reasonableness of Kant's
doctrine, but I must confess that I still find great difficulty
in the fact that causal law is for Kant imposed upon appearances
by the transcendental synthesis of imagination.
One side of this doctrine is easy enough to understand.
The concept of causation, while we do not become consciously
aware of it till experience has developed, seems, like the law
of non-contradiction, to be presupposed at a very early stage;
and in fact, if Kant is right, to be presupposed as soon as
we can be said to be aware of changes in physical objects.
It is in the nature of the human mind to think in terms of causes
and effects long before it is consciously aware that it docs
so. In our everyday experience we cannot restrict ourselves,
unless possibly by an effort of will, to the apprehension of
given appearances, but starting from this frail basis we have
before us at every moment a world which we construct in
memory and in imagination controlled by thought. In this
construction the concept of causality consciously or uncon-
sciously plays a leading part, and only by its help can we know
1 When we fail to find a teleological connexion and have to be
satisfied with a merely mechanical, we are said only to miss an
additional unity (cine Einheit mehr)\ see A 687-8 = B 715-16.
XLV § 8] THE ARGUMENT FOR CAUSALITY 279
an objective world extending through space and time as an
ordered and systematic whole.
So far Kant's doctrine offers little difficulty, and seems to
me manifestly true, at least as a prima facie description of the
facts. But there is another side to this which is very hard to
believe. The orderly world which we construct on the basis
of our sense-perceptions is confirmed at every moment by these
continually changing sense-perceptions themselves. Our sense-
perceptions must occur in an order compatible with the causal
order of the objective world;1 and Kant's doctrine is that in the
last resort the causal order is imposed upon our sense-
perceptions by the transcendental synthesis of imagination.
This difficulty I cannot attempt to discuss adequately here.2
It may be that the difficulty is partly due to our tendency not
to take the Copernican revolution seriously, and not to
recognise that time is only a form of our sensibility which
has nothing to do with things-in-themselves. I do not find
it difficult to suppose that our minds are such that to them reality
must appear as physical bodies in space which must conform to
the laws of geometry ; but for some reason I do find it difficult
to suppose — and I imagine that many share this difficulty —
that our minds are such that to them reality must appear,
not only as a succession of changes in time, but as a succession
of changes in time which must conform to causal law.
There are two ways of avoiding this difficulty.3 One is to
1 By this I mean that when we perceive an objective succession,
our sense-perceptions, as contents, are for Kant events in the pheno-
menal world, and their succession is causally determined. It is much
harder to believe that the transcendental synthesis determines the
order of actual sense-perceptions (or given appearances) than that it
determines the order of possible sense-perceptions. There is a further
difficulty in the fact that our sensations are caused by physical objects,
and that while primary qualities of objects are the same for all men,
the secondary vary from individual to individual. The first difficulty
concerns what Price (in Perception) calls ' horizontal' causality,
while the second difficulty concerns what he calls Vertical' causality.
2 It is connected with the doctime of double affection, and was one
of the problems which Kant attempted to work out in the Opus
Postumum. a Compare Chapter XXXI §§ 4-5.
a8o THE ANALOGIES OF EXPERIENCE [XLV §8
assert that the transcendental synthesis of which Kant speaks
is a pre-conscious and noumenal synthesis which somehow
constructs the whole physical world for us before we begin
to know it. For this view I can find no basis in Kant, nor does
it seem to me to have the least plausibility as a metaphysical
theory. The other way is simply to assert that Kant's doctrine
of transcendental synthesis is a mistaken kind of psychological
doctrine which need not be taken seriously. I feel sure that
this view is wrong; for it seems to me quite clear that there is,
and must be, a transcendental synthesis by which we construct
one time and one space, and that this construction does
necessarily impose certain characteristics on the world which
we experience. The difficulty is to understand how it can impose
a causal order on the succession of my actual sense-perceptions.1
1 I do not think Kant would claim that we have 'insight* (Emsicht)
— that is, the insight of reason — in a matter of this kind; see
A 171 -= B 213.
CHAPTER XLVT
CAUSALITY AND CONTINUITY
§ i. Kant's Concept of Causality
Kant offers us no detailed analysis1 of the concept of causality
such as we are familiar with in philosophical studies of science
to-day. What he attempts to prove is no more than necessary
succession, which he interprets as succession in accordance
with a rule. If the event a occurs, then the event /3, other
conditions being the same, must always follow.
I think it is a mistake to infer from this that by causality
Kant meant necessary succession and nothing more. His
business is to prove what he calls the schema of necessary
succession ; but in so doing he believes himself to show both
that phenomenal objects must conform to the pure category
of ground and consequent, and that the pure category receives
'sense and significance' when it is translated into terms of
time and so is transformed into cause and effect . He regards
the cause as a ground of the effect, but as a ground which
must precede the effect,2 while a merely logical ground does
not precede its consequence. More precisely, the cause is
(or contains) the ground of the existence of the effect, it is a
principium fiend i ?
The cause of which Kant speaks is the efficient or effective
cause. He defines it as a cause through acting force.4 The
1 Some blight attempt at analysis is made in Mcfuphysik, pp 41 fT.
2 Compare A 91 B 124, 13 234, A 202 — B 247 — and many other
places.
3 Sec Metaphysiky p. 41. The logical ground (tat to) is there said to
be the ground of possibility or the pimcipium cssendi. The three
straight lines in a triangle are its ground, but not its cause. The ground
of knowledge, on the other hand, is the principtum cognoscendi. Compare
also dc Vleeschauwer, La deduction transcendentale, I, p. 106.
4 'eine Ursache durch cimvirkende KrajtS Metaphystk, p. 42. Kant
regards the habit of appealing to final causes alone as 'the cushion of
a lazy philosophy* (em Polstcr dcr faulen Philosophic); compare
A 689 -= B 717.
282 THE ANALOGIES OF EXPERIENCE [XLVI § i
'predicates' of causality are force, action and passion.1 Causality
leads to the concept of action or activity, the concept of action
leads to the concept of force, and so to the concept of substance.2
The relations dealt with in the Analogies are essentially dyna-
mical relations.3 Kant, so far as I can see, simply accepts the
concepts of Newtonian physics in this connexion, and makes
no attempt to alter or modify the concept of causality. I do not
think it will be denied that for Newton the cause was supposed
to 'produce' the effect.4
It is indeed often maintained5 that for Kant causality can
be nothing more than regular succession, because for him
objects and events are only appearances or ideas, and there
can be no activity or causal efficacy in ideas.6 Such a contention
seems to me unconvincing. The fact that the world is only
an appearance to human minds is no reason why it should not
appear to human minds as made up of substances acting causally
upon one another and displaying real efficacy or dynamical
causality. The only difficulty is to know what can be meant
by 'real efficacy' ; but this difficulty is not confined to the Critical
Philosophy. Kant quite certainly believed that his doctrine
was compatible with the physics of his time, and indeed was
the only possible justification for the scientific concepts which
were actually in use.
It may be added that for Kant causality implies the possi-
1 A 82 = B 108.
2 A 204 - B 249. In A 648 -- B 676 force is identified with the
causality of a substance.
3 A 2 15 — B 262. The distinction between commumo and commercium
in A 213-14 - B 260-1 also serves to emphasise the same point.
4 Compare Lenzen, University of California Publications in Philo-
sophy', Vol. 15, p. 72. Kant himself uses the word 'produce1 (erzeugcn)
in connexion with causality; see, for example, A 208 -- B 254 and
A 474 = B 502 ; also the heading in A 1 89.
6 E.g. by Paulsen, Immanucl Kanty sixth edition, p. 189.
6 Kemp Smith, Commentary, p. 373, also accepts this contention,
but maintains that on Kant's phenomenalist (as opposed to his
subjectivist) views he is able to recognise genuinely dynamical activities.
He has, however, to admit that Kant's phenomenalist view of the
causal relation 'receives no quite definite formulation either in this
section or elsewhere in the Critique*.
XLVI §2] CAUSALITY AND CONTINUITY 283
bility of prediction. We can state the causal relation in the
form 'if A, then B', or 'if A is posited, B must follow'. This
analogy with the form ot judgement does not, however, mean
that the relation of cause and effect is in any concrete instance
intelligible to us a priori. In this respect Kant agrees with Hume.
We can discover the cause of a given effect, or the effect of a
given cause, only by means of empirical experience.1 Our
a priori knowledge is confined to the statement that every
event must have a cause.
§ 2. The Successiveness of Cause and Effect
The three main questions in regard to causality discussed
by Kant in the observations which, as usual, he appends to
his proofs are (i) the successiveness of cause and effect, (2) the
connexion between substance and causal activity, and (3) the
continuity of change. The second of these questions has
already been discussed.2 We must now consider the other two.
Kant has expressed the Principle of causality in the first
edition3 by the formula: 'Everything that happens (that is,
begins to be) presupposes something upon which it follows
in accordance with a rule*. In simpler language, every event
has a cause upon which it necessarily follows. Kant thinks
it necessary to meet the objection that in some cases the effect
does not follow the cause, but is simultaneous with it.4 The
heat of the room, for example, is simultaneous with the heated
stove which is its cause. It may even be urged5 that this is true
of most causes and effects.6 We fail to notice this because it
takes some time for the cause to have its full effect, but the
beginning of the effect is always simultaneous with the cause.
1 A 206-7 = 6252. Compare A 171 — 6213 and also A 41 = B 58.
2 See Chapter XLII § 9. 3 A 189. 4 A 202 = B 247-8.
6 I take it that Kant is still expounding the objection with which he
has to deal. Kant's reply begins later with the words 'Now we must
not fail to note . . .'.
0 If Kant were speaking in his own person I think he would have
said 'all'. That he says 'most* suggests that he is still thinking of a
rather crude objection. He says in the next sentence that the beginning
of the effect is always simultaneous with the cause.
284 THE ANALOGIES OF EXPERIENCE [XLVI § 3
Kant's reply is obvious enough. When we say that the effect
follows the cause, we do not mean that the cause comes to
an end, and there is then an interval of time after which the
effect begins. What \ve are dealing with is the order of cause
and effect in time, and this does not mean that there is a passage
or interval of time between them. On the contrary, although
the time between the causality1 of the cause and the effect
is a vanishing quantity, and cause and effect are simultaneous
in the sense that there is no gap between them, this does not
alter the fact that cause and effect are in a temporal succession.
It means only that the temporal succession is continuous.2
This discussion is, I think, intended to prepare the way for
the doctrine of the Third Analogy.
§ 3 . The Continuity of Change
Kant's account of the continuity of change is both more
difficult and more important.3 It is difficult in itself, and it
seems to contradict the doctrine set forth in the Anticipations.4
1 This phrase is used because a cause may in a sense be present
without producing the effect, if there is some impediment which
prevents it from doing so. Compare Metaphysik, p. 43.
2 Kant gives two illustrations to show that in cases of seeming
simultaneity we distinguish effect from cause by order in time. These
are (i) the popular one that if we lay a bullet on a cushion, there
follows a hollow in the cushion, but if there is a hollow in the cushion,
it is not followed by the presence of a bullet; and (2) the experiment
of surface-tension made first by Segner in 1751, who was led thereby
to the discovery of capillary attraction. If we fill a nanow glass by
dipping it into a large vessel of water, the surface of the water becomes
concave in the glass. 3 A 206 -= B 252 ff.
4 A 171-2 — B 212-13; compare Chapter XXXVIII § 7. The con-
tradiction lies in the fact that the continuity of change was there
asserted to belong to universal natural science (which I take to be
Rational Physiology or Rational Physics), and not to Transcendental
Philosophy; here it is discussed without any apology or explanation,
whether because Kant had changed his mind on the subject or because
he was unable to keep away from the problem in spite of recognising
that it ought to be dealt with in another place. It is true that in the
present passage he reaffirms his earlier doctrine that we have not the
slightest a priori conception of the way in which anything can be
changed; but I cannot see that there is any real difference between
dealing with the form of change (which he now proceeds to do) and
XLVI § 3] CAUSALITY AND CONTINUITY 285
It is important because of its bearing on the special proof of
causality from the nature of time (Proof V), and also because
of the light it throws on the doctrine of the Anticipations.
We have not the slightest conception of how change is pos-
sible, but are entirely dependent upon experience.1 This,
however, applies to change as something concrete, the succession
(or exchange) of given states of a substance. We can abstract
from the content of these states and consider a priori the form
or condition of change in general, and we do so in relation to
the law of causality and the conditions of time. The form or
condition of change seems to be identified with the bare
successiveness of change;2 and Kant is asking 'What can be
said a priori about change on the sole ground that it is a
succession in time (in complete abstraction from the empirical
character of the states of which it is a succession)?'
When a substance passes from state a to state /?, t^ (the
moment at which j3 occurs) differs from and is subsequent
to tl (the moment at which a occurs). Between these two
moments there is always a time, however short, which may be
represented by A, — tL.
State j8 differs from and is subsequent to state a. The
difference must be regarded as a difference only in quantity,
that is, in degree,3 since we arc ignoring the qualitative differ-
dealmg with the causality of change in general (which he there excluded
from Transcendental Philosophy). The reference to causality does not
imply any difference, for heie the form of change is considered 'in
accordance with the law of causality'. If the statement in the Anticipa-
tions were concerned only with motion and the present statement with
change, the contradiction would disappear.
1 It should be observed (i) that Kant identifies knowledge of
moving forces with knowledge of the successive appearances which
'designate' these forces; (2) it is as motions that the appearances
designate moving forces ; and (3) he is concerned only with change as
change of state (not of relative position). Thus a change of velocity is
a change of state, but motion (change of place) at a uniform velocity
is not a change of state but simply a state (of motion).
2 The form or condition of change is equated with the succession
(or happening) of the states.
3 A reference to degree seems to be called for here, though it is
not made explicit by Kant till A 208 = B 254. Kant gives as his reason
(in A 208 — B 253) for asserting difference in quantity the fact that all
286 THE ANALOGIES OF EXPERIENCE [XLVI § 3
ences or empirical content of the states which are exchanged.1
a may then be taken as zero in relation to )3, and the change is
a coming into existence of j3 — a.2
Hence just as there is always a time between two moments,
so between the two states in these moments there is always a
difference of quantity.3 The transition or passage from one state
to another takes place in a time which is contained between
two moments (the moment at which a occurs and the moment
at which j8 occurs). The two moments are the limits of the time
of the change, and therefore the limits of the intermediate
state4 between state a and state j3. As such limits they belong
to the whole change ; they mark its starting-point and its finish.
Kant takes this as proving that the continuity of change,
which in the Anticipations he asserted, on the ground of
intuitive evidence,5 to be possible,6 is necessarily present in all
actual change.7
the parts of an appearance are always quantities ; but presumably he is
not speaking of parts which are outside one another, and the statement
seems to presuppose the doctrine of the Anticipations. This is con-
firmed by the fact that he refers to states as 'reality in the appearance*
(reahtas phaenomenon).
1 This would seem to imply that when litmus paper changes from
red to blue, the change can be treated as a change in degree (of colour) ;
but perhaps Kant has in mind only primary qualities.
2 This quantity may be either positive or negative. If the change is
from 70° F. to 80° F., what has happened is the addition of 10° F.
(80° F. - 70° F. - 10° F.). If the change is from 70° F. to 60° F.
what has happened is the subtraction of 10° F. (60° F. — 70° F.
= - 10° F.).
3 This of course applies only when the two states are assumed to be
different states.
4 I suppose the existence of an intermediate state is assumed on the
ground that time must be filled. ° A 162 -= B 201, A 180 = B 223.
6 B 208, A 168 = B 210. Compare A 143 = B 182-3.
7 Kant gives two other versions of this proof in Metaphysik, pp. 54
and 56.
(i) Nothing passes out of one state into another immediately, that
is, per saltum, but the transition from one state to another happens
in such a way that the thing must pass through all the intermediate
states. Thus one can say generally 'Omnis mutatio est continual.
Every state ( ? change) has two termini : a quo and a d quern. Each of
these two states is distinguished as in a different moment. In every
transition the thing is in two different moments. The moment in
XLVI § 3] CAUSALITY AND CONTINUITY 287
So far Kant has dealt only with the continuity of change.
He now proceeds to bring in causation. Every change has a
cause which shows its causality in the whole time in which the
change takes place. Hence the cause does not bring about the
change suddenly, all at one moment, but in a period of time,
so that just as the time increases from the initial moment ^ to
the final moment J2, the quantity of reality (which is equal to
j8— a) is produced through all the intermediate grades between
a and )3.
Kant's answer to the question 'What can be said a priori
about change?' — or in his own language 'How can a thing pass
from state a to state /??' — is (i) that the change must be con-
tinuous, and (2) that its continuity must be due to the continuity
of causal activity.1
which the thing is in one state is different from the moment in which
it comes into the other state. But between two moments there is a
time, just as between two points there is a space. Hence the transition
occurs in time; for in the moments in which it passes from A to B,
there is a time in which it is neither in A nor in B, but is in mutation
or transition between the two.
The conclusion stated above is then said to follow.
(2) There is no state which follows immediately upon another. For
if a body passes from one state into another, there must be a moment
in which it goes out of the first state and a moment in which it comes
into the second state. Between these two moments there is a time in
which it is neither in the one state nor in the other. Therefore it is in
an intermediate state, which is a ground why it passes over into the
second state.
It must be remembered that the lectures on Metaphysics — the style
of which differs so much, especially m the use of short sentences,
from the Kntik — are printed from the notes of students, and are not
free from the inaccuracies to be expected. I have modified the language
in places. I cannot, for example, believe that Kant said 'Alle mulatto
ist continual
1 He adds that a causal activity, so far as it is uniform, is called a
'moment', and that the change does not consist of 'moments' but is
produced by moments as their effect. It will be remembered that in
A 168-9 — B 210 he called the degree of reality as a cause a 'moment',
e.g. the 'moment* of weight, and suggested that it was called a
moment because the apprehension of degree was not successive but
momentary. According to Adickes (Kant als Natutforscher, Vol. I,
p. 25) Kant uses 'moment* in seven different senses, but on this I
offer no opinion.
288 THE ANALOGIES OF EXPERIENCE [XLVI § 4
§ 4. The Law of Continuity
It will be observed that in the proof just given there is no
attempt made to derive causation from the continuity of time
as there was in Proof V, and that Kant argues directly from the
continuity of time to the continuity of change. He is not arguing
(or at any rate not arguing explicitly) that change must be con-
tinuous, if we are to perceive it in a time which is continuous.
This argument is followed up by what is generally regarded
as a second argument.1 I think it is intended rather to be a
summary or explanation of what has been already set forth.
Like Kant's summaries in general, it ignores points previously
made (it makes no reference to causation), and it makes explicit
what was previously only implicit.
The ground of the law of continuity in change is this: that
neither time nor the appearance in time is composed of smallest
possible parts;2 and that in change a thing passes from one
state to another through all the infinite parts (or degrees)
intermediate between the two states.3 This seems a statement
of the law of continuity rather than of its ground, and can
hardly be called an attempt at proof.4
The utility of this doctrine in science is, as Kant says, a
question outside the scope of the Kritik. But he believes, as
regards motion, that nothing can move from one place to
another without passing through all the intermediate places;
that nothing can pass from rest to a degree of motion, or from
1 A 209 — B 254.
2 That is, it is not composed of simple parts incapable of further
division; or, as Kant says in the following sentence, no difference
(in degree) of a state, and no difference in the quantity of times, is the
smallest possible difference.
3 Kant, in popular language, speaks of the state of the thing as
passing through the parts to the second state, and of the second
state as growing out of the first; but a state does not pass or grow at
all, it is only exchanged for another state. Incidentally it may be noted
that when Kant speaks of differences in degree as always smaller than
the difference between a and zero, he is referring to absolute zero
(and not to a as the relative zero from which the change starts).
4 It may perhaps be intended to make explicit a principle pre-
supposed in the previous argument.
XLVI § 5] CAUSALITY AND CONTINUITY 289
a degree of motion to rest, without passing through the infinite
intermediate degrees of motion; and that nothing can change
its direction without either coming to rest and starting afresh
or else moving continuously through a curved line (and not an
angle).1
§ 5. Continuity as the Formal Condition of Apprehension
Kant himself warns us of the danger of accepting such proofs
too easily, a danger of which we are acutely conscious in the
present state of science. He seems to feel that the proof above
given is especially to be distrusted, because it is a dogmatic
proof, that is, as I have said, a direct proof from the nature of
time to the nature of change in time. For this reason he supple-
ments the dogmatic proof by a Critical explanation.2 He attempts
to show that the distrust of the previous argument is not really
justified, because in spite of appearances we are only antici-
pating our own apprehension. He assumes, as always, that it
must be possible for us to have an a priori knowledge of the
conditions of our own apprehension or our own experience.
His argument is interesting, because it throws light on the
continually repeated doctrine that what understanding deter-
mines is inner sense.
All increase in empirical knowledge, and every advance
in sense-perception, is nothing but an extension of the deter-
mination of inner sense, that is, an advance in time.3 This
is true whatever be the character of the objects known, whether
we are concerned with empirical objects or with pure intuitions.
1 Metaphysiky pp. 56-7. Changes of velocity or direction are changes
of state, although uniform motion in one direction is not a change
of state.
2A2io-'B255. This also is commonly regarded as a separate
and independent proof, and the supposed repetition of the same proof
'with unessential variations' is said to imply a composite origin for
these paragraphs. See Kemp Smith, Commentary, p. 380. I think that
an understanding of the relation between the paragraphs diminishes
the force of this contention.
3 Yet many commentators insist that for Kant knowledge is timeless,
and even noumenal.
VOL. II K
290 THE ANALOGIES OF p;XPERIENCE [XLVI § 5
This advance in time — the advance of our experience — deter-
mines everything, and is determined by nothing other than
itself. It determines even the time in which it itself takes place.1
Hence, Kant goes on, every transition in sense-perception
to something which follows in time is a determination of time
through the production of this sense-perception ; and since time
is always and in all its parts2 a quantity, the production of
a sense-perception, considered as an intensive quantity, must
pass through all the degrees (of which none is the smallest
possible degree) from zero3 up to the determinate degree of the
sense-perception in question.
From this Kant concludes that it is possible to understand
how we can have a priori knowledge of the law of change (so
far as the form of change is concerned). All such knowledge
does is to anticipate our own apprehension, whose formal
condition, as present in us prior to, and independently of , given
appearances, must be intelligible a priori.
It seems to me obvious that Kant intends this argument to
supplement, and be supplemented by, his original contention
that different states (or sense-perceptions) as occupying
different moments must have a filled time between them.
1 This, if we may judge from the following sentence, seems to be
the general sense of the very obscure statement : 'die Tede desselben smd
nur in der Zeit, und durch die Synthesis dersclben, sie aber mcht vor
thr gegeben*. The last six words are especially obscure, and Vaihmger
emends lsiey to 'siW, while Wille emends 'ihr* to 'ihnen*.
To discuss all the possibilities — none of which is certain — would
take too much time. I should like the sentence to mean that while
the parts of experience are given only in time and through the synthesis
of time, nevertheless time is not given prior to (or independently of)
the synthesis; compare A 452 n. = B 480 n. Although the advance of
experience is an advance in time, time itself is determined, and indeed
produced (see A 143 — B 182), by the advance of experience, which is
essentially a synthetic act. Compare the statement about the concept
of succession in B 155.
2 This phrase seems intended to imply that no part of time is the
smallest possible, for every part of time is a quantity of time and not
a point of time.
3 To judge by A 208 --•= B 253, zero here is the starting-point of the
transition and may be represented by a, the sense-perception from
which the transition starts.
XLVI § 5] CAUSALITY AND CONTINUITY 291
Taken by itself it would hardly be intelligible ; and if the original
argument is rejected, this one is entirely without force.
This doctrine is closely connected with the Anticipations.
It seems intended to show, not only that between a sensation
and zero there is an infinity of different degrees of the same
sensation — this is supposed to have been proved already —
but also that we must necessarily pass through these degrees
to arrive at the required sensation. Furthermore it is based on
the nature of time, and such a basis is absolutely essential for
the proof of Principles, although in the Anticipations the
connexion between time and degree was by no means made
sufficiently clear.
Kant's argument, so far as I understand it, takes it to be
already proved that no part of time is the smallest possible
part of time and no degree is the smallest possible degree ; or,
in other words, whatever two points of time we take there will
always be another point between them, and whatever two
degrees we take there will always be another degree between
them. He then maintains that since any two degrees occupy
two different points of time, any intermediate point of time
must be occupied by an intermediate degree and so ad infinitum.
The continuity of time implies the continuity of change.
This doctrine he regards as worthy of acceptance because
the states which possess these degrees are possible or actual
sense-perceptions and because time is the form of our sensi-
bility. If time were a thing-in-itself, and if states belonged to
things-in-themselves, such a proof would not be acceptable.1
Kant rightly, I think, refuses to take time for granted, and
(insisting that time is determined only through the advance
in our sense-perception by means of the synthesis which is
experience) he seems to argue (although his statement is not
1 It would contradict Kant's central principle that we cannot have
a priori knowledge of thmgs-in-themselvcs. But the objection may be
raised that Newton's time (apait from its inconceivability) would give
us ground for a similar proof, and I find it difficult to be certain of
Kant's answer to such an objection; compare Chaptei VIII § 6.
Perhaps his answer here would be that absolute time cannot be
perceived.
292 THE ANALOGIES OF EXPERIENCE [XLVI § 5
sufficiently explicit) that this empirical determination of time
as a continuous extensive quantity is impossible unless the
succession of sense-perceptions by which time is filled is itself
a continuous change in intensive quantity or degree.
The resemblance of this argument to the fifth proof of
causality is obvious, although in the present passage it is not
causality, but continuity of change, which is inferred directly
from the continuity of time, and the continuity of causality
(causality being taken as proved) is inferred from the continuity
of change.
This latter inference is set forth in the long and intricate
sentence which constitutes Kant's final paragraph. Just as
time contains the a priori condition of the possibility of a con-
tinuous advance of the existing to what follows, so under-
standing (in virtue of the unity of apperception)1 contains the
a priori condition of the possibility of a continuous determination
of all appearances (as regards their temporal position) by means
of the law of cause and effect. It is only because of this possi-
bility, only because of the inevitable sequence of causes and
effects, that our empirical knowledge of time-relations is valid
for all time, and is therefore universally or objectively valid.
Here again we come to Kant's central contention — that
objective succession is essentially necessary succession. If we
are to know, not merely that appearances have been appre-
hended by us in succession, but that they succeed one another
in a common objective world, then their relative position in
one homogeneous and continuous time must be determined
by understanding in accordance with the law of cause and
effect.
The whole of Kant's argument rests, I believe, on the suppo-
sition that absolute time cannot be perceived and that events
in the physical world are only appearances (possible or actual)
of a reality which in itself we have no reason to regard either as
changing or as unchanging or as having any kind of temporal
predicate. The difference between the special proof from time
AA 2IO-H = B 256. Note that here we have one of the few
passages in which an appeal appears to be made to the pure category.
XLVI § 5] CAUSALITY AND CONTINUITY 293
(Proof V) and the others is not so great as is commonly supposed.
In all his arguments Kant is maintaining that unless succession
were necessary, we could not experience a world which changes
in one homogeneous and continuous time, and that experience
which is not experience of such a world could not be called
human experience at all. Whatever be the obscurities in his
exposition, and however doubtful be the validity, and even in
some cases the meaning, of the different steps of his advance,
I cannot help thinking that at the very least he has called atten-
tion to a problem whose very existence is too commonly ignored,
and that the solution he suggests has not yet been superseded
by any other.
CHAPTER XLVII
THE THIRD ANALOGY
§ i. The Principle of Interaction
The Principle formulated in the Third Analogy is called in
the first edition 'the principle of communion'.1 In the second
edition it is described more elaborately as 'the principle of
coexistence in accordance with the law of interaction2 or
communion'.
The two formulations of the Principle are as follows :
I. First edition — All substances, so far as they are coexistent,
stand in thorough-going communion (or mutual interaction).*
II. Second edition — All substances, so far as they can be
perceived in space as coexistent, are in thorough-going interaction*
The second formula has two advantages over the first. By
the reference to perception it brings out the Critical character of
the Principle; and by the reference to space it makes explicit
Kant's view that the substances of whose interaction he speaks
are spatial substances.
By 'communion' or 'interaction' Kant means the reciprocal
or mutual causality of substances in regard to their accidents.
This is explicitly stated by Kant both in the first and in the
second edition.5 The third category of relation (like the third
category of other classes) springs from a combination of the
1 'Gemeinschaft.'The Latin translation is 'comtnumo* or 'commercium'.
Kant is speaking of a real or dynamical communion (tanimercmm). See
A 213 — B 260 and A 214 — B 261.
2 'Wechselwirkung.' The Latin translation is 'actio mutua\ See
M.A.d.N. 2. Hauptstuck (IV 545). * Interaction' and 'communion*
are here equivalent terms, but it would be more convenient if
'communion* were used for the pure category and 'interaction1 for
the schematised category; compare Chapter XXXIII § 4.
3 A 211. 'Mutual interaction1 may be thought a superfluous reitera-
tion, but Kant's words are 'Wechselwirkung untcreinander\ 4 B 256.
6 See B in, B 112, A 144 -= B 183, A 221 = B26g, A 244 = B 302
et passim. This is involved even in the description of the category given
in A 80 — B 1 06, where communion is equated with interaction
XLVII § i] THE THIRD ANALOGY 295
first two categories; but it is nevertheless not a derivative
concept.1 Even if we can show that substance and causality
are necessary conditions of experience, it does not follow that
substances 'influence* one another. Leibniz, for example,
maintained that they did not.
The empirical illustration which Kant gives of interaction
is the fact that in a body the different parts (which are of course
substances) mutually attract and repel one another; and
the outstanding example of what he means is the law of gravi-
tation. Kant also says expressly that the third law of mechanics —
in all communication of motion action and reaction are always
equal — is an application of the category of interaction to
matter.2 These illustrations all serve to confirm the view
between agent and patient. Compare also letter to Schulz in 1784
(X 344), translated by Kemp Smith, Commentary, p. 199.
Kemp Smith (Commentary, pp. 387 ff.) denies that the category of
communion can be reduced to 'a dual application of the category
of causality'. So far as this denial is directed against the mis-
understandings of Schopenhauer, it is legitimate, but Kemp Smith
appears to reject the view that communion is to be equated with the
mutual or reciprocal causality of substances; for his language seems
to imply that the terms 'cause' and 'causality' ought to be excluded
from the description of the category. For this doctrine he offers no
evidence fiom Kant other than the fact that in the second edition 'Kant
is careful to employ the terms ground and influence in place of the
terms cause and causality'.
To this it may be replied: (i) that Kant expressly describes com-
munion as mutual causality in the second edition (B 111-12); (2) that
(as Ewmg has pointed out) in what is alleged to be the earliest
of Kant's proofs (A 214 --- B 261) the terms 'ground' and 'influence*
are already used; and (3) that Kant always regards a cause as a real
(but not a logical) ground, while 'influence' (influ\us) is a technical
term for transitive causal action, the action of one substance upon
another outside itself. Compare Bin, and also Baumgarten, Meta-
physica§zii (XVII 71) 'mjluxm (actio transiens) est actio substanttae
in substantiam e\tra se. Actio, quae non est mfluens, est immanens'.
There may be grounds for maintaining that Kant was mistaken in
regarding the interaction of substances as equivalent to their reciprocal
causality, but I can see no giounds for denying that this was his
doctrine; nor am I able to understand what Kemp Smith's alter-
native explanation of the category is. 1 B in.
2 M.A.d.N. 2. Hauptstuck (IV 544-5 and 551). The words used
are 'Wirkung* and ' Gegenwtrkung' ', which latter is equated by Kant
296 THE ANALOGIES OF EXPERIENCE [XLVII § i
that for Kant communion or interaction is what he asserts it
to be — namely the reciprocal causality of substances.
Professor Prichard gives another vivid illustration of Kant's
meaning. * Suppose two bodies, A, a lump of ice, and B, a fire,
close together, yet at such a distance that they can be observed
in succession. Suppose that A passes through changes of
temperature al a2 a3 . . . in certain times, the changes
ending in states c^ a2 a3 . . ., and that B passes through
changes of temperature bt b2 b3 . . . in the same times,
the changes ending in states & j82 j83 . . . Suppose also,
as we must, that A and B interact, i.e. that A in passing through
its changes conditions1 the changes through which B passes,
and therefore also the states in which B ends, and vice versa,
so that a2 and a2 will be the outcome not of al and ax alone,
but of #! and a19 and b± and /?x, jointly. Then we can say,
(i) that A and B are in the relation of influence, and also of
interaction or reciprocal influence, in the sense that they
mutually (not alternately) determine one another's states'.2
The general character of the doctrine which Kant seeks to
establish seems to me sufficiently clear. And if he is able to
prove that phenomenal reality must consist of substances in
interaction, and cannot consist of substances whose states
(as also by Baumgarten, Metaphysica § 213) with ' react w'. Kant in
Metaphysiky p. 61, distinguishes ' Ruckwirkung* as 'reactio' from
'Gegenwirkung' which is 'resistentia* or 'reactio rcststens' ; but this
seems to be a refinement which is not applied in the present case.
Kant is particularly interested in motion; and attraction and
repulsion are for him moving forces. lie does not discuss, as I think
he ought, the position of secondary qualities in this connexion, but
they are caused by motion.
1 I should prefer to say 'causes' or 'influences', but I suppose
Prichard says 'conditions', not to deny the causality of A, but to imply
that A is not the only cause.
2 Kant's Theory of Knowledge, p. 303. The detailed working out of
this illustration ought to be studied, but it is too long to quote here. I
would only add further from the same passage '(4) that if we perceive
A and B alternately, and so only in the states ax a:i . . . /A2 //4 . . .
respectively, we can only fill m the blanks, i.e. discover the states
a2 a4 . . . /fj /J3 . . . coexistent with /?2 [\ . . . and a± u3 . . . respectively,
if we presuppose the thought of interaction'.
XLVII §2] THE THIRD ANALOGY 297
succeed one another (according to causal law) in complete
independence of all other substances and all other similar causal
successions — then manifestly his doctrine is of importance
and adds a great deal to what he has hitherto professed to prove.1
The question is whether he is able to prove it.
§ 2. The Meaning of Coexistence
Interaction is the condition of our knowledge of objective
coexistence — such is the thesis which Kant has to prove. But
the definitions which he gives of such coexistence give rise to
difficulties. In the first edition Kant's definition is as follows:
'Things are coexistent, so far as they exist in one and the same
time'.2 In this definition — since all things exist in one and the
same time — -Kant must mean by 'time' either an instant of
time or a part of time.3 The latter would appear to be the mean-
ing with which he is chiefly concerned ; and perhaps the word
'simultaneity' should be reserved for existence in the same
instant.
There is a further difficulty about the meaning of 'thing'
in this definition. A 'thing' like the earth or the moon (the
examples given in the second edition) comes into being and
passes away; and so it might be regarded as only a temporary
determination of permanent substance (or as a substance4
only so far as determined for a certain length of time in a
particular way). In that case WTC could speak of things as
coexisting, just as we can speak of states or determinations
or accidents of substance as coexisting. Kant himself, however,
seems to identify thing and substance ; for he goes on to speak
1 Compare Lindsay, Kant, pp. 128-9. Apart from the principle of
interaction we should be reduced, as he says, to *a streaky view of
causation' — the world might be 'made up of a lot of quite independent
chains of causation'. 2 A 211 ~- B 258.
3 I suppose that to be simultaneous is to exist at the same instant
of time, while to coexist is to exist cither at the same instant or through
the same part (or period) of time. Coexistence is a wider term than
simultaneity.
4 Such a substance is composed of parts which are themselves
substances.
VOL. II K*
298 THE ANALOGIES OF EXPERIENCE [XLVII § 3
of the coexistence of substances as if it were identical with
the coexistence of things.1 But since all substances are perma-
nent, it immediately follows that all substances coexist always,
both in every moment of time, and in every part of time,
and in all time taken as a whole. When we know that any
substance exists, we know that it coexists with all other sub-
stances, if indeed it is proper to ascribe temporal predicates
to substances at all.2
It is possible that a way out of this difficulty is to be found in
the technical use of 'existence'. We speak of the existence of
accidents as 'inherence', and of the existence of substances as
'subsistence'; but this distinction is misleading, for we are
apt to imagine that the substance exists in one way and the
accident in another.3 If we refuse to make the separation, and
if we say that the accidents are the ways in which substance
exists, then by the coexistence of substances Kant may mean
coexistence in respect of certain accidents. And this, I think,
is what we must take him to mean.
In the second edition Kant defines coexistence as the existence
of the manifold in the same time.4 The reference to the manifold
would seem to imply that it is the accidents of substance which
coexist,5 and so perhaps may be taken to support our inter-
pretation. At any rate I can see no other interpretation which
will make sense.
§ 3 . The Proof in the Second Edition
The proof added in the second edition6 may be considered
first. It is clearly meant to run parallel to the proof of causality
which was added in the second edition (Proof I).7
'6258.
2 Pochard (Kant's Theory of Knowledge, p. 306) denies that we can
properly do so. -* A 186-7 ~ B 230. 4 B 257.
5 Such a series of accidents of one substance (or set of substances)
as constitutes the life or history of a 'thing' may also be taken to
coexist with another series of the same kind. The earth and the moon
coexist in this sense.
6 B 256-8. 7 B 233-4. Compare Chapter XLIII § 3.
XLVII § 3] THE THIRD ANALOGY 299
I. Kant starts out from the assertion that 'things' are coexistent
when the sense-perception of the one can follow reciprocally on
the sense-perception of the other. By 'reciprocally* he means
that we can either see A and then B, or B and then A, as we
please. We can see first the moon and then the earth, or vice
versa (just as we can see first the top and then the bottom of
the house, or vice versa1). And because our sense-perceptions
of these objects can thus follow one another reciprocally, we
say that the objects are coexistent.
In this assertion Kant would seem to be considering 'things'
whose states are taken to be constant ; or at least he is ignoring
the possibility that the things in question may be changing their
states. He has already pointed out, in the Second Analogy,
that where there is an objective succession (as in the case where
the boat is moving downstream), this reciprocal succession
cannot occur. We can see the boat first higher up and then
lower down, but we cannot see it first lower down and then
higher up.2
Such a doctrine seems plain and obvious enough, but there
may seem to be a certain amount of obscurity on one point.
Is Kant maintaining that when things are coexistent, a reciprocal
succession of sense-perceptions must be possible? Or is he
maintaining that when a reciprocal succession of sense-percep-
tions does take place, then the things must be coexistent ?
I may here seem to be making too much of a very small
point, but it is to be noted that in speaking of objective suc-
cession (which ought to be an exact parallel) the inference is
from the objective succession to the impossibility of reciprocal
succession (or reversibility) in the sense-perceptions, and not
vice versa.3 Furthermore, in the passage which immediately
follows, 'from the fact that things arc posited in the same time*
1 A 190 = B 235 and A 192 = B 237-8. In Pochard's example
we can see first the ice and then the fire or vice versa. A reciprocal
succession can also be described (perhaps more clearly) as a reversible
succession. 2 A 192 -= B 237.
3 B 234. Compare also A 192 = B 237, where the inference s m the
same direction.
300 THE ANALOGIES OF EXPERIENCE [XLVII § 3
we conclude1 'that the perceptions of them can follow one another
reciprocally'. Here the inference is from objective coexistence
to the reciprocal succession (or reversibility) of sense-percep-
tions, and not vice versa.
We are clearly entitled to argue from the coexistence of objects
to the reversibility of our sense-perceptions of these objects.
If we wish to argue in the reverse direction, we can do so only
under certain assumptions ; for we have no right to describe
our sense-perceptions as reversible (or as irreversible), unless
we assume that these sense-perceptions reveal to us (or are
identical with) the states of real objects which are permanent
substances.2 Apart from this assumption we could say only that
our sense-perceptions come to us in the order in which they do
come: there could be no ground for saying that this order
was reversible, and still less for saying that it must be reversible.
The argument of the Third Analogy (like that of the Second)
manifestly rests on the First Analogy as its presupposition.3
Once \v e assume our sense-perceptions to be sense-perceptions
of objects (or substances), then, as Kant asserts, we are entitled
to say that because the sense-perceptions of these objects can
follo\v one another reciprocally, the objects are coexistent.
We can discover the reversibility of our sense-perceptions by
experiment — but only on the supposition that the objects
of our sense-perception arc permanent substances.
If we fail to see this, we may wrongly imagine that Kant is
trying to state the criterion whereby we pass from awareness
of a merely subjective succession to knowledge of objective
coexistence. Such a process of transition from the merely
subjective to the objective docs not and cannot take place:
on that point I agree with Professor Prichard. I do not, however,
believe that Kant is attempting to describe such a process;
and if he were, his attempt would be manifestly unsuccessful.
Kant, as always, is taking experience for granted and
1 B 257, ( :abzunehmcn\ Kant says we have no perception of absolute
time by \vhich to conclude this, but he implies that we do conclude
it by means of a pure concept of the understanding.
2 Compare Chapter XLV § 4. 3 Compare B 232-3.
XLVII § 3] THE THIRD ANALOGY 301
attempting an analysis, not of its growth, but of its necessary
presuppositions. Here he is taking for granted what he claims
to have proved in the First Analogy, namely that we experience
real objects as permanent substances ; and this implies (what we
all accept" by common sense) that we can experience coexistent
objects.1 If we assume that we experience coexistent objects,
then (and then alone) can we say that our sense-percep-
tions of these objects must be reversible. And we can also
say that if by experiment we discover our sense-perceptions
to be reversible (on the supposition that we are perceiving
real objects), then the objects must be coexistent. The rever-
sibility of our sense-perceptions is then a criterion by which
we can distinguish objective coexistence from objective suc-
cession. It is not, and it could not be, a mark whereby we are
entitled to go beyond a merely subjective succession and affirm
an objective coexistence.
There is another point to be noted. Even in cases where we
arc perceiving an objective succession, it is possible for imagina-
tion to place the sense-perceptions in an order different from
that in which they are 'taken up'.2 Hence by a combination
of imagination and sense-perception \ve could, although
doubtless with difficulty, make a reciprocal succession of
appearances such as Kant describes.3 This possibility borders
on the fantastic, and Kant does not discuss it ; but it is worth
mentioning, since it suggests that in ordinary circumstances
we have no difficulty in distinguishing, by simple inspection,
an appearance to sense-perception from an appearance to mere
imagination.4
1 This does not mean that we can perceive two coexistent objects in
one moment of time, but that when we see first the moon and then
the earth, or vice versa, we assume that we are experiencing two
coexistent objects.
2 B 233. Compare A 201 — B 246.
3 We could see the ship lower down, and then imagine it higher up,
and see it lower down again, and then imagine it higher up, and so on.
This does not justify us in supposing that the ship occupies all these
positions at the same time.
4 This possibility is mentioned by Professor Kemp Smith (Com-
mentary, p. 386). Another suggestion which he makes on the same
302 THE ANALOGIES OF EXPERIENCE [XLVII § 3
II. We cannot perceive time itself, so as to conclude
(from the fact that things are placed or posited in the same
time) that the perceptions of them can follow one another
reciprocally.
The statement that we cannot perceive time itself (or absolute
or empty time) is the usual doctrine which lies at the root of all
the Analogies. It should, however, be observed that the con-
clusion which we cannot make with the help of a perception
of absolute time is nevertheless the conclusion which we do
make, and upon which Kant's argument rests.
It is not clear how the perception of absolute time, if that were
possible, could help us to this particular conclusion, which
(in the absence of such perception) we must make by means of
the concept of interaction. Even if the appearances of A and B
were given to us with the moment of their occurrence in
absolute time as it were stamped upon them, we should still
have before us only the series at /?2 a3 j34 a5 j86 . . . (or what-
ever the series was), and we should not have before us what
we really require, the series a^ a2/?2 a3j33 . . . and so on.
Perhaps Kant means that if we could perceive the series
ai d3 as • • • in relation to absolute time, we could fill in the
gaps in accordance with the law of continuity; and similarly
in the case of the series /?2 /J4 j86 . . .l
III. Since we do not perceive empty time, the synthesis
of apprehension taken by itself enables us to say only that in the
subject there is a sense- perception a zvhen there is no seme-percep-
pagc is less happy. lie asserts that we might have 'a reversible con-
tinuous series* which did not justify an inference to coexistence. The
example he gives is that of playing a series of notes, and then playing
it backwards. This is, however, not a reversible series at all, but a
reversed series — which is a very different thing. A reversible series is
one which can be taken up or perceived in any order at any time, while
the series in question can be taken up only in one order, the order in
which it is played (whether it is played backwards or forwards makes
no difference). It might as well be objected that a boat can reverse its
engines and go upstream.
1 It is unnecessary to discuss Kant's meaning in further detail, since
the whole supposition is put forward only to be rejected.
XLVII § 3] THE THIRD ANALOGY 303
tion b and vice versa.1 By mere apprehension we could not say
that the objects A and B coexist, nor could we say that they
must coexist in order that the sense-perceptions may be able to
follow one another reciprocally.2
This statement seems to me obviously true. Mere appre-
hension, apart from the element of thought, cannot give us
objects, and still less can it give us coexistent objects: it can
give us at the most mere ideas.3
There is, however, a further point. Kant appears to imply
— and surely he is right — that where we have what we take to
be a reversible series of sense-perceptions, we assume, not
only that we arc perceiving coexistent objects, but that these
objects must coexist, if the series of our sense-perceptions is
to be reversible. We cannot derive such an assumption from
mere apprehension; but it is an assumption which we all
make. Furthermore it is an assumption of necessity, and it
appears to me that here, as always, Kant is endeavouring to
discover the element of necessity which is involved in objectivity.
He is in fact trying to determine the element of necessity which
is involved in our experience of objective coexistence ; and it is
the presence of this element of necessity which alone entitles
him to assert the presence of a pure concept of the under-
standing.4
1 B 257. We could not, in my opinion and I believe in the opinion of
Kant, say (on the basis of sense-perception in abstraction from thought)
even that the series was reversible. We could say only that it took place
in the order in which it did take place, and even this would require some
element of thought.
2 Here again this is just what we can, and must, say, if we presuppose
that in sense-pel ccption states of objects are given to us. This, however,
is a presupposition of thought, to which alone is to be ascribed the
concept of an object in general.
a When we regard given ideas as appearances of an object, we are
employing the category of substance and accident, and this cannot
be given in mere apprehension.
4 This seems to be borne out by the fact that Kant begins his next
sentence by saying that consequently a pure concept of the understand-
ing is required; but he complicates this, as so often, by adding a
further reason why it is required, namely in order to say that the
reciprocal succession of sense-perceptions is grounded in the object.
304 THE ANALOGIES OF EXPERIENCE [XLVII §3
If this is correct, the argument is parallel to the argument
of the Second Analogy. In the Second Analogy it was easy to
discover the element of necessity implied or presupposed in
objectivity ; for if the succession we perceive is objective, then
the succession of our sense-perceptions must be necessary.
Here it is not so easy; but, as Kant implies,1 when we take
ourselves to have an experience of coexistent objects, zee assume
that the objects must coexist in order that the reciprocal succession
of our sense-perceptions may be possible. I take this to mean only
that we assume the reciprocal succession of our sense-perceptions
to be necessarily grounded in, or conditioned by, the coexistence
of objects?
Such an assumption cannot be based on mere sense-
perception (\\hich can never give us necessity); nor can it
be based on a perception of absolute time (since we have no
such perception).
IV. Kant then proceeds to assert that we consequently
require a certain concept of the understanding in order to say
1 I think this is implied; for the failure of apprehension to shov
that the objects must coexist (in order that the reciprocal succession
of our sense-perceptions may be possible) seems to be his justification
for affiimmg the presence of the category of interaction in experience.
2 Kant cannot mean, at this stage of the argument, that the objects
themselves coexist necessarily, or that the coexistence of the objects
(or of their states) is determined by a necessary law.
I interpret Kant's statement in this way, both because this seems to
be implied by the following sentence, and because, if interpreted as
asserting more than this, the statement, taken on the level of common
sense, \vould be manifestly false. This is clear enough, if we think of
objects as things-m-themselves. Consider first the case of objective
succession on that hypothesis. We can say that if wre are perceiving
events, or if the succession of our sense-pciceptions is necessary, there
must he succession in the obj'ects; but it would be ludicrous to
infer from this that we knew the actual succession in the objects to
be a necessary succession, that is, one determined by causal law. All
that is necessary is a matter-of-fact succession in the objects and
nothing more. Similarly (on the same hypothesis) we can say that if
there can be a reciprocal succession in our sense-perceptions, there
must be coexistence in the objects ; but it would he idle to pretend, on
such grounds, that we knew this coexistence to be necessary in the
sense of being determined by a necessary law.
XLVII § 3] THE THIRD ANALOGY 305
that the reciprocal succession of sense-perceptions is grounded
in the object1 and in this way to know that the coexistence is
objective?
Let us leave over for the moment the nature of this concept,
and consider only the purpose for which it is required. This
purpose seems to be merely a variation of what has already been
said : we have to justify our assumption (which cannot be derived
from mere apprehension) that the objects must necessarily
coexist if the reciprocal succession of our sense-perceptions of
these objects is to be possible. We arc considering the question
now from the side of the reciprocal succession of our sense-
perceptions ; and we are asserting that where the order of our
sense-perceptions is taken to be reversible, we say or assume
that this reversibility must have its ground in the coexistence
of the objects perceived. This seems to me to be true ; according
to Kant it can be justified only in virtue of a certain concept
of the understanding.3
V. We now come to the crux of Kant's argument. If we are
to justify the common-sense assumptions which we all make,
we require a pure concept of the understanding^ a concept of the
1 We should expect him to say 'objects' (or 'coexistence of the
objects'), unless he means merely 'objectively grounded'. Compare
A 214 -- B 261, where a subjective succession is said to rest on an
objective ground, and this in turn is equated with 'being referred to
appearances as substances'.
2 'und das Zugleichsein dadurch ah objektiv vorziistellenS
3 In the Second Analogy Kant maintains that if there is an objective
succession perceived, the subjective succession of our sense-percep-
tions must be irreversible ; and if the subjective succession of our sense-
perceptions is irreversible, there must be an objective succession
perceived. In the Third Analogy he maintains that if the objects
perceived coexist, the subjective succession must be reversible; and
if the subjective succession is reversible, then the objects perceived
must coexist. None of these statements has any meaning except on
the assumption that what we perceive is an object or permanent
substance; but if we accept this assumption, together with the view
that a permanent substance is not a thing-m-itself, we require the
category of causality to justify our assumptions in the Second Analogy,
and we require the category of interaction to justify our assumptions
in the Third Analogy. Such I take to be Kant's view in brief.
3o6 THE ANALOGIES OF EXPERIENCE [XLVII § 3
reciprocal succession of the determinations of those things which
coexist outside one another in space*
It will be observed that whereas previously we were con-
cerned with a reciprocal succession of sense-perceptions, the
succession of which Kant now speaks is a reciprocal succession
of 'determinations' or 'states' of the things themselves.2 On
Professor Prichard's view this transition from sense-perceptions
to states of a thing is a mere confusion. I believe on the contrary
that it is a deliberate identification, and that (whether the
identification be possible or not) what is present in sense-
perception is, on Critical principles, the state of the object.
If we take the Critical Philosophy seriously and set aside all our
natural prejudices, we must recognise that for it a sense-per-
ception is not something which lies between us and the object,3
but is a state of the object immediately present to our minds.
As Kant everywhere insists, the object is composed of such
possible or actual sense-perceptions bound together in a neces-
sary synthetic unity.4
The method of argument is the same as that of the Second
Analogy, although less clearly expressed. Kant first of all
asserts a necessity which must govern our sense-perceptions,
if our knowledge is to be objectively valid ; and then he reminds
us that since our sense-perceptions are identical with the
states of objects, that necessity must govern these states, if
our knowledge is to be objectively valid. I need not here
repeat the comments which I formerly made.5 1 would, however,
again insist that all this has no meaning unless we presuppose,
in accordance with the First Analogy, that in genuine percep-
1 13 257 I have added 'in space', which seems to be implied. Kant
himself brings in space a few lines further down. The need for a pure
concept — it can hardly be too often repeated — arises because we
cannot know objective coexistence by means of mere apprehension
or by a perception of absolute time.
2 It is perhaps possible that Kant considers this transition to have
been already made or implied in IV above, but I do not think so.
3 That is, it is not a so-called Zwischendtng.
4 This necessary synthetic unity implies (among other things) that
the sense-perceptions are regarded as states of a permanent substance.
5 See Chapters XLIII § 5, IV, and XLV § 2.
XLVII § 3] THE THIRD ANALOGY 307
tion we are immediately aware of the states of permanent
substances in space. Kant's problem in the Second and Third
Analogies is to determine the conditions under which our
experience of succession and coexistence in the states of
permanent substances can be valid, it being assumed throughout
that such permanent substances are not things-in-thcmselves.
It is more difficult in the case of interaction to state the nature
of the necessity involved,1 when we cease to regard appear-
ances as sense-perceptions and regard them instead as states of
the objects. What we have seen is that in experience of objective
coexistence we assume the reciprocal succession of our sense-
perceptions to be grounded on the coexistent objects, and only
so can we have knowledge of such objects. We are now re-
minded that the sense-perceptions (whether actual or possible)
are themselves states of permanent substances, and that
consequently, if our common-sense assumption is to be
justified, the reciprocal succession of the states must be grounded
on the coexistent objects.
The question then arises how we are to interpret the phrase
'reciprocal succession'. I do not think that Kant can mean by this
only the succession actually perceived. When we say that there
can be a reciprocal succession of sense-perceptions, we mean
that there is a possibility both of the succession a± b» a3 i4 . . .
and of the succession b1 a* b3 #4. . . ,2 We can have either
succession of sense-perceptions, though we cannot have both.
If we now remember that, on Critical principles, actual and
possible sense-perceptions are to be regarded as states of
permanent objects (or substances), we can say that there is a
possibility both of perceiving the series of states ax |32 a3 j34 . . .
and of perceiving the series of states ^ a2 j83 a4. . . . We can
perceive either series, but not both together.
I take it that when Kant asserts the reciprocal succession of
1 Kant's own statement quoted above is too vague, and must be
supplemented in the light of what follows.
2 There is a possibility of taking the rt's and 6's in any order we
please, for example, aL 62 ^3 a\ • • •» but this we may ignore. It is
assumed in this notation that a and b are simultaneous.
3o8 THE ANALOGIES OF EXPERIENCE [XLVII § 3
sense-perceptions to be grounded in the coexistent objects,
he has in mind both the possible successions of sense-percep-
tions. Similarly when he speaks of the reciprocal succession
of the states of things coexisting outside one another in space,
he must have in mind both the series a1 j32 a3 j84 . . . and the
series Pl a2 /J3 a4. . . . These must have their ground in the
things A and B.
It seems legitimate enough to infer, as Kant appears to
infer, that the whole series a^ a^o a3/?3 a4/?4 . . . must have
its ground in the things A and B.1 There is more difficulty
in the inference that the whole series is determined by A and B
together? and that the series c^a,, a3 a4 . . . is not determined
separately by A, nor the series ^ ^82 j83 ^ determined separately
by B. I presume this is supposed to follow from the fact that the
reciprocal succession of sense-perceptions (and so of states)
must have its ground in the coexistent objects (or in the co-
existence of the objects).
I confess that I should have liked to see a fuller justification
of this inference. Manifestly if the objects were things-in-
themselves, it would (on a common-sense view) follow from
their coexistence that the order of our sense-perceptions must
be reversible ; but it could not follow that the states of the two
coexistent objects must be determined by the two objects
jointly. Kant's inference, if it is legitimate, depends on the
doctrine that objects are not things-in-themselves.
Whatever we may think of this inference, Kant is clearly
maintaining that coexistent objects must mutually determine
one another's states, and that unless this is presupposed,
1 We must remember that possible, as well as actual, sense-percep-
tions arc to be regarded as states of objects. It is, I think, a matter of
indifference whether the states «1 «2 a3 a4 have the same degree or a
different degree of the quality «, and whether the states //x /f2 fi3 /?4
have the same degree or a different degree of the quality /?. When
the degree is the same, we have a continuance of the objects in the
same state — the case of the earth and the moon. Where the degree is
different, we have a change in the states of the objects — the case of
the fire and ice.
2 The exact significance of this must be considered later; see
Chapter XLVII I § 4.
XLVII § 3] THE THIRD ANALOGY 309
we could not know that the order of our sense-perceptions
must be reversible, and we could not know that the objects
coexist. The doctrine stated is a necessary presupposition of
our experience of objective coexistence, provided we accept the
view that objects are possible and actual sense-perceptions
(or ideas) combined together in necessary synthetic unity. If
we suppose that objects are things-in-themselves, we could
never infer from their coexistence that they must necessarily
interact.
Such is Kant's argument. Its difficulty is obvious, but
before we reject it, we must be sure that we are not rejecting
it on the basis of an unconscious transcendental realism.
Kant is entitled to have his argument evaluated — at least
in the first instance — on the basis of his own presuppositions.
VI. The rest of the argument offers no difficulty. The concept
which Kant has asserted to be necessary is a concept of the
relation of substances, in which one substance1 contains
determinations or states whose ground is contained in the
other. This relation is a relation of 'influence', or of the causal
action of one substance upon another. When this relation of influence
is mutual or reciprocal? as Kant has argued that it is, the concept
of the relation is the concept of communion or interaction.
VII. The concept of interaction is therefore a necessary con-
dition of our experience of objective coexistence.
VIII. It is therefore a necessary condition of all objects of
experience, so far as these objects coexist.
1 The object is assumed to be a substance on the basis of the First
Analogy. As we have seen, this is assumed throughout.
2 B 258. The sentence in which this is stated seems to be corrupt,
but the general sense is clear.
CHAPTER XLVIII
THE THIRD ANALOGY (Continued)
§ i. The Proof in the First Edition
Kant's argument in the first edition1 is of a looser texture.
Curiously enough space plays a more prominent part than
in the argument of the second edition. As we have seen,2 in
the interval between the two editions space was recognised by
Kant to be of vital importance for the proof of substance;
but apparently when the new edition was about to be published,
he decided that he must rest his case primarily upon the
character of time.
I. Kant asks what is the criterion or mark by which3 one
recognises the coexistence of things. His answer is 'By the
fact that the order in the synthesis of apprehension is reversible,
or (as he here says) indifferent'. If A, B, C, D, and E are co-
existent, we can see them in any order,4 while if they occur
successively, we can see them only in the order in which they
occur.5
Here although A, B, C, D and E may be 'things', they
cannot be substances, for substances cannot come into existence
or pass away.
II. At this stage Kant adopts the method used in the so-called
indirect proof of the Second Analogy (Proof III) — he supposes
that the conclusion which he wishes to prove is false. The
1A2ii = B 258 fF. (three paragraphs).
2 See Chapter XLII § 3.
3 tWoran* not *wie\ Compare the ordinary German idiom *Woran
erkennen Sie thri?' ('By what do you recognise him?').
4 It is also true that if we can see A, B, C, D, and E in any order,
they must be coexistent.
6 Note that the inference is, in this case, from the fact that the
succession is objective to necessity in the order of apprehension, and
not vice versa. It should also be noted that what belongs to past time
cannot be 'apprehended* in the technical sense of * apprehension*.
XLVIII §i] THE THIRD ANALOGY 311
supposition he makes is that substances coexist without inter-
acting, and he asserts that in that case their coexistence could
not be perceived. He still regards the substances as spatial
substances, and he suggests (without offering any reason)
that if the substances did not interact, they would be separated
by completely empty spaced If they were so separated, then —
presumably on the assumption that our apprehensions of them
must always be successive — we could recognise that the
appearances perceived existed at the time we perceived them,
but we could not decide whether the appearances2 (considered
as appearances of objects) were themselves successive or
co-existent.3
Kant does not explain why on such a hypothesis we could
not distinguish objective coexistence from objective succession ;
nor does he explain whether this is obvious on the basis of
ordinary experience (or contemporary science), or whether it
is obvious only on Critical presuppositions. His conclusion,
however, seems in any case to follow directly from the
1 Perhaps he is assuming that they are separated in space (for if they
were combined in space they would be one substance). If the substances
so separated interact, then apparently the intervening space is filled —
one would like to be told with what (compare § z below). If they do
not interact, the intervening space is empty.
2 Here Kant seems to be thinking of a series of states of substance
such as constitutes a thing or an object. It appears to be irrelevant
whether such a series is composed of states that are qualitatively
different or qualitatively alike.
3 Kant's conclusion would follow from the fact that we cannot
peiceive absolute time and that the synthesis of apprehension by itself
(as always successive) cannot give us either objective succession or
objective coexistence. Furthermore there is no possibility of knowing
that the succession of our sense-perceptions is reversible (or irre-
versible), unless we take these sense-perceptions to be states of
permanent substances; and permanent substances fill space by their
matter (their powers of repulsion and attraction) ; but the peculiarity
of the present argument is that Kant appears to rest his conclusion
solely on the assumption that apart from interaction substances would
be separated by empty space. I presume that the conclusion is supposed
to follow from this assumption because empty space cannot be per-
ceived and the chain of our sense-perceptions would be interrupted;
compare A 213-14 = B 260-1.
3i2 THE ANALOGIES OF EXPERIENCE [XLVIII § i
general account of apprehension with which we are now
familiar.
III. Since, however, we do distinguish objective coexistence
from objective succession,1 there must be more in experience
than mere apprehension, which (although it does indicate
the existence of what is apprehended) cannot by itself make
this distinction.2 In addition to the bare existence of A and B
(which we know through apprehension3) there must be something
through which A determines Exposition in time and B reciprocally
determines A's position in time* Only so can we have empirical
knowledge that A and B coexist.5
The difficulty here is to know in what sense A and B 'deter-
mine' each other's position in time. If we are to know that
A and B coexist, the position of A must be determined rela-
tively to B and the position of B relatively to A. Consequently
their relative position is, I take it, on Kant's view necessarily
determined6 — in the sense that it is not imaginary or arbitrary:
we cannot regard A and B as other than coexistent. This
again implies that they necessarily coexist, since they are not
things-in-themselves, but only appearances to us. Objective
coexistence must, for Kant, be necessary coexistence ; but it is
not easy to decide whether he is saying this or something more
in the present passage. We have to remember that in the case
of objective succession, although the succession must be
1 This is clearly the supposition on which Kant's argument rests.
2 This depends on the supposition that apprehension is always
successive. See Chapter XLII § i.
3 This is implied in what precedes, though strictly speaking we
require more than apprehension if we are to know the existence of an
object (as opposed to a mere idea).
4 This Something* is not absolute time, for absolute time cannot be
perceived', compare A 200 = B 245. This important qualification is
here omitted by Kant, no doubt because, after having repeated it so
many times, he expects it to be understood.
6 At this point Kant speaks of A and B as substances, but when he
speaks of them as coexisting, he clearly means, not coexisting as
substances (for all substances coexist), but coexisting as substances in
the possession of certain perceivable determinations, coexisting, for
example, as earth and moon. ° Compare B 234.
XLVIII § i] THE THIRD ANALOGY 313
necessarily determined, it is the cause which determines the
effect, not the effect which determines the cause.1 In the case
of objective coexistence does he wish to assert, not only that
the coexistence is necessarily determined, but that in some
further sense the coexistent objects determine each other's
position in time, and that this determination is in some ways
analogous to the determination of effect by cause? At this
stage he can scarcely intend to identify such temporal deter-
mination with causation; for he goes on to explain in the next
sentence that such temporal determination can take place only
by means of causation. If we are to distinguish, even temporarily,
between determination of position in time and causal action,
I cannot see that A and B determine each other's position in
time except in the sense that their coexistence is taken to be
necessary.2
IV. Now when one thing determines the position of another
in time, it can do so only by being the cause of that thing, or
of the determinations of that thing.3
It is on this assertion that the whole argument of the first
edition turns. It deserves — to say the least — a fuller discussion
than it receives.
The principle appears to be stated quite generally: it is
not restricted to the case of coexistence. The difficulty, as
before, concerns the meaning to be attached to 'determining
the position of another thing in time'. If we take this to mean
'causing' or 'acting causally upon', the statement is tautologous.
1 B 234, A 194 = B 239, A 199 — B 244. Even as regards parts of
time, it is the earlier time which determines the later (in the sense that
we can get to the later only through the earlier); see A 199 B 244.
2 If Kant does intend to identify 'determining position in time* with
'causing', what is the ground for saying that coexistent objects must
act causally on one another? No doubt if A affects and is affected by B,
then A and B must be coexistent. But it is quite another thing to say
that if they arc coexistent, each must affect, and be affected by,
the other.
3 What Kant himself says is this : 'Now only that which is the cause
of another thing or of its determinations determines the position of the
other thing in time*.
3i4 THE ANALOGIES OF EXPERIENCE [XLVIII § i
If Kant means by it merely that the temporal position of one
thing is determined relatively to the position of another, then
the inference to causality seems to be invalid. If we consider
two successive events X and Y, their position relatively
to one another may be determined, and indeed • necessarily
determined, without X being the cause of Y. If the succession
XY is objective and therefore necessary, then according to
Kant it is causally determined ; but the fact that it is causally
determined need not mean that X is the cause of Y, for Y may
be caused by something else. Similarly, one would imagine,
we might hold that A and B can coexist only if their coexistence
is necessary and so is causally determined ; but the fact that it
is causally determined need not imply that A and B must act
causally on one another.
If Kant's argument rests on what he has proved in the Second
Analogy, then his conclusion does not follow. Even if we could
get over this, there is still a further difficulty. The Second
Analogy dealt with objective succession, whereas here we are
concerned with objective coexistence, and coexistence seems,
at any rate at first sight, to be incompatible with causation;
for the effect must succeed the cause. We may perhaps be able
to avoid this difficulty by maintaining that the transition between
cause and effect is continuous, and that there is no interval
of time between them j1 but at the very least the question ought
to have been raised, especially as the causality with which we
are here concerned is reciprocal causality.
Perhaps Kant does not mean to state his principle generally
and is concerned only with things which coexist, and whose
position in time must therefore be determined relatively to
each other. He appears to hold that our experience of such
coexistence presupposes the coexistence to be necessary,2
or presupposes that this relative determination is necessary
1 A 203 = B 248. Compare § 4 below.
2 This is supposed to hold only on the supposition (i) that objects
are not things-m-themselves, (2) that experience is more than arbitrary
imagination or immediate sense-perception, and (3) that we have no
direct perception of absolute time.
XLVIII § i] THE THIRD ANALOGY 315
determination. If so, we have established the schema1 which
entitles us to apply the category of reciprocal causality or
interaction. But this contention is much more complicated
than the similar contention in regard to cause and effect, and
a fuller discussion of its grounds and implications would have
been of immense advantage.
V. One substance cannot be the cause of another substance ;
for no substance comes into being, but is permanent. Hence
if one substance acts causally on another, it can be the cause
only of the determinations or states of the substance on which
it acts.2
VI. Therefore (i) if A and B are two substances known to
coexist (in the sense that each of them is in a certain state,
or series of states, during the same period of time), (2) if know-
ledge of such coexistence is possible only on the presupposition
that A determines B's position in time and B determines A's
position in time, and (3) if such determination must be causal
determination — then each substance must contain in itself the
causality of certain determinations in the other, and also certain
effects of the causality of that other?
This sums up the whole argument of the first edition. We
may put the conclusion more simply by saying that the two
substances must stand in dynamic interaction (whether immediately
or mediately)* , if their coexistence is to be known in any possible
experience.
VII. The rest of the argument is only the common form by
which all Kant's Critical arguments can be ended. The condition
1 This schema is described as the coexistence of the determinations
of one substance with those of the other in accordance with a universal
rule; see A 144 - B 183-4.
2 It is of course not the only cause of these determinations, but it
may be the principal cause, as when the fire causes the ice to melt.
3 We could, I think, say more simply that each substance must cause
certain states in the other and that each substance must have certain
of its own states caused by the other.
4 Kant gives some indication later of the meaning of the clause m
brackets, which by itself is obscure. Compare § 4 below.
316 THE ANALOGIES OF EXPERIENCE [XLVIII §2
of experience is necessarily the condition of objects of
experience, and therefore substances can coexist only if they
interact.
§ 2. Interaction and Sense-Perception
In accordance with his usual method Kant adds two further
paragraphs to the proof. These are commonly regarded as
two additional and independent proofs. The first paragraph1
seems to me to be merely an appendix, wrhich seeks to find
confirmation of the theory of interaction in the ordinary facts
of sense-perception. The second paragraph2 has more claim
to be considered as an independent proof, but Kant himself
says that it is meant to elucidate what he has already said.3
It should be regarded as, at the most, a supplementary state-
ment of the original proof, intended to bring out points not
made sufficiently clear.
Kant begins by explaining that he uses the German \\ord
'Gcmeinschaf? in the sense of 'cotmnercium' (dynamical com-
munion or interaction), and not in the sense of 'commwiio*
(mere togetherness in space); and he asserts that together-
ness in space could not be empirically known apart from
interaction.4
For confirmation of this assertion he appeals to the facts
of sense-perception as revealed by empirical psychology.
1 A 213-14 — B 260-1. 2 A 214-15 = B 261-2.
3 *Zur Erlauterung kann folgendes dienen.'
4 When Professor Pnchard says (Kant's Theory of Knowledge, p. 307)
that 'the apprehension of a body in space in itself involves the apprehen-
sion that it exists together with all other hodics in space', he is (i) using
the \\ord 'apprehension* in a non-Kantian sense, for however loose
may be Kant's use of 'apprehension', it is never taken, as here, to mean
a priori knowledge of what is not directly present to the senses; (2) he
is using the word 'body' as equivalent to 'substance' (which in strict
parlance should be avoided); and (3) he is treating 'togetherness' in
space as something quite general, whereas Kant is thinking of it as
involving a definite position in space of one body relatively to other
bodies. It is in the latter sense that Kant maintains we cannot have
empirical knowledge of togetherness in space (or coexistence in time)
apart from interaction.
XLVIII §2] THE THIRD ANALOGY 317
In one of his long and complicated sentences he propounds
a variety of theories whose meaning and interconnexion is
not altogether clear.
(i) Only continuous ' influences' in all parts of space can lead
our senses from one body to another; (2) light, which plays
between our eye and the heavenly bodies, causes a mediate
interaction1 between us and them, and thereby establishes
their coexistence ; (3) we cannot change our position empirically,
or rather we cannot be empirically aware of our changes of
position, unless matter everywhere makes perception of our
position possible; and (4) it is only through their reciprocal
influence (or interaction) that the parts of matter in different
places can exhibit their coexistence,2 and so exhibit (although
only mediately) the coexistence3 of the most remote objects.
All this is difficult. It has been suggested or implied by Kant
that if substances did not interact, the space between them
would be completely empty.4 We are now given some hints
as to what does fill space, and this appears to be identified
(i) with continuous 'influences', (2) with light, and (3) with
matter. A possible conclusion would seem to be that when
space is filled with 'continuous influences', it is filled with
'matter in interaction', one example of which is light. This
accords with the theory that 'what fills space' is matter.
1 'Genieinschaft*, in view of the previous sentence, must be inter-
preted as equivalent to 'cammercium? or 'interaction*.
2 ' Zugleichsem9 (translated by Kemp Smith as 'simultaneous
existence').
3 'Koexislenz* (translated by Kemp Smith as 'coexistence'). I
presume that there is no difference in sense between 'Zuglcichsem9
(the word usually used by Kant) and lKoe\istcuz9 (which is only the
Latin translation). The sentence is obscure; but I do not think Kant
is suggesting that the parts of matter establish their 'simultaneous
existence* by interaction and thereby establish their 'coexistence', as if
these two things were different. Nor can I see what he does mean,
unless he means that the parts of matter actually perceived establish
their coexistence through interaction with one another and with our
bodies, and thereby establish the coexistence of remote objects which
we do not perceive, although only mediately through their interaction
with the bodies we do perceive.
4 See A 212 --- B 259 and § i, II, above.
3i8 THE ANALOGIES OF EXPERIENCE [XLVIII §2
Furthermore we have the doctrine (based on empirical
evidence) that sense-perception involves interaction between
our bodies and the bodies perceived,1 and that remote bodies
interact with our bodies mediately through their interaction
with the intervening matter.2 Hence sense-perception is
possible only because all parts of matter (and therefore all
substances) are in interaction.
These statements seem to me to be meant not as a proof,
but as an illustration, or perhaps a confirmation, of the doctrine
ot interaction.
Kant goes on to maintain that without interaction every
sense-perception of spatial objects would be broken off from
every other, and the chain of ideas which constitutes experience
would have to begin afresh with every new object.3 It would
in fact cease to be a chain; for every link in it would lack
connexion with previous links, and so would fail to stand
in time-relations at all.4 He adds that he does not profess to
refute the possibility of empty space by this doctrine, but only
to show that it can be no object of experience.5
1 This doctrine is here stated without the slightest element of
ambiguity — especially in what is said about light and the eye — and I
believe with Adickes that it is an essential part of the Critical Philo-
sophy. Compare Metaphysik, p. 1 1 1 and also p 77.
2 We can say that the intervening space is filled with continuous
influences, if the causal action of a body is transmitted from one part
of matter to another until it affects our sense-organs. I take it that
the ether would be regarded as matter on this view.
3 I take this to rest on the view that if substances did not interact,
they would be separated by an empty space which we could not
perceive; compare A 212 = B 258-9.
4 We must, I think, take this to mean objective time-relations. This
would be obvious on Kant's theory, because apart from interaction
we should be unable to distinguish objective coexistence from objective
succession.
6 Compare Chapter XXXVIII § 8. Kant always displays a proper
caution in his attitude to the mechanical theory of 'atoms and the
void*. All that he maintains is that it cannot be established by empirical
evidence, but is a metaphysical assumption of a highly doubtful kind.
XLVIII §3] THE THIRD ANALOGY 319
§3. Interaction and the Unity of Apperception
Kant's final 'elucidation'1 of his position brings in the
doctrine of apperception, upon which all the Critical proofs
necessarily rest.2
All appearances, as contained in one possible experience,
must be combined under the unity of apperception. This —
the central doctrine of the Transcendental Deduction — is
here expressed in an unusual form, for Kant says that all
appearances must stand in communion of apperception.3
This might perhaps mean that all appearances are parts of a
whole which mutually exclude and determine one another,
and so are subject to the pure category (as opposed to the
schematised category) of communion. But it seems more
likely to mean merely that they must possess that necessary
synthetic unity which is implied in the unity of apperception
and articulated in the whole scheme of categories.
Hitherto Kant has been speaking of all appearances (so
far as they are combined by thought into objects). lie now
proceeds to deal with objects which are combined by thought
in a special way — namely, as standing to one another in a rela-
tion of coexistence. When thought combines objects in this
way (or, more simply, when we think of objects as coexisting),
the objects must reciprocally or mutually determine4 their
1 A 214-15 — B 261-2.
2 Similarly the unity of apperception is referred to at the close of the
section dealing with the Second Analogy. See A 210 = B 256 and
compare A 2 16 -- B 263 and A 2 17 = B 264.
3 The word used is 'Gemeimchajt* in the sense of communio, which,
as we have seen, does not involve dynamical connexion. A comtnumo
of apperception seems to mean only 'togetherness' in apperception, as
communio spatri means 'togetherness' in space. The word 'Gemewschaft'
might here refer to the pure category of communion, which is the
concept (of the synthesis) of a whole whose parts mutually exclude and
determine one another; see Chapter XXXIII § 4. But I think we shall
be on safer ground, if we interpret it in a much more general sense.
4 Here 'determine' can scarcely mean 'causally determine'; but it is
difficult to sec what it does mean, unless it means that they are mutually
exclusive parts of a spatial whole and that their temporal position or
date is determined, not by their relation to absolute time, but by their
relation to one another. The same kind of difficulty was encountered
in A 212 = B 259 — see § i, III, above.
32o THE ANALOGIES OF EXPERIENCE [XLVIII § 3
position in one time, so as to constitute a whole. This is a par-
ticular kind of subjective communion,1 in the sense that it exists
for thought.
If this subjective communion (or the togetherness of appear-
ances at one time as a whole for thought) is to rest on an objec-
tive ground, if in other words the appearances thought of as
together in one time are to be regarded as coexistent objects
in space2 (and not merely as combined together in one time
by an arbitrary act of the mind),3 there is necessary a certain
condition, which Kant goes on to state. The sense-perception
of one of the coexistent objects* must, as a ground, make possible
the sense-perception of the others^ and vice versa. Only on this
condition can we avoid attributing to the objects the succession
which is always present in our sense-perceptions (considered,
not as states of an object, but as elements in our successive
apprehension) ; and only on this condition can we say that the
objects coexist.
The whole argument turns on the 'condition' which I have
put in italics, but unfortunately the interpretation of Kant's
1 'Gememschaft.' All ' togetherness' for thought has been called
communion, which as existing for thought is so far subjective. Here
we arc dealing with the special case where togetherness for thought is
togetherness in one part of time. Kant docs not mean by this merely
that we think of them together at one time, but that we think of them
as-bemg-together-at-one-time. He probably means also — although he
does not say so — that we think of them as-bemg-together-m-one-
space-at-one-time.
2 Kant's own expression is 'If this subjective communion is to rest
on an objective ground or be referred to phenomenal substances'.
Here again he seems to be thinking of substances as coexisting, but by
Coexisting' he means * being in a certain state during the same period
or part of time.' We might say: '// the objects thought of as together are
to be regarded as coexisting substances', provided we understand 'coexist-
ing' in the sense I have explained.
3 Such an act would be an act of imagination rather than of thought,
for thought always involves assertion of an object; but this side of
thought Kant has here so far ignored.
4 Or coexisting substances in the sense suggested in the last note
but one.
5 The plural seems the most natural interpretation of 'der andcrcn'
here, but it may be singular, as Kemp Smith takes it. This certainly
gives the simpler case.
XLVIII §3] THE THIRD ANALOGY 321
statement is perhaps even more difficult than usual. I take what
Kant calls the 'ground* to be equivalent to 'cause'. One sense-
perception considered as an element in our apprehension can
hardly be the cause of another, so we must assume that the
sense-perceptions in question are to be regarded as states of
an object. Even so there is still an element of uncertainty.
If we take the simple case of two objects A and B with states
ax a2 a3 a4 . . . and ft ft ft ft . . ., does Kant mean that
ax must be the partial cause of ft, ft must be the partial cause
of a3, a3 must be the partial cause of ft, and so on ? Or does he
mean that the two simultaneous states ax and ft are related to
one another partly as cause and partly as effect P1
The two interpretations may not in the end be so different
as they look at first sight, but the second one seems to be the
most natural way of taking Kant's words. In either case we
have at every moment the reciprocal causality of coexistent
substances ;2 and in either case we have to face great difficulties
in the argument.
In the first case, while the objects are coexistent, the states
which are causally connected are successive ;3 and the causality
of the states is reciprocal only in the sense that #2 is partly
caused by av and a2 is partly caused by ft. Even this could
not be established on the basis of the Second Analogy; for
the Second Analogy professes to prove only that the succession
dj )82 must be causally determined, not that ax must be the
cause of ft. We must have a new argument resting, not on
succession, but on simultaneity, and unless we have such an
argument, Kant's conclusion seems unjustifiable.
1 The fact that aA and /Jj cannot be perceived simultaneously does
not exclude this interpretation, since for Kant the states of an object
are not only actual, but also possible, sense-perceptions.
2 In the first case not only is /*2 the joint product of ax and pv
but also a2 is the joint product of /^ and ax : we are not confined to
the states which we actually perceive, but are concerned also with the
states which ex hypothesi we could have perceived. I am assuming that
a substance 'acts' as a cause in virtue of its states.
3 Even this is true only where the objects are changing, as in the
case of the fire and the ice. When the objects are unchanging, there is
no objective succession in the states.
VOL. II L
322 THE ANALOGIES OF EXPERIENCE [XLVIII § 3
This suggests that we must accept the second interpretation,
which seems in any case to be the more natural. If so, the rela-
tion of reciprocal causality must hold, not only between
coexistent substances, but also between simultaneous states
of these substances. Our actual sense-perceptions-are always
in a succession, and even if we regard them as states of an
object, they cannot be in a reciprocal relation of cause and
effect. Kant must have in mind the possible, as well as the actual,
sense-perceptions ; and he appears to be saying that if we are
to perceive two objects A and B as coexistent in space, we must
presuppose that the simultaneous states c^ and j3x are in a
relation of reciprocal causality, and so too with a2 and j82,
and with a3 and ]83. Only so can a reversible series of states,
which we take up successively in apprehension,1 be regarded
as revealing coexistent objects.
What is the reason for Kant's assertion? We must assume
that the simultaneous states cannot be perceived together,2
and also that we cannot perceive an absolute time in reference
to which each perceived state could be dated.3 If so, the simul-
taneity of states can be objectively determined only if it is
necessarily determined ; or in other words we can claim to know
that the states are simultaneous in the object only on the
presupposition that they are necessarily simultaneous. This
seems to be a particular case of Kant's more general principle
that the temporal position of states relatively to one another
can be objectively determined only if it is necessarily deter-
mined; but he appears to assume that because we are here
concerned with necessary simultaneity (and not with necessary
succession), the necessity must, so to speak, work equally in
1 We take up, for example c^ //2 0$ />4 . . ., but if the series is reversible
we could equally take up //j «2 /'a "4- • • • If so> *t seems legitimate to
hold that ctj and /?t are simultaneous. Compare reciprocal succession
in Chapter XLVII § 3, V.
2 Even if they could, there would still, I think, be a question whether
the states were simultaneous in the objects.
3 If this could be done, presumably we should be entitled to fill in
the gaps, that is, to assume, on the ground of continuity, the existence
and character of the states which we had not perceived.
XLVIII § 3] THE THIRD ANALOGY 323
both directions (and not in one direction only). At any rate,
just as objective succession must be necessary succession, so
objective simultaneity must be necessary simultaneity ; and just
as we are entitled to apply the schematised category of cause
and effect where we find necessary succession, so, Kant appears
to hold, we are entitled to apply the schematised category
of interaction where we find necessary simultaneity. Without
this presupposition the empirical relation of coexistence cannot
be met with in experience.1
This argument, if correctly interpreted, is full of difficulty,
and even its conclusion raises serious problems. It suggests that
not only must coexistent things mutually determine the simul-
taneous states of one another, but that the simultaneous states
must themselves mutually determine one another in the sense
of being reciprocally cause and eifect — a relation which many
philosophers since Schopenhauer have maintained to be
impossible. Clearly if there is interaction between simul-
taneous states, there is interaction between coexistent sub-
stances, as Kant immediately goes on to assert.2 It is not so
clear that interaction between coexistent substances implies
a relation of interaction (or reciprocal causality) between their
simultaneous states.
There is a further manifest difficulty in the conclusion.
Even if we accepted this doctrine in the case of a fire melting
1Aai4-i5 — Ba6i. I take 'coexistence* here to be the coexistence
of substances or things, which of course implies that they must have
simultaneous states.
2 A 214- 1 5 - 6261. Kant speaks of a reciprocal influence or real
commcrcium of substances. He adds that this commercium makes the
appearances a composition reale. A compositum is a whole which is
possible only through its parts: it is opposed to a totum, where the
parts are possible only in the whole (A 438 = B 466). This accords
with the statement (A 218 n. =- B 265 n.) that the unity of the world
whole is a mere consequence of the tacitly assumed principle of inter-
action. A compositum reale is opposed to a compositum ideale, such, for
example, as space would be, if it were not, strictly speaking, a totum ;
see A 438 — B 466.
'Compositio* in B 201 n is used in a different sense; for it concerns
the synthesis of the homogeneous manifold only.
324 THE ANALOGIES OF EXPERIENCE [XLVIII § 4
ice,1 there seem to be other cases where it does not apply.
When I look at the earth and then at the moon, I do not assume
that the colour or brightness or shape or size which I see in the
one is the cause of the colour or brightness or shape or size
which I see in the other. It is not possible to regard every
perceived state of a substance as causing and caused by all
simultaneous states of another substance — at any rate if we
are concerned with principal causes. The states with which
Kant is concerned appear to be states of motion or of moving
forces, states in virtue of which matter, and so substance,
may be said to fill space. If so, the doctrine requires a more
detailed exposition than it receives.
§ 4. Interaction and Coexistence
I do not think it can reasonably be doubted that the concept
of interaction is the most fundamental concept of science.
Scientific laws are not expressed in the form 'A is the cause
of B', but in the form of equations;2 and the world as known
to science is not a series of causal successions parallel to, and
independent of, one another, but is rather a system of functional
relations between measurable quantities.3 Kant's description
of the concept of interaction in terms of 'substance' and 'cause1
may be antiquated; but I imagine that it could be restated
in more modern terms, or at least that the concept which must
take its place will be regarded by the future historian of science
as in the direct line of evolution from the concept described
by Kant.
If we look at the question from the standpoint of Kant's
own period, it seems clear enough that the isolated concepts
1 Even this is perhaps a case of mediate interaction, if it takes time
for the heat of the fire to reach the ice. Gravitation is presumably a
case of immediate interaction.
2 For example, the law of gravitation, of which Kant is thinking, is
expressed in the equation
d*
3 Compare Schlick, University of California Publications, Vol. 15,
p. in.
XLVIII § 4] THE THIRD ANALOGY 325
of substance and causation require to be combined into the
concept of interaction between substances, and that by such
combination we have a new and independent concept. Indeed
had the argument not been so complicated, there would have
been only 'one Principle of the Analogies — the Principle of
Interaction — just as there is only one Principle of the Axioms
and one Principle of the Anticipations.
A knowledge of eighteenth-century science would, I think,
help to make clear much that seems to be obscure in Kant's
exposition — notably the empirical examples which he gives at
the conclusion of the argument in the first edition.1 Lacking
such knowledge, I am compelled to make my criticisms in a
way that may be naive. I can only hope that for this very reason
they may be useful to those whose ignorance in these matters
is as great as my own.
As we have seen, Kant generally speaks of interaction as
taking place between coexistent substances ; but he is concerned
primarily with the substances of which we have empirical
knowledge, substances whose accidents remain relatively
constant so that they can be spoken of as 'things' (like the earth
and the moon). Coexistent substances in this sense are said
to be cordinated in such a way that each is simultaneously and
reciprocally a cause in relation to the determinations or states
of the other.2 Such a description appears to be justified in
Professor Prichard's example of the fire and the ice, or again
in Kant's own example of the parts of a body which reciprocally
attract and repel one another.3 We know that for Kant substances
are 'the first subject' of all causality,4 and that 'action' is a
sufficient empirical criterion of substantiality.5 Every substance
must contain in itself the 'causality' of certain determinations
in the other substance, and at the same time the effects of the
causality of that other.6 The reciprocal causality of coexistent
substances in respect of their determinations is clearly implied
1 A 213 ^B 260. 2 See B 112.
3 Sec B 112. It should be remembered that all parts of a body are
themselves substances. 4A2O5 = B25i.
5 A 205 = B 250. 6 A 212 = B 259.
326 THE ANALOGIES OF EXPERIENCE [XLVIII § 4
in all such phrases as 'dynamical communion', 'interaction',
'commercium', and 'reciprocal influence'. On this point I have
no doubt at all.
Without enquiring closely into the nature of the causality
exercised by substances we may, I think, say that a substance
exercises causality in virtue of its accidents or states.1 1 presume
that we have to discover empirically the state of a substance
in virtue of which it exercises causality upon the state of another
substance. This is always Kant's view in regard to particular
applications of the principle of causality; and manifestly
(if we are concerned with principal causes) we cannot take one
state of a substance at random, and say that in virtue of this
state the substance exercises causality upon all the states of
other coexisting substances. It is not, for example, in virtue
of its shape or colour that fire reduces the temperature of
ice.2
If we take the simple case when two substances A and B
interact in virtue of their states a and j8, we may suggest that
on Kant's view a2 is caused by j8j and a± jointly, and similarly
]82 is caused by ax and jSj jointly.3
This appears to be a plausible interpretation of Kant's
doctrine. Nevertheless the question arises whether he does not
mean more than this. On this view it might be said that in the
1 Kant, I think, is primarily concerned with the 'moving forces' in
virtue of which matter fills space — particularly those of attraction and
repulsion.
2 I do not mean to deny that a substance may exercise causality in
regard to all the states of coexisting substances — perhaps Kant holds
that it does. But clearly there is, so to speak, a main line of causation.
The heat of the fire causes the ice to melt, and thereby it may cause
the ice to change its colour and shape; but although the colour and
shape of the fire may be connected with its heat, the colour of the fire
does not cause the ice to change its colour, nor does the shape of the
fire cause the ice to change its shape ; and still less does the colour of
the fire cause the ice to change its shape or the shape of the fire cause
the ice to change its colour. I imagine that for Kant all interaction of
substances is due to moving forces, but the relation of these to other
qualities of substance stands in need of elucidation.
3 I need hardly say that I am taking «1 and /^ to be the simul-
taneous states of A and B which immediately precede the stages a2
and /?2.
XLVIII §4] THE THIRD ANALOGY 327
coexistent substances A and B the states which are simultaneous1
arc not in a relation of cause and effect ; and on the other hand
the states which are in a relation of cause and effect are not
simultaneous, but successive. Clearly at every instant the
coexistent substances are in a relation of interaction or reciprocal
causality; for at every instant each contains in itself a state
which is partly caused by the action of the other. But does
Kant mean also that the simultaneous states are themselves in a
relation of reciprocal causality so that each is at once the cause
and effect of the other ?2
If Kant holds the latter doctrine, it must be because the
action of causality is continuous.3 The time between the
causality of the cause and its immediate effect can be a
vanishing quantity, so that cause and effect can, in a sense, be
regarded as simultaneous.4 For this view Kant's previous
1 By * simultaneous' I mean 'occurring at the same instant of time*.
2 In symbols, can we say that a2 is partly the effect of /?2, and /?2
partly the effect of a2? 3 A 208 = B 254.
4 A 203 — B 248. Let us represent the interaction of two things A
and B thus :
If we remember that the series at a2 a3 a4 afi . . . and the scries
Pi !'<> /'a 1^ /s - . . ate really continuous series, and if we remember
also that there is no passage of time between cause and effect, we may,
so to speak, close up the above diagram like a concettina, and in the
limiting case we seem to have something like this :
al « ----- > Pi
/36
328 THE ANALOGIES OF EXPERIENCE [XLVIII§4
discussion1 has prepared us; but it must be remembered that
although there is no interval or passage of time between cause
and effect, the temporal relation or order still remains ;2 and
it is difficult to reconcile this with the reciprocal causality of
simultaneous states.3 I am not prepared to say that it is
impossible.
So far as I can see, the text of the Third Analogy is not con-
clusive on this point. There can be no doubt that Kant is
primarily concerned with the reciprocal causality of coexistent
substances, not with the reciprocal causality of simultaneous
states. There is, I think, only one passage4 which seems to
point clearly to the latter view. Kant says that the perception
of the one substance must as ground make possible the percep-
tion of the other, and vice versa. If we take 'perception', as I
have done, to be equivalent to state of a substance, this appears
to indicate that there is a relation of reciprocal causality between
simultaneous states. But even here it is perhaps barely possible
for him to mean only that ax is the ground of /J2, and $> the
ground of a3, although in that case it is difficult to see how
this assertion could be justified.5
This problem, I imagine, could be settled with comparative
ease in the light of eighteenth-century science and perhaps
of Kant's own scientific writings.6 I must confine myself to
raising the question, and I do not think it should be really
difficult to answer.
Connected with this problem is the difference between
immediate and mediate interaction. Repulsion and attraction
I imagine to be for Kant examples of immediate interaction,
1 A 202-4 = B 247-9. 2 A 203 = B 248.
3 I do not think there is any difficulty about the reciprocal causality
of coexistent substances.
4 A 214 = B 261. It must be remembered that ' Erschetnung* need
not mean a perceived state, but may be a thing or substance.
1 Wahrnehmung' (sense-perception) might, I think, be used as equivalent
to ' Erscheinung' in this sense, but I find it difficult, or even impossible,
to suppose that it is so used in this passage.
6 Compare § 3 above.
6 See especially for the third law of motion M.A.d.N. 3 Haupt-
stuck, Lehrsatz 4. (IV 544 ff.).
XLVIII § 5] THE THIRD ANALOGY 329
and he may here suppose that there is reciprocal causality
between simultaneous states of coexistent substances. In the
case of mediate interaction there appears to be a lapse
of time involved. He certainly regards light as producing
a mediate* communion or interaction between the heavenly
bodies and the human eye ;x and although this is a very special
case, it would seem to imply that a period of time may be
required for mediate interaction to take place.
In such a case, although the bodies which interact are
coexistent, the determining state of the one body is not neces-
sarily coexistent with the determined state of the other. The
star may have ceased to shine before I see its light. Indeed
it may be said that not even the bodies need coexist; for the
star which I now see may have been broken up before I was
born. If so, it is only the substances which coexist, and hence
it may be thought that Kant's principle tells us nothing; for
we know a priori that all substances coexist, since they are
necessarily permanent. This criticism is not, I think, valid.
Kant's principle tells us that a particular substance which
had at one time the empirical characteristics of a star coexists
with another substance, namely my body, in a form which,
if we had sufficient knowledge, we could now describe. This
remains true, even if the star has been broken up into several
substances now distributed throughout space.
§5. KanCs Proof of Interaction
On the method of Kant's proof I need add little to what
I have already said. The arguments in the first edition are by
themselves insufficiently clear, and even the argument of the
second edition leaves much to be desired. Nevertheless the
1 I confess I do not understand what is the action of the human eye
upon the heavenly bodies; but perhaps the following passage from
Professor Broad (Scientific Thought, p. 172) gives some indication of
what Kant means. 'When a beam of light from the sun strikes upon
any surface on the earth it produces a pressure on that surface. If
there be any reaction from the earth, it will be exerted primarily on
the surface of the ether next to the earth, and will not be conveyed
back to the sun in less time than light takes to travel between the two.'
VOL. II L*
330 THE ANALOGIES OF EXPERIENCE [XLVIII § 5
method employed is the same as the method of the Second
Analogy. Kant holds that (if it be granted that we experience
objective coexistence) there is a presupposition of necessity
in our sense-perceptions, and this necessity must belong to
the states of the objects we perceive, provided we accept the
Critical doctrine supposed to have been already established —
that an object is made up of possible or actual sense-perceptions
combined in a necessary synthetic unity. He is quite right in
maintaining that such a proof, if it is possible at all, is possible
only on Critical presuppositions. There is more danger of
falling into incidental fallacies in the proof of interaction,
because the concept of interaction involves greater complication
than the concept of cause and effect; but the fundamental
method employed would seem to be valid either in both cases
or in neither. Although I feel much uncertainty as regards the
details, the whole argument seems to me essentially Critical;
and it is concerned, not with an alleged process by which we
pass from the subjective ro the objective, but with the conditions
which are presupposed by our experience. I hope I have at
least persuaded the reader that Kant is putting forward a novel
argument with a definite meaning, and not merely deceiving
himself with words.
On questions of detail I would add only two points. In the
first place I do not think that Kant's argument must rest upon
the doctrine that we cannot directly perceive coexisting states
of bodies, but the fact that he seems to hold this view of per-
ception is apt to arouse suspicion in his readers. Thus he does
not even raise the question whether we cannot actually see
the earth and the moon at the same time, as seems obvious,
at least when the moon is rising or setting. In the second
place Kant might have given to space a more prominent part
in his argument without departing from his Critical method.
He himself recognised, at any rate after the publication of the
first edition, that it is space which makes interaction possible;1
and if substance and causation are necessary to represent
empirically the unity and successiveness of time, interaction
1 See Erdmann, Nachtrdge LXXXVI.
XLVIII §5] THE THIRD ANALOGY 331
would seem to be necessary to represent empirically the
unity of space. If Kant had been living to-day, I think he would
have held that interaction (which combines the concepts of
substance and causality) is necessary to represent the unity
of space-time.
The whole argument raises further questions which cannot
be discussed here — notably the coexistence of minds or ideas
and the unity of the world- whole. These questions belong to
the Dialectic, and it need only be said at present (i) that since
for Kant souls are not permanent substances, it looks as if our
ideas must be regarded empirically as states of our bodies (which
are substances) and their coexistence determined like that of
any other states of substance;1 and (2) that the unity of the
world-whole is a consequence of the principle of interaction
and not a presupposition of it.2
1 This may be questioned, but it seems to me the inevitable outcome
of Kant's doctrine.
2 See A 218 n. = B 265 n., and compare A 215 — B 261-2.
BOOK XI
THE POSTULATES OF EMPIRICAL
THOUGHT
CHAPTER XLIX
POSSIBILITY
§ i. The Principles of Possibility, Actuality , and Necessity
Kant's account of the Postulates of Empirical Thought1
is simpler and easier than the proofs of the Analogies. It does
little more than set out in systematic form the presuppositions
upon which the whole argument has hitherto proceeded.
Hence it is called an 'explanation* or 'elucidation'2 and not
a 'proof; and its business is to explain what is, in the Critical
Philosophy, the meaning of the three categories of modality,
namely, possibility, actuality, and necessity. Kant found
it unnecessary to restate his explanation in the second edition,
as he restated the proofs of the other Principles. He does,
however, add a new section on the Refutation of Idealism,
which will be reserved for separate consideration.3
The formulation of the three Postulates is as follows :
(1) That which agrees with the formal conditions of experience
(as regards intuitions and concepts) is possible*
(2) That which is connected5 with the material conditions
of experience (sensation) is actual.
(3) That of which the connexion* with the actual is determined
1 A 218 = B 265 ff. Compare also Chapter XXXVI § 2.
a 'Erlauterung.' 3 See Chapter LI.
4 We may put this more clearly by saying that what agrees with the
formal conditions of experience, that is, with the conditions of intuition
(space and time) and with the conditions of thought (the unity of apper-
ception and the categories), is possible. 5 'zusammenha'ngt.'
6 ' ZusammenJiang.' ' Zusammenhang* here (and, as a verb, in the
definition of actuality) is equivalent to * Verkniipfung\ or 'nexus', the
technical term for 'connexion' ; see B 201-2 n. The word 'Verkniipfung*
is used in A 227 = B 279. The connexion spoken of is by means of the
Analogies, and it seems to me a mistake to blame Kant, as Kemp
Smith does (Commentary, p. 397), for defining actuality without
reference to the Analogies. Compare the formulation in A 376 : 'What
is connected with a sense-perception in accordance with empirical
laws is actual*. Empirical laws presuppose the Analogies.
336 THE POSTULATES [XLIX § i
according to universal conditions of experience is necessary (or
exists necessarily).
These three statements are intended to be definitions of
the possible, the actual, and the necessary, and we are entitled
to convert them simply. They are concerned with real (and
not with merely logical) possibility, actuality, and necessity.
That is to say, they are concerned, as is indicated by the
parenthesis in the Third Postulate, with possible, actual,
and necessary existence, or with the possibility, actuality,
and necessity, not of thoughts, but of objects*
Hitherto we have been attempting to prove that if an object
is to be an object of a spatio-temporal human experience,
it must have in itself certain necessary characteristics or deter-
minations; it must have extensive and intensive quantity, and
be a substance (with changing accidents) in causal interaction
with all other similar substances. Possibility, actuality, and
necessity are not characteristics of objects in the same sense,
and they are not contained in the concept of the object con-
sidered only in itself. Our concept of an object may be com-
plete,2 and yet we may still ask whether the object itself is
only possible, or whether it is also actual; and if it is actual,
we may ask whether it is also necessary. These questions,
Kant believes, are concerned, not with the content of the
object, but with its relation to our mind or with the way in
which we cognise it.
1 Compare Metaphysik, p. 28. Real possibility is agreement with
the conditions of a possible experience. The connexion of a thing
with experience is actuality. This connexion, so far as it can be known
a priori, is necessity.
2 Kant's discussion of definitions (in A 727 — B 755 ff.) suggests
that completeness is never found in empirical concepts, but only in
factitious and mathematical concepts. In his lectures on Logic inner
completeness is attributed also to pure concepts of reason ; Log. EinL
VIII (IX 62-3). Outer completeness (Ausfuhrhchkeit) is, however,
denied to these in A 728-9 = B 756-7; and if so, inner completeness
should presumably be denied also. Outer (or extensive) completeness
involves the clarity of the coordinate marks in a concept: inner (or
intensive) completeness involves the clarity of the subordinate marks in
a concept.
XLIX § i] POSSIBILITY 337
Just as Kant connected logical possibility, actuality, and
necessity with understanding, judgement, and reason in their
logical use? so he here connects what we may call real or
material possibility, actuality, and necessity2 with under-
standing, judgement, and reason in their empirical use, that
is, as applied to experience.3 In his final summary4 he expresses
the same view without the use of these technical terms. The
Postulates add to the concept of an object only the cognitive
power in which it originates and has its seat. If the concept
is merely in the understanding,5 and agrees with6 the formal
conditions of experience, then its object is possible; if it is
connected with sense-perception or sensation (that is, with the
matter of the senses) and is determined through the senses
by means of understanding,7 then its object is actual; if it is
determined through the connexion of sense-perceptions in
1 Sec A 75 n. B 100 n. Sec also A 130-1 = B 169 and A 304
— B 360-1 and compare Chapters IX§ 2 and XXXIII § 5. The logical
use is the general (or formal) use, studied by Formal Logic in abstrac-
tion from all differences in objects.
2 That is, the possibility, actuality, and necessity of objects, not of
thoughts
1 If an object is to be possible, it must be conceived by understanding
in accordance \\ ith the formal conditions of experience ; if it is to be
actual, it must be asserted by the power of judgement on the basis of
sense-perception ; if it is to be necessary, it must be inferred by reason
to be determined in accordance with the universal laws of experience,
that is, in accordance with the Principles of the Understanding, and
especially the Analogies.
It should be noted that the power of judgement (which subsumes
an actual case under a concept) rests either on pure or on empirical
intuition. Kant refers expressly in the present passage to the empirical
power of judgement to show that \\e are concerned with empirical
intuition or sense-perception.
4 A 234 =-= BaS6.
6 Here taken in the nanow sense (as opposed to judgement and
reason)
6 Kant says 'is in connexion with' (Verknupfung), but this is not the
technical meaning of iVeiknuf>fung\
1 Here, I think, * understanding' is that form of understanding (in
the wider sense) which is called the power of judgement. The reference
to understanding shows that for Kant existence is not to be found by
sense apait from thought.
338 THE POSTULATES [XLIX § i
accordance with the categories,1 then its object is necessary.2
The content of the concept is the same in all these cases,
but its relation to the mind is different.
It will be seen that Kant is explaining real possibility,
actuality, and necessity by reference to experience.- Possibility
depends on the form of experience, actuality primarily on
the matter of experience, and necessity on the combination
of the two. His doctrine therefore differs expressly from any
rationalist doctrine which maintains that by pure reason
apart from experience we can know the possibility, the actuality,
and even the necessity, of things.3 In particular he is in these
definitions restricting all the categories to a merely empirical
use and excluding their transcendental use4 by means of pure
reason alone. The categories in their purely logical significance
are, as we have so often seen, identical with the empty forms
of judgement. If they are taken as concepts of an object in
general, then they have 'sense and significance' only as concepts
of an object ot possible experience.5 They do not give us
1 This is the work of reason in its empirical use — I presume in
seeking higher conditions for the conditioned (A 309 — B 365),
although this work can never be completed. The Concepts' of which
Kant speaks are the categories.
2 I feel some difficulty about the use of the word 'determined* in
the statements about the actual and the necessary. A concept is
determined, if it is related to given intuition, and intuition is deter-
mind, if it is brought under a concept. The first of these senses seems
to be used as regards the actual; but as regards the necessary there
must be, in addition to the determination of the concept, a determina-
tion of the object (or of its connexion with sense-perception) through
the categories.
3 Such possibility, actuality, and necessity may be called absolute,
as opposed to the possibility, actuality, and necessity of Kant which
is hypothetical and relative to experience; compare A 232 -- B 285.
4 See Chapters XI § 4 and LIV. If we can regard objects as
possible, actual, and necessary only by reference to experience, this
must apply to the objects thought by means of the categories.
6 The categories of quantity are concerned, as we have seen in
Chapter XXXIII § 5, with the synthesis of the form of intuition;
the categories of quality are concerned with the synthesis of the matter
of intuition ; the categories of relation are concerned with the synthesis
of the form and matter of intuition. We must not, however, think that
there are three syntheses; for there is only one synthesis with dis-
XLIX§z] POSSIBILITY 339
absolute knowledge of things in-themselves ; indeed as applied
to things-in-themselves they are empty.
The necessity for a discussion of the Postulates should
be manifest. Throughout the Principles an appeal has been
made to the possibility of experience, and so of objects of
experience. In the Analogies Kant has argued that the objective
or the actual, as opposed to the subjective or imaginary, must
be governed by necessity. Without some explanation of the
use of these terms, the argument would be incomplete. To
say that the Postulates are due merely to what Professor
Adickes calls Kant's ' Systematic ', and to what Professor Kemp
Smith calls Kant's 'architectonic', seems to me erroneous.1
Kant has shown what objects must be, if they are given to
intuition and if they exist in relation to one another in a common
space and time. He has still to show what relations they must
have to the mind which knows them.
§ 2. The Interdependence of the Categories of Modality
The categories of modality, like all other categories, neces-
sarily apply to all objects of experience, so that every object
of experience is both possible, actual, and necessary. Possibility
tmguishable aspects. By supposing that there are three separate
syntheses, we take far too seriously abstractions which are necessary
only for purposes of analysis, and attribute to Kant all sorts of errors
and distortions which seem to me remote from his actual doctrine.
Perhaps it should be added that the synthesis with which a category
is concerned is always itself a formal synthesis. Whether the synthesis
deals with the form (that is, with the pure manifold) of intuition, or
whether it deals with the matter (that is, with the empirical manifold)
of intuition, or with both form and matter, the category is the concept
of the synthesis in general and ignores differences dependent on
differences in the given matter.
1 Adickes in his commentary even asserts that the Postulates are
not Principles, because they do not make experience possible. The
Postulates, like other Principles, state conditions apart from which
experience is impossible ; for the objects of experience must be possible,
actual, and necessary, not absolutely, but in relation to our minds.
Adickes' further objection, that men have experience without any
idea of the way in which the possible and necessary depend upon the
powers of the mind, shows a curious blindness to what Kant meant
by the a priori conditions of experience.
340 THE POSTULATES [XLIX § 2
is no wider than actuality,1 and actuality no wider than necessity.
The category of necessity, like the third category in every
class, combines in itself the other two categories: it combines,
in short, possibility and actuality.2
The fact that the three categories of modality must apply
to any and every object does not make it superfluous to dis-
tinguish these categories from one another; we might as
well suggest that it is superfluous to distinguish any category
from any other, since they must all apply (if they are to be
categories at all) to any and every object. It may, however,
be thought that the other categories apply to objects in virtue
of distinguishable aspects in the objects, while this cannot
be so in the case of the categories of modality, since they
are concerned only with the different relations of the total
object to the knowing mind.3
I do not think that this criticism is sound. We are no doubt
considering the object in its relation to the mind ; but Kant's
whole point is surely that the object has different relations
to the mind in virtue of different aspects in it which we have
already discussed. Every object has a form imposed by the
mind, and in virtue of that form the object is possible. Every
object has a matter given to the mind and synthetiscd under
that form; and in virtue of the matter so given and synthetised,
the object is actual.4 Finally every object is a combined whole
of form and matter, which means that it is a substance whose
accidents are causally determined ; and in virtue of this deter-
mination the object is necessary.
1 See A 231 = 6284.
2 Compare B in. I must confess that I still find obscure Kant's
statement in this passage that necessity is simply existence which is
given through possibility itself. When we infer the necessary existence
of the effect from the cause, existence is given through the formal
conditions of experience, but we must always start from what is
actual.
3 I think this is what Professor Kemp Smith must mean when he
says (Commentary », p. 393) that 'one and the same definition adequately
covers all three terms alike1.
4 The matter need not be given directly, it may be inferred in virtue
of known causal laws.
XLIX §2] POSSIBILITY 341
It is tempting to suggest1 that the synthesis of quantity
gives us the possibility of the object, the synthesis of quality
its actuality, and the synthesis of relation its necessity. This
has the great merit of simplicity ; and it makes an object possible
in virtue of its conformity to the nature of time and space, a
doctrine not without a certain plausibility, Nevertheless the
teaching of the Postulates is more complicated than this;
for possibility is said to involve conformity with the formal
conditions, not of intuition, but of experience in general;
and these formal conditions (the objective form of experience
in general) are said to contain all synthesis demanded for
knowledge of objects.2 This is a clear allusion to the categories,
and confirms the definition of possibility in the First Postulate
itself.
We must, I think, take Kant to mean that an object is possible
so far as it conforms, not only to space and time, but also to
the categories — that is, to all the formal conditions of experience.
An object is actual so far as it is connected with the material
conditions of experience, that is, with sensation. The fact
that this 'connexion' must be in accordance with the categories,
and in particular with the categories of relation, manifestly
docs not mean that the actuality of an object is the same thing
as its possibility: possibility and actuality are still distinct
from one another. It may, however, be maintained that there
is no real difference between actuality and necessity; for
when we say that an object is necessary, or exists necessarily,
so far as its connexion with the actual is determined in accor-
dance with the universal conditions of experience, we are saying
no more than has already been said in our definition of the
actual.
The reference to the universal conditions of experience
(in distinction from the formal and material conditions) can
hardly constitute the difference between actuality and necessity ;
1 I did so provisionally in Chapter XXXIII § 5. There is some
support for this in A 180 =- B 223, if what is called 'the synthesis of
mere intuition (that is, of the form of appearance)* can be identified
with the synthesis of pure intuition (which I have called above the
synthesis of quantity). * A 220 = B 267.
342 THE POSTULATES [XLIX § 3
for these universal conditions appear to be only the formal
and material conditions taken together; and, as we have seen,
formal as well as material conditions are necessary to actuality.1
At the most the reference to universal conditions could indicate
only a difference of emphasis; when we consider an object
as actual, we emphasise the material conditions of experience,
and when we consider it as necessary we emphasise the com-
bination of formal and material conditions. A difference of
emphasis is hardly enough to establish a distinction between
categories.
This criticism appears to me sound so far as it goes, but it
fails to notice the word 'determined*. An object possesses
actuality, if, for example, it is connected as a cause with what
is given as an effect. It does not, however, possess necessity,
except in so far as it is determined as the effect of a given cause.2
Kant's distinction is not stated too clearly, but it is there
none the less, and it is brought out in his discussion of the
Third Postulate.
The categories of modality (like those of quantity, quality,
and relation) are interdependent; but this is no reason why
we should regard them as indistinguishable.3
§ 3. Thought and its Object
If Kant had confined himself to elucidating the meaning
of the categories of modality, his exposition would have been
more simple. It would have been clear that every object must
be possible, actual, and necessary, and that the three categories
must apply to every object of experience. Kant, however,
1 I think the reference to material conditions (not merely to matter)
itself indicates the presence of something else, namely form.
2 Compare A 194 = B 239 and many other passages in the Second
Analogy.
3 The difficult account of the schemata of modality (in A 144-5
= B 184) suggests that to know the possibility of a thing we must
know that it is at some time or other; to know its actuality we must
know that it is at a definite time ; to know its necessity we must know
its relation to the whole of time (presumably by knowing the chain of
causes through which it is produced).
XLIX § 3] POSSIBILITY 343
concerns himself also with a wider question — whether the
categories of modality (and consequently all the categories)
apply to objects beyond experience.
Even on Kant's view, as I have so often insisted, the pure
categories have a prima facie claim to apply to objects beyond
experience; for in themselves (as derived from the nature
of understanding) they have no reference to sensuous intuition.
On the ordinary rationalist view there is a still wider claim
that by means of concepts we can know objects not given to
sensuous experience. Such claims raise the whole question
of the relation of thought to its objects. They also raise the
question whether we are entitled to regard objects as possible
in some sense other than that which Kant has ascribed to
real possibility.
If the claim to know objects by means of concepts apart
from sensuous intuition is maintained, then clearly such know-
ledge must be a priori knowledge. On Kant's view a priori
knowledge can be justified only by reference to the forms
or conditions of experience, and in particular by reference
to the forms or conditions of sensuous intuition ; but in con-
nexion with the First Postulate he takes it upon himself to
examine the main types of concept, and to consider whether
by themselves they can give us knowledge of possible objects
and so possess objective reality. This is a source of complication
in his exposition.
These complications we shall discuss in due course. At
present we must keep it clear in our own minds that for Kant,
as I have said, possibility is no wider than actuality, and actuality
is no wider than necessity. The latter contention seems to
me to be established beyond a doubt by the doctrine of the
Analogies, which alone is concerned with existence. It may be
suggested that the former contention is more doubtful; for
if we can think an object without knowing it — and Kant
habitually makes this distinction — then it would seem that
on his theory the sphere of possible objects must be wider
than that of actual objects.
Such a suggestion would be erroneous: we cannot make
344 THE POSTULATES [XLIX § 3
an object possible by mere thinking. I can think what I will,
so long as I do not contradict myself; but in such a case although
the thought is a (logically) possible thought, it does not follow
that a corresponding object is (really) possible.1 Such a thought
or conception is a problematic judgement; and for Kant a
problematic judgement is one in which affirmation or denial
is taken as possible (optional):2 it is accompanied by con-
sciousness of the mere possibility of the judgement.3 For the
real possibility of the object (or the objective validity of the
thought) more is required than consistent thinking.4 The
fact that we can think what we do not know does not extend
the range of possible objects beyond that of actual objects.
It may be objected that a thinking or conceiving thus divorced
from the affirmation of reality exists only by a kind of abstraction
from our whole experience of the actual or the real. I do not
see why Kant should deny this : it is his central doctrine that
our concepts are empty apart from reference to the matter
of intuition. Nevertheless in conception the matter given
to sense can be combined in ways which we do not know
to be possible, and we must still ask whether such a concept
refers to a possible object. We can also entertain a concept
without affirming its objective reality — this is involved in
what is called 'supposing' and even in the making of hypotheses.
Such supposing no doubt cannot occur independently of
experience of the actual, but Kant nowhere asserts that it can.
Kant is surely right in saying that although we can conceive
the existence of God and the immortality of the soul, we are
not thereby entitled to assert straight away that God's existence
is either possible or actual or necessary, and that the soul is
possibly or actually or necessarily immortal. It may be held
that these are not instances of genuine conceiving or thinking;
but once we begin to distinguish genuine thinking from what
1 B XXVI n. 2 A 74 - B 100.
3 Log. § 30 (IX 108-9). Compare also A 286-7 - B 343, where it is
said that the concept of a noumcnon (as the object of a non-sensuous
intuition) is problematic, that is, is the idea of a tiling of which we
can neither say that it is posbib'e nor that it is impossible.
4 A 220 - B 268.
XLIX § 4] POSSIBILITY 345
only seems to be thinking, we have to face a scries of difficulties
which, so far as I know, have never been satisfactorily solved.
Whether Kant is using the most suitable terminology or not
is a matter of minor importance. He is calling attention to a
real problem, and I do not think we can put his doctrine
out of court on the ground that if we know a thing to be possible,
we know it to be actual and necessary.
§ 4. The First Postulate
The First Postulate insists that if things are to be possible,
the concept of these things must agree with the formal conditions
of an experience in general;1 in other words, the concept
must agree with the forms of intuition (space and time) and
with the unity of apperception.
It should be noted that Kant is dealing with the possibility
of things. Here the thing is said to be possible if its concept
agrees with the formal conditions of experience, whereas
it was implied in the original formula that the possible thing
itself must agree with the formal conditions of experience.
In this there is no contradiction ; for if the concept of a thing
agrees with the formal conditions of experience, the thing
conceived must agree with the formal conditions of experience.
When Kant attributes this agreement to the concept, he means
that what is conceived (the content of the concept) must agree
with the formal conditions of experience; but his language
indicates that, apart from such agreement, what is conceived
might be, not a thing, but a mere phantom of the mind.
Strictly speaking, the thing is possible, while the concept
of a possible thing is said to have objective reality or (in the
case of a priori concepts) transcendental truth.2 Such is Kant's
1 A 220 = B 267. Compare A 234 = B 286.
2 A 220 .= B 268 and A 221-2 B 269. A concept has objective
reality (or validity), if it refers to a possible object of experience. It
has no objective reality, if it refers to a mere ' Hirngespmst* or phantom
of the mind. When Kant says that it has transcendental truth, he is
thinking only of concepts whose objects are known a priori to be
possible, as is manifest from the context. An empirical concept can
have objective reality, but not transcendental truth : an a priori concept
can have both, and if it has one, it has the other.
346 THE POSTULATES [XLIX § 5
exact terminology, to which he adheres when he is being
careful ; but at times1 he speaks of the possibility of a concept,
implying that the concept of a possible object is itself a possible
concept.
This more careless usage has a real disadvantage, because
for Kant the possibility of a concept is mere logical possibility,
and a concept is logically possible, if it is consistent with
itself (whether its object is a possible object or not).2 Never-
theless the usage is natural enough. It indicates no change
of doctrine or confusion of thought ; and the intelligent reader,
if he were not examining Kant with great care, would probably
fail to notice the difference in terminology, and would make
the necessary adjustments unconsciously.3
§ 5. Possibility in Relation to Different Types of Concept
Kant recognises four types of concept.4 There are empirical
concepts, pure concepts,5 factitious concepts, and mathematical
1 E.g. in A 222 — B 269. In B XXVI n. Kant equates the real (as
opposed to the logical) possibility of a concept with its objective
validity. 2 Compare B XXVI n.
3 It is because of this carelessness of terminology that Professor
Adickes in his edition charges Kant with inconsistencies which can be
explained only by an application of the patchwork theory. The
elaborate structure which he erects on this frail foundation — even
Professor Kemp Smith (Commentary, p. 397) seems to ha\ e some mild
qualms about it — is an admirable illustration of the fantastic lengths to
which the patchwork theory has been carried.
Adickes' services to Kantian studies have been so great that one
wishes to avoid harsh judgements about him of the type which he too
often passed on other people. I think it can be said that he grew
wiser as he grew older, though he certainly never lost the defects of
his qualities. But one is sometimes tempted to say of his edition of the
Kntik (and of his other early works) what he himself says about
Simmers Dissertation on the Monadologia Physica (in Kant als
Naturforscher, p. 165 n.): 'He repeatedly charges Kant with obscurity,
but the alleged obscurities have first of all been introduced by
himself.
4 See A 727 = B 755 ff. and Log. §§ 3-5, and compare Chapter IX §5.
6 Pure concepts in the strictest sense are concepts (or categories) of
the understanding — we may for the present purpose ignore the Ideas
of Reason.
XLIX § 5] POSSIBILITY 347
concepts.1 It is necessary to consider Kant's theory of possibility
in regard to all these types of concept. We must remember
that for Kant to conceive an object is to hold together or
synthetise different elements, and (since to conceive involves
a consciousness, clear or obscure, that we are conceiving) a
concept is always a concept, not only of the object, but also
of the synthesis by which the different elements in the object
are held together.2
I. With the possibility of objects of empirical concepts
Kant is not really concerned.3 Empirical concepts are general-
isations from experience, and we know that their objects are
possible only because we know that they are actual.4 As general-
isations from experience, empirical concepts must inevitably
conform to the formal conditions of the experience from
which they are derived ; but if we know that there are actual
dogs in the world, we know that dogs are possible without
enquiring into the relation between the concept of dog and
the formal conditions of experience; and we cannot know
that dogs are possible, except by knowing that they are actual.6
1 Mathematical concepts are a kind of factitious concept, but their
objects can be constructed a priori in pure intuition, and they are often
regarded as pure concepts, although not as pure concepts of the
understanding (in the strict sense).
2 Compare A 220 = B 267. The synthesis thought in a non -factitious
concept belongs to experience, either as borrowed from experience
(empirical concepts) or as grounded on the form of experience (pure
concepts). The form of experience is said to contain every synthesis
necessary for knowing an object.
3 Nevertheless I take it, when we say that they are possible, we
mean that they are possible in the sense explained by the First
Postulate.
4 A 223 -- B 270. Compare A 220 = B 267. Both of these passages
show that Kant's concern is with the possibility of things known
through a priori concepts.
5 Compare A 451 = B 479, where Kant asserts that if we did not
know by experience that change is actual, we could never know a priori
that it was possible.
It may be objected that we can know a dog to be possible in the
sense of the First Postulate, because it is conceived as a substance and
so on. Kant seems to me to deny this, and to be right in denying it. A
dog, simply so far as it is a substance, must be a possible object, if a
348 THE POSTULATES [XLIX § 5
What Kant is concerned with is the possibility of objects
known independently of experience and therefore through
a priori concepts; and his doctrine is that we cannot know
such objects to be possible merely by an examination of the
concepts. We must always consider whether the concept
agrees with or expresses the formal conditions of experience.1
Under a priori concepts Kant seems here to include not
only the categories (pure concepts in the strictest sense) and
mathematical concepts (pure concepts in a looser sense),
but also factitious concepts. At any rate he considers the
problem of possibility in relation to all three.
II. As regards the categories, he points out that the mere
possession of the concepts of substance, causality, and inter-
action does not by itself prove that there are possible things
to which these concepts apply.2 We know the objective reality
or transcendental truth of such concepts, or in other words
we know that their objects are possible, only because we
know that they express a priori the necessary relations of sense-
perceptions in every experience. We know this independently
of experience (although not of course before experience);
but we do not know it independently of all relation to the
form of experience in general and to the synthetic unity in
which alone objects can be empirically known.3 That is to say,
we know that if there is any experience at all, it must be ex-
perience of such objects; for if we grant that experience is
always experience of objects which are in one time and space,
and which must be conceived by one and the same mind,
then we have proved (or so Kant believes) that the objects
substance is a possible object; but what we are concerned with is the
possibility, not of substances in general, but of that special kind of
substance which is known as a dog. Apait from experience of dogs
(or of their causes or effects), we could never know that a dog was a
possible object.
1 A 223 - B 270-1. I have retained the original formula with the
addition 'or expresses', since Kant regards the categories as being
themselves formal and objective conditions of an experience in general.
The categories may be said to express, as well as to agtee with, such
conditions. 2 A 221 — B 268-9. 3 A 222 — B 269.
XLIX § 5] POSSIBILITY 349
must be permanent substances which possess changing acci-
dents and interact causally with one another. Apart from
relation to the form of experience, that is, to time and space
and the unity of apperception, we could have no such know-
ledge. The- same principle of course holds for the categories
of quantity and quality.1
III. As regards factitious concepts, there would seem to
be two main types — if we exclude mathematical concepts —
although Kant does not himself say so. All factitious concepts
are in a sense independent of experience ; for the combination
of the elements thought in them is an arbitrary product of
the mind and is not found in experience itself. But in some
factitious concepts the elements combined are primarily
empirical, as when we talk of a ship's clock (Kant's own rather
surprising example2) or of chimaeras and centaurs. Kant seems
here to have in view mainly the factitious concepts which we make
by combining elements that are primarily a pi iori, and which
therefore have some show of being a priori concepts themselves .3
Once \ve have pure concepts such as substance, force,4
and interaction, \\e can use the stuff given to us in sense-
perception for the purpose of making new concepts; but the
objects so conceived are mere phantoms of the brain,5 unless
the combination of their elements is found in actual experience.6
The examples given are the concept of a substance which is
permanent in space without filling space,7 the concept of a
1 Note also that we cannot know the objects thought in the categories
to be possible apart from intuition, or even apart from outer intuition ;
see B 288 and B 291. a A 729 = B 757.
3 I do not mean to assert that this distinction could be philo-
sophically maintained, but only that it seems to be at the back of
Kant's mind. The same tendency is present in A 96. The examples
there given were 'spirit' and 'God*.
4 This is connected with causality (as a 'predicable'). See
A 82 = B 1 08. 5 'Hirngespinste.'
6 A 222 = B 269. Compare also A 729 = B 757 : 'For if the concept
depends on empirical conditions (for example, a ship's clock), the
object and its possibility is not yet given through this arbitrary concept.1
7 This was apparently something invented as intermediate between
matter and mind.
350 THE POSTULATES [XLIX § 5
power1 of foreseeing the future (and not merely predicting
it by means of inference), and the concept of spiritual inter-
action (or some form of telepathy). Such concepts, in spite
of the a priori character of their elements, cannot be shown,
like the categories, to have possible objects on the ground
that they express necessary conditions of experience. The
possibility of objects of this kind must either be shown by
the actual existence of these objects in experience or it cannot
be shown at all. Kant believes that in these particular cases
it cannot be shown at all, and the concepts are mere arbitrary
combinations of thought with no claim to objective reality.2
We may sum up Kant's position with regard to factitious
concepts by saying that (whatever be the character of the
elements which are arbitrarily combined in them) they are to
be treated as empirical concepts, and the possibility of their
objects can be proved only by showing that such objects are
experienced (directly or indirectly). Possibility in such cases
is known only as an inference from actuality.
IV. The remaining case is the case of mathematical con-
cepts, which are sometimes taken to be a special class of facti-
tious concepts. They are arbitrary constructions of the mind
and are independent of experience, but they have the special
1 Kant calls it a 'ground-force* (Grundkraft), which is more than a
mere 'power* though less than an 'action*.
2 Kant adds, somewhat obscurely : 'As regards reality, it is obviously
out of the question to think this in concrete without calling experience
to our aid : for reality is connected only with sensation, the matter of
experience, and does not concern the form of relations . . .'
(A 223 = B 270). He may mean that the factitious concepts with which
he has dealt are concerned with the form of relation — substances,
powers, interactions. Factitious concepts which are more concrete in
that they are concerned with reality or sensation — such as concepts
of centaurs and chimaeras — need not be discussed; for it is obvious
in their case that the mere possession of the concept does not show
the thing to be possible in abstraction from actual experience. Or he
may, and I think he does, mean that even in the case of the concepts
discussed, since their possibility must be shown a posteriori, an appeal
to reality is involved, and this must involve sensation and not a mere
play of invented concepts.
XLIX § 5] POSSIBILITY 351
characteristic that they can — in Kant's terminology — be
constructed a priori, or in other words the intuition corre-
sponding to them can be 'exhibited* a priori}- For this reason
they are also described as a kind of pure concept.
There is some plausibility in the view that by simple in-
spection of a mathematical concept we can tell that its object
is possible.2 Even here, however, we must distinguish between
the logical possibility of the concept, which (since it depends
only on the absence of self-contradiction) can be known from
the concept itself, and the real possibility of the object, which
cannot be so known. Thus the concept of a figure enclosed
by two straight lines is logically possible ; for there is no logical
contradiction between the concept of a figure and the concept
of two straight lines and their combination.3 But there is no
corresponding object possible, for such a figure cannot be
constructed in space.4
Even if we take a concept like that of triangle, we do not
know that its object is possible merely from the fact that it
can be constructed a priori in space. Such a construction
gives us, not an object in the strict sense (for that must always
have an empirical matter), but merely the form of an object.6
Such a pseudo-object might be a mere product of the imagina-
tion, and we must have other grounds for saying a priori
that objects such as triangles are possible objects of experience.
Our real ground for asserting a priori the possibility of triangles
is that space is a formal a priori condition of outer experience,
and that the same figurative6 synthesis whereby we construct
a triangle a priori in imagination is therefore identical with the
1 A 713 = B 741. Compare A 719 = B 747 and also Log. Eml. Ill
and § 1 02 (IX 23 and 141). We can also say that their object can be
* exhibited', or 'constructed' a priori in intuition.
2 A 223 = B 271. 3 A 220 = B 268.
4 On the supposition that space is Euclidean.
5 A 22 3 = - 6271. The same doctrine is expressed in B 147; compare
A 156 - B 195.
6 lbildende.y This is the synthesis speciosa (or figurative synthesis)
opposed to the synthesis intellectual!* of the concept or judgement
in B 151.
352 THE POSTULATES [XLIX § 5
synthesis exercised in the apprehension of appearances for
the purpose of making, not a mathematical, but an empirical,
concept of triangle.1
The same principle holds for the possibility of continuous
quantities and indeed for quantities in general. The concepts
of such quantities are known to have objective reality, not from
the character of the concepts in themselves, but because
they express the formal conditions of experience as found
in time and space.
Kant is surely right in saying that if we take Euclidean
space to be a necessary condition of human experience, we
know a priori that triangles, squares, circles, and hyperboloids
are possible objects of experience. This knowledge is inde-
pendent of our having actually seen or touched figures of this
kind. It rests only on our knowledge of space and our know-
ledge that space is a condition of experience.2
If there is any doubt on this matter, it must be based on
the view that to know the possibility even of a mathematical
figure, we must know, not only that it is compatible with
the nature of space, but also that it is in accordance with
the causal laws of experience. These laws might be such
that nature never could produce hyperboloids (or approxi-
mations to them); and we know that it can do so only if we
have actually experienced hyperboloids, or if wre have experi-
enced objects which we know to be connected with hyperboloids
1 This is simply a statement of Kant's central doctrine that every
empirical synthesis of apprehension (which combines the matter of
intuition) is also an a priori synthesis of imagination (which combines
the form of intuition). I think it would be more exact to say that the
a priori synthesis is present in the empirical synthesis than to say that
it is identical with it.
2 If Euclidean space is not a necessary condition of experience, Kant's
doitimc must be modified; but even so, if space-time is a necessary
condition of experience, we can still say a priori that some concepts
refer to possible objects of experience and others do not.
It may be objected that in this sense we can equally know a piiori
that chimaeras are possible objects. This is, however, true only if we
take 'chimaera' to mean a body of a certain shape. It is not true, if we
take 'chimaera' to mean a living organism.
XLIX § 5] POSSIBILITY 353
either as effects or as causes. In such a case we should know
hyperboloids to be not only possible, but also actual and
even (in the last case) necessary.
There is, I think, something to be said for this view, and
it has the advantage of making the possible no wider than the
actual and necessary. Perhaps Kant would hold that if we
know a hypcrboloid to be compatible with the nature of space,
we know that we could ourselves construct an actual hyper-
boloid, and therefore know that it is a possible object of experi-
ence.1 The whole criticism, however, suggests that we should
concern ourselves with the possibility, not of pure mathematical
figures (which are only pseudo-objects), but of the imperfect
approximations to them in nature ; and in that case the concepts
in question are empirical.2
Kant's doctrine is relatively simple and, I think, sound. He
is not offering us an elaborate analysis of the meaning of real
possibility, but only asking how far we can have a priori know-
ledge of the possibility of objects. He declares it futile to
imagine that because we can invent concepts which are not
self-contradictory, therefore objects corresponding to these con-
cepts must be possible. We can say that a concept must have
possible objects only if the concept expresses the necessary
conditions of experience, either as a category or as a mathe-
matical concept ; in the case of all other concepts we can know
their objects to be possible only if we know them to be actual.
Since the categories have sense and significance only by refer-
ence to space and time, and since all mathematical concepts
depend on pure intuitions of space and time, our a priori
knowledge of the possibility of objects depends on the fact
that space and time are conditions of experience, and the
Leibnizian discussions in regard to possible worlds other than
the world we know are nothing but a waste of breath.
Time and space are separable from empirical intuition
only by an act of abstraction or elimination; and in a general
remark added in the second edition3 Kant insists, not only
1 The difficulty is that in that case the possible seems to be wider than
the actual. 2 Compare A 239-40 = B 299. 3 B 288 ff.
VOL. II M
354 THE POSTULATES [XLIX § 6
that we cannot comprehend the possibility of a thing by means
of the mere category (apart from the reference to conditions
of experience), but also that we require to have at hand an
intuition, and indeed an outer intuition. I take this intuition
to be empirical.1 The reference to outer intuition is important
for the Refutation of Idealism.
§ 6. The Possibility of Experience
I confess I should have liked Kant to explain also in this
connexion how the phrase 'possible experience ' is related to
the present account of possibility. Can we say that experience
(like an object) is possible because it agrees with the formal
conditions of experience ? Is the possibility ascribed to experi-
ence of the same nature as the possibility ascribed to objects ?
It may be thought that the possibility of experience must
be something different from the possibility ascribed to objects
within experience. The subject is a difficult one, but I suggest
that the close connexion between experience and its object
makes it almost impossible to uphold this view of Kant's
doctrine. We can know an experience to be possible only if
it conforms to the formal conditions of experience which our
argument professes to have established.
The difficulty of this is that it appears to involve us in a
vicious circle. Are we to maintain that the categories must
apply to objects because they express the conditions of a
possible experience, and then to maintain that experience is
possible because it (or its concept) is in conformity with the
categories ?
The argument would be a vicious circle, if Kant had merely
asserted that as a matter of fact the categories are assumed
in experience, and are therefore conditions of experience,
and therefore experience is possible only through conformity
to them. But this, as I have pointed out already,2 is not his
1 Compare A 156 = B 195, where the idea of space and time is said
to be a mere schema which would have no meaning, unless the repro-
ductive imagination called up objects of experience.
8 Compare Chapter XXX § 5, and also Chapters XXXVI § 4 and
XLV§7-
XLIX § 6] POSSIBILITY 355
argument at all. What Kant has maintained is that if we analyse
experience into its elements, we can understand that it must
involve both intuition and thought. We can understand that
space and time are the necessary forms (or conditions) of
intuition, not only because we can have no intuition apart
from them, but also because we have a priori knowledge
of their own nature when we eliminate the element of empirical
intuition. We can also understand that the thought involved
in experience must have unity (the unity of apperception),
and that this unity must manifest itself in certain necessary
forms (the forms of thought). Starting from these ultimate
principles, he claims to have proved that the categories express
the necessary conditions of experience and must apply to any
and every object of experience.1
What Kant claims in the last resort is that experience is
possible only if it is experience by one thinking mind of objects
given to intuition in one time and space: all the rest of his
doctrine is supposed to be derived from this. Such a view of
experience, however supported by insight into the necessary
character of space and time and discursive thinking, is taken
to be an ultimate fact beyond which it is impossible for us
to go.2 To talk of other kinds of possible experience is empty
and meaningless speculation. Other forms of intuition and
thought cannot be conceived by us; and even if they could
be conceived, they would not belong to our experience as the
only kind of knowledge in which objects are given to us.3
We have to do only with the synthesis by human thought and
imagination of the matter given to us under the forms of space
and time. The a priori knowledge which we possess has no
claim, on Kant's view, to be knowledge of ultimate reality: it
is all relative to the human experience we actually enjoy. By
analysis of that experience we can discover certain conditions
which have a kind of intelligible necessity in themselves and
1 The pure categories are derived from the forms of thought, and
their schemata are derived from the necessity of synthetismg the given
manifold in one space and time.
2 B 145-6. 3 A 230 = B 283. Compare B 139.
356 THE POSTULATES [XLIX § 6
in relation to experience in general. For this reason we regard
them as conditions of experience, and we claim that we know
experience to be possible if it conforms to these conditions.
An experience which does not conform to these conditions
we cannot conceive at all, and still less can we know it to be
possible. From these ultimate conditions the categories are
supposed to be derived; and it is not a vicious argument to
assert that therefore the categories are objectively valid as
expressing necessary conditions of a possible experience,
and experience itself is possible only if it is in conformity
with them.
CHAPTER L
ACTUALITY AND NECESSITY
§ i. The Second Postulate
The Second Postulate affirms that what is connected with
the material conditions of experience (namely sensation) is
actual. This means that for knowledge of the actuality1 of
things, we must have sense-perception, here explained to
be sensation of which one is conscious.2 To say this is not
to say that we rmist have, or even that we must have had,
an immediate sense-perception of the thing which we affirm
to be actual. We can say that a thing is actual, if it is connected
with any actual sense-perception in accordance with the
Analogies. The back of the house which we do not see is as
actual as the front of the house which we do see, and so are
the unseen atoms of which it is composed. The example Kant
himself gives3 is a magnetic matter penetrating all bodies;
and if modern science is right in asserting that protons and
electrons arc necessary to explain the phenomena perceived in
the laboratory, then we may say that on Kant's principles such
protons and electrons exist. They exist just as much as the houses
and trees which we see, and they could be perceived if our
senses were finer. The crudity of our senses is not to be taken
as determining the form of a possible experience in general.4
1 lWirkluhkeit.' 'Existence', it will be remembered, is the term
used for the being in lime of substances and their accidents, while
'reality' is the term used for the qualitative matter given in sensation.
I do not think there is any essential difference between existence and
actuality — Kant uses the two terms as equivalent even in the present
passage — but reality, although necessary to existence, is not identical
with it. There are degrees of reality, but there are no degrees of
existence ; for a thing either exists or does not exist.
2 A 225 = B 272. Compare A 120, B 147, and B 160; also A 116,
6207, and A 374. Sensation must be 'taken up* into consciousness,
or be 'apprehended', in order to be sense-perception.
3 See A 226 — B 273, and compare A 492-3 = B 521.
4 This accords with Kant's description of the possible, in which
no reference is made to the limitations of our organs of sense.
358 THE POSTULATES [L § i
Kant does not restrict existence to the present, and he
believes that the cause exists jus't as much as the effect. Hence
from the present existence of fossils we are entitled to affirm
the past existence of animals now extinct. Whether Kant
believes we can know existence in the future is perhaps more
doubtful. He says that we can know things before perceiving
them, and therefore we can know them comparatively a priori*
This may be compared with another statement2 that if we
undermine our house, we can know a priori, although not
entirely a priori, that it will fall in. In the present passage,
however, he may be speaking only about things at present
existing which we have not yet perceived.
It must not be forgotten that this doctrine applies only
to the world of appearances, and not to things-in-themselves,
with reference to which 'existence' in time has no meaning.
By sense-perception and thought we have before us a world of
appearances spread out in infinite time and space and connected
by the law of interaction. But this world is still only a world
of appearances (actual and possible), as Kant is careful to
remind us. With the clue of the Analogies we can pass from
our actual sense-perception to the thing in the series of possible
sense-perceptions ,3
Kant's central contention is that unless we have a starting-
point in sense-perception, we can say nothing about the existence
of things. The concept of a thing contains absolutely no mark
of its existence.4 However complete the concept may be,
however fully we may be able to think a thing with all its
inner determinations, we can never justifiably pass from the
concept to an affirmation of the existence of the thing con-
ceived. We have seen that in some cases we can, by considering
the conditions of experience, pass from the concept to the
affirmation that the thing conceived is possible5; but nothing
1 A 225 = 6273. 2 B 2.
3 A 226 = B 273. Compare also A 493 = B 521.
4 A 225 = B 272.
5 Even this we cannot do without intuition, and even outer intuition ;
see B 288 and B 291.
L § i] ACTUALITY AND NECESSITY 359
except sense-perception can entitle us to affirm its actual
existence.
This doctrine is a preparation for Kant's attack on the
Ontological Proof of God's existence.1 Without prejudging
this question, or considering the ultimate issues which it
raises, we may say that at least as regards the existence of
finite things Kant's position is fundamentally sound.
Kant is not asserting that existence belongs only to the
matter in complete separation from the form of experience;
and the suggestion that he is making such an assertion seems
to me, in view of the references to the doctrine of the Analogies,2
to be untenable. When Kant says that sense-perception is
the only mark of actuality, we have no right to separate this
statement from its context, and to suppose that for Kant
sense-perception by itself, apart from thought, can give us
knowledge of existence.3 The most we can say is that this is a
rather loose way of asserting that all our categories and all
our concepts will never give us the mark of actuality which
sense-perception alone can supply.4 Kant's doctrine is not
so easy that we need add unnecessarily to its difficulties.
1 A 592 = B 620 ff. 2 Compare p. 335 n. 6.
3 Compare also A 234 -= B 286, where the object is said to be actual,
if it is connected with perception (sensation as matter of the senses),
and is thereby determined by means of the understanding. Kant's account
of the difference between dreams and waking experience also bears
out the view that actuality or existence is known through a combina-
tion of sense-perception and thought: indeed to deny this is to give
up the whole Critical doctrine. Compare B 233-4, A 201-2 = B 246-7,
A 376, A 451 = B 479, A 492 = B 520-1, A 493 = B 521, and ProL
§ iiAnmerk. Ill (IV 290).
4 Kemp Smith (Commentary, p. 398) also attributes to Kant the
corresponding doctrine that there are 'mere concepts' which have no
reference to the contingently given. This is based on Kant's statement
that 'in the mere concept of a thing no mark of its existence can be
found* (A 225 = B 272). Kant's statement is obviously true, if we can
in any way (and surely we can) consider, or entertain, a concept with-
out having knowledge that a corresponding object exists ; and I cannot
see any ground for taking it to involve a theory of the concept
incompatible with the Critical, or indeed with any other, philosophical
view. Still less can I see in it any reason for the assertion that Kant's
thinking is 'perverted* by the influence of Leibmzian rationalism.
360 THE POSTULATES [L § i
It should be sufficiently clear from what has been said,
and indeed from the doctrine of Kant throughout the Kritik,
that while the essential mark of the actual is a connexion
with sense-perception, the connexion (which is a necessary
connexion in accordance with the Analogies) is a's essential
to knowledge of the actual as is sense-perception itself.1 Indeed
Kant's very formula shows this ; for he does not say that the
actual is either what is given in sensation or what is connected
with sensation. He says on the contrary that the actual is what
is connected2 with sensation. The merely given in sensation
is of all things the most subjective, unless it is connected with
a substance as one of its accidents ; and what exists — in the
technical sense — is not a mere sensation, but the substance
of accidents connected with the sensation. The accidents
are the ways in which the substance exists; and to recognise
them as accidents of an existing substance is to recognise,
however 'obscurely', that they are parts of a system which is
causally determined throughout.
It follows that the actual is also the necessary. This does
not excuse us from the obligation of distinguishing actuality
from necessity, although the two are so closely bound up
together that we can distinguish them only by abstraction.
Furthermore we must remember that it is one thing to recog-
nise that every object must be possible, actual, and necessary,
and quite another thing to recognise the possibility, actuality,
and necessity of any particular object. The general doctrine
of the categories does not free us from the duty of looking
for empirical evidence when we seek to apply the categories,
and even the categories of modality, to particular objects.
1 It may be objected that our knowledge of the actual is pnmanly
by means of perception, and that when we know the actual in virtue
of connexion, our knowledge is indirect. This is in a sense true, but
even in direct perception we must connect what is given with a
substance, if we are to be aware of an object , and we must (however
'obscurely') regard the given accidents as having a place in an ordered
world, and therefore as determined by causation and interaction
(although we need not know the actual cause empirically).
2 This connexion, as I pointed out above, is connexion by means
of the Analogies. Compare also A 374 and A 376.
L § i] ACTUALITY AND NECESSITY 361
Thus, although we know a priori that if an object exists, it
must be necessary (in the sense of being causally determined),
we do not understand the necessity of this particular object
till we have discovered empirically the chain of causes by which
this particular object is determined.
One more point must be added for the sake of completeness.
Kant does not here distinguish logical from real actuality,1
as he distinguishes logical possibility and necessity from real
possibility and necessity. Logical actuality is a characteristic
of asscrtoric judgements, and is identified by Kant with (logical)
truth:2 truth in this sense seems to involve (i) assertion (or
reference to an object) and (2) agreement with the formal
laws of understanding;3 hence it might be described as a
claim to truth rather than truth itself. For real actuality we
require something more: we require that the object asserted
should be connected with sense-perception in accordance
with the Analogies. Although for Kant such real actuality
or existence in time is impossible apart from human minds
and human judgements, it is not made by mere thinking,
and depends on sense as well as thought. This is the doctrine
against which Caird, from his Hegelian standpoint, consistently
protests;4 but I think that modern philosophy as a whole
1 Or formal from material actuality.
2 See A 75-6 — B 101 ; compare Log. § 30 (IX 108) and EinL II
(IX 1 6 and 20). I take it this truth is logical truth, or the general
form of truth, with which alone Formal Logic is concerned (see
A 59 — B 84 and compare A 151-2 — B 191 and A 191 — B 236):
what we may call material truth involves correspondence with a
particular object; but Formal Logic ignores the differences between
objects, and cannot tell us whether a proposition is true in the sense
of corresponding with its object.
3 This second point I take from A 59 = B 84, which seems to give
a clearer statement of what is said obscurely in A 76 --= B 101. Kant's
illustration is taken from a hypothetical syllogism in which the
antecedent (which is only problematic in the major premise) is
assertoric in the minor. When it is assertoric, it is said to indicate
that the proposition is bound up with the understanding in accordance
with its laws. I confess that the precise meaning of this statement is
not to me wholly clear : it is not repeated in the lectures on Logic.
4 For example, see The Critical Philosophy of Kant, Vol. I, p. 596 (if
I have understood it aright).
VOL. II M*
362 THE POSTULATES [L §2
is on this subject more inclined to agree with Kant than with
Hegel.1
§ 2. The Third Postulate
The Third Postulate2 asserts that the necessary is that whose
connexion with the actual is determined in accordance with
the universal conditions of experience. These conditions are
the Analogies. Actual things, that is, the bodies which con-
stitute the physical world, are themselves actual only so far
as they are connected through the Analogies with their appear-
ances revealed to us in sense-perception, so that it is not
to be thought that the actual can be known to us apart from
the Analogies. Nevertheless we now take the actual for granted,
and consider what is implied by our knowledge of necessity.
We are concerned, not with the logical or formal necessity
to be found in the connexion of concepts and judgements in
accordance with the laws of thought,3 but with the real or
material necessity for the existence of objects in accordance
with the Analogies.
We have seen that the actual existence of objects can never
be known a priori by mere concepts apart from sense-perception,
any more than it can be known by mere sense-perceptions
apart from concepts, and in particular apart from the Analogies.
The same is true of the necessary existence of objects. We
cannot know such necessary existence merely from concepts.
The knowledge that objects necessarily exist is dependent
on their connexion with the actually perceived, a connexion
which must be in accordance with the universal laws of ex-
perience.
The only kind of existence which we can know to be necessary
in accordance with these laws is the existence of the effects
of causes which are given to us and taken as actual. It may
seem odd of Kant to assert only that given the cause we know
the effect to be necessary, and not also that given the effect
we know the cause to be necessary. I think Kant's reason
1 Meyerson, for example, seems to accept the Kantian antithesis.
2 A 226 == B 279 ff. 3 Compare A 76 = B 101.
L § 2] ACTUALITY AND NECESSITY 363
is that the cause makes the effect necessary, but not vice versa}-
Although the cause is no doubt necessary (for everything
actual is necessary), it is not necessary qud cause, but only qua
effect of something else.2
Since substances, as permanent, cannot be the effect of
anything, we can have no insight into the necessity for the
existence of substances.3 We can know only that their states
must exist; and this we can know, in accordance with the
empirical causal laws discovered by science, only from a
knowledge of preceding states (given to us in sense-perception)
which are the causes of their existence.
The criterion of necessity is therefore the causal law expressed
in the Second Analogy,4 and this is a law of experience and
of experience alone. It applies only to the phenomenal world,
and in the phenomenal world it applies only to the states
of substance and not to the substances themselves. Real necessity
is therefore not absolute, but hypothetical, necessity.5 That is
to say, we cannot by mere concepts, not even by the concept
of 'God', know a priori that the object must exist; but by the
1 We know that if the effect is actual, the cause is actual, but this
does not enable us to understand the ground of the existence of the
cause. The effect in relation to the cause is only a causa cognoscendi,
while the cause in relation to the effect is a causa essendi or a causa
fiendi.
2 Compare the repeated assertion (found, for example, in
A 194 — B 239) that the event (or effect), as the conditioned, gives a
sure indication of some condition, but the condition determines the
event. All this seems to me to imply that for Kant causation is more
than uniform succession; for if it were mere uniform succession, the
cause would be as necessary in relation to the effect as the effect in
relation to the cause.
3 We know a priori that substances must be possible (A 220-1
= B 268-9); for if there is to be experience of objects in one time
and space, it must be an experience of the states of permanent sub-
stances. We may also be said to know a priori that all substances must
be permanent. To say this is not to say that we know the grounds or
causes why particular substances exist, and so why these particular
substances are necessary: our knowledge of necessity is confined to
their accidents.
4 Kant might equally, or perhaps even better, have said the Third
Analogy. 5 A 228 = B 280. Compare Metaphysik, p. 27.
364 THE POSTULATES [L § 3
aid of experience we can say that, granted the cause is actual,
the effect must exist. We can therefore affirm the necessary
existence of objects by thought and without actual experience
of these objects, but we can do so only if we have experience
of their cause.
In this respect also Kant's doctrine would appear to be
sound. I do not think he should be taken to mean that only
when we are actually experiencing the cause can we say that
the existence of the effect is necessary. On such a principle
necessary existence would be confined to the future. I take
the principle to be more general, and to mean that wherever
we know a cause to be actual, whether that cause is present
or past, there we can say that its effect is necessary. We can
do so of course, not in virtue of our a priori knowledge of the
general causal principle, but in virtue of the empirical causal
laws discovered by science in accordance with that principle.
Apart from such empirical laws, while we could know that the
cause must have some effect, we could not know what its
effect was.
§3. Some Traditional Conceptions
In his usual manner Kant adds some general observations
after his main task is accomplished.
The first is only of historical interest. Of the four traditional
principles (in mnndo non datur hiatus, non datur saltus, non
datur casus, non datur fatum)* Kant asserts the third to be a
consequence of the Second Analogy, since the affirmation
of the universal principle of causality is a denial of blind
chance. The fourth, he declares, belongs to the Principles
of Modality, since the doctrine of the Third Postulate — that
the necessary is the conditionally or hypothetically necessary —
is a denial of blind fate or unconditioned necessity. He hints
further that the denial of discontinuity (saltus) is connected
1 A 229 — B 282. 'Casus* is, I think, equivalent to 'Cluck' and
'faturn* to ' SchicksaV ', which are said to be 'usurpterte Begiiffe'(pscudo-
concepts) in A 84 -= B 117. In A 74 — B 99 the word for 'casus* is
fZufall\
L § 3] ACTUALITY AND NECESSITY 365
with the assertion of continuity in the Anticipations (although
the proof of this was given in the Second Analogy1) ; and that
the denial of the void (hiatus or vacuum) is connected with the
account of quantity in the Axioms (although he himself dis-
cussed it in the Anticipations and in the Third Analogy2). I
think he derives some pleasure from the affirmation that the
question of empty space is a matter for 'ideal reason', which
goes beyond the sphere of possible experience. He is always
anxious to insist that the materialists who believe in atoms
and the void are speaking, not as scientists, but as unconscious
metaphysicians.3
We can afford to smile at Kant's preoccupation with phrases
which have no longer a living part in our tradition, at his
desire to fit these phrases into the framework of the categories,
and at the ingenuity and plausibility which, to my mind at
least, he displays in doing so. But the suggestion that his
attempt is a grotesque example of pedantry seems to me much
more grotesque than the attempt itself. We must look at
Kant's work in the setting of a formahstic age, where he stands
as a giant shaking off the chains which weighed men down.
It is natural that he should adjust his doctrine to traditional
conceptions ; and it is obvious that if his discovery of the com-
plete list of categories were sound, then all true traditional
doctrines must fit into that list of categories and ought to be
shown to do so. We can see to-day that he was mistaken;
but we ought to see also that he was not unreasonable, and
that what is regarded as mere pedantry is a proper attempt to
work out his conclusions to their logical end.
1 A 207 — 0253 ff.
2 A 172 ---- B 214 ff. and A 214 = B 261. There is a certain plausi-
bility in saying that discontinuity is primarily discontinuity in the
qualitative matter of intuition (as treated in the Anticipations) ; and
that the void is a question of the nature of space, which is the quanti-
tative form of intuition dealt with in the Axioms.
3 Compare A 173 — B 215.
366 THE POSTULATES [L § 4
§ 4. Leibniz fan Possibility
When we turn to his remarks on Leibniz's doctrine of possi-
bility, we are faced with matters of more importance.1 The
question is asked whether the field of the possible is wider
than that of the actual, and the field of the actual wider than
that of the necessary.2
Kant regards these as questions not for understanding
but for reason, not for the Analytic but for the Dialectic.
He takes them to be asking whether phenomena can fit only
one system of experience3 or whether they might fit into several
different systems of experience. To such a question under-
standing can give no ans\\er, since it is concerned only with
the rules which govern the one experience that we have and
the one world that we know. It has to do only with the synthesis
of what is given, not with the other possible worlds of which
this is alleged to be the best. We cannot conceive other forms
of intuition or of thought; and if we could, such forms of
intuition and thought would have no place in the human experi-
ence in which alone understanding plays its part.
Nevertheless Kant finds it impossible to refrain at this
stage from some remarks about the Leibnizian doctrine. He
points out that in any case the poverty of the conclusions
reached, on the basis of a supposed wide realm of possibility
extending beyond the world we know, is obvious enough in
1 A 230 = 6282.
2 Here again the charge is brought against Kant that he suddenly
uses the word 'possible' in a difTeient sense. But this question was
perfectly familiar to the audience for which he was writing, and he has
to discuss it in order to bring out the fact that it presupposes a false
meaning of ' possibility'. I do not think his method of exposition here
would offer any difficulty to contemporary readers. It certainly indicates
no confusion on the part of Kant.
3 It is very clear from what he says here and a little later that he
regards the phenomenal world as one experience, not in the sense
that it is all present to one all-embracing mind, but in the sense that
it forms one system of actual and possible sense-perceptions of which
my actual sense-perceptions are a necessary part. He calls it a 'series*
of appearances and identifies it with a single all-comprehensive
experience in A 231-2 — B 284. Compare A no.
L §4] ACTUALITY AND NECESSITY 367
itself. He suggests that because we can say 'All the actual is
possible* and can convert this proposition into 'Some possible
is actual', we therefore imagine that there must be many things
possible which are not actual. Finally he turns to a more serious
argument." It may seem that the possible must be wider than
the actual, because something must be added to the possible
if it is to become actual.
This, however, is precisely what Kant denies.1 Actuality
is not another quality added to things which are already
possible. If anything were to be added to the possible, it
would itself be impossible. What is added is not an additional
quality in the object, but a relation to the knowing mind. A
thing is possible, on Kant's doctrine, if it agrees with the
possible conditions of experience. What can be added for
my understanding2 is connexion with some sense-perception ;3
but if any possible object has such a connexion, it is not only
possible, but actual (whether I perceive it immediately or not).
On the basis of what is given to sense-perception I can,
by means of understanding and with the aid of the Analogies,
arrive at wider knowledge of the actual objects in the one
phenomenal world or all-embracing system of human experi-
ence. On this basis of the given I have, however, no means of
deciding whether my sense-perceptions could fit into a quite
different phenomenal world and a quite different system of
experience ; and if I am to work without this basis of the given
I have still less means of deciding such a question, for apart
from given matter thinking is quite impossible.4
What is possible under conditions which are themselves
1 A 231 = 1*284.
2 Kant says this is added 'zu meinem Verstande*. Does this mean
'to my understanding' or 'for my understanding' ?
3 Kemp Smith (Commentary, p. 402) asserts that Kant is here giving
'the correct Critical definition of the possible by combining the two
first postulates'. It would be odd indeed if this were so, but (as Kant
himself points out) when the addition is made we are defining, not
the possible, but the actual. What the passage does show — if it needed
any showing — is that for Kant the actual is not the matter apart from
the form of experience. 4 Compare A 96.
368 THE POSTULATES [L § 5
only possible1 — and this is the only sense of the possible which
Kant recognises — is not possible absolutely or in all respects.
We can ask and answer the question 'What is possible under
conditions of possible experience ?' If we ask whether the possi-
bility of things extends beyond experience, we are asking a
question about absolute possibility, which we have no possible
means of answering. This question has been raised here only
because of the common belief that the concept of absolute
possibility is one of the concepts of the understanding.2 The
problem must at present be left in obscurity, since its discussion
really belongs to the Dialectic.
§5. The Meaning of the Word 'Postulate'
Kant in conclusion explains why he uses the word 'postulate'
for the Principles of Modality.
He does not use the word 'postulate', as was apparently
done at the time, for propositions which are immediately
certain or self-evident. He believes that such propositions,
although they cannot be 'deduced' in the ordinary sense of
'inferred' — the Principles, as we have seen, are a matter for
the power of judgement, and not for reason — can be 'deduced'
in the Kantian sense, that is, 'justified' by showing their
relation to possible experience. Merely to accept self-evidence
at its face value is fundamentally opposed to the whole spirit
of Criticism; Kant regards it as legitimate in science, but not
in philosophy. Once we admit self-evidence as ultimate, we are
faced with a whole host of audacious pretensions claiming
such self-evidence; and nothing is more usual than for the
deliverances of common sense or tradition (in themselves no
guarantee of truth) to be mistaken for axioms, that is, for
propositions which have a genuine measure of self-evidence.
1 I think that by 'conditions which are themselves only possible
Kant may mean 'conditions of possible experience' ; only if conditions
are conditions of possible experience can we show them to be really
possible (or objectively valid); but the phrase is obscure. In A 374
space (the condition or form of outer intuition) is said to be the idea
of a mere possibility of togetherness (Beisammensetns).
2 A 232 -= B 284-5.
L § 5] ACTUALITY AND NECESSITY 369
All synthetic a priori propositions demand, if not a proof, at
least a deduction or justification. In Kant's language we must
answer the question how they are possible, before we can admit
their claims to philosophical acceptance.1
What Kint has called the Postulates are, however, in a special
position. Although, like the other Principles, they are synthetic,
they add, as we have seen, nothing to the necessary character-
istics of the object. What they add to the concept of the thing
is not a necessary quality of the thing itself, but a necessary
relation to the mind which knows it; or, in other words, they
refer to the action of the mind by which the concept is produced.2
It is because of this reference to the mind's action that Kant
chooses the word 'postulate' for the Principles of Modality.
In mathematics a postulate is a practical pro position. It concerns
only the synthesis by which we construct an object and produce
the concept of an object. It tells us, for example, with a given
line to describe a circle from a given point. Such a proposition
cannot be proved, because the procedure which it enjoins is
the very act through which we first of all produce the concept
of a circle.3
In the same way the Postulates of Modality are concerned
with the synthesis (or aspects of synthesis) through which
alone the concepts of possibility, actuality, and necessity
can arise; and they add nothing to the concept of the thing
other than its relation to the mind which knows it.
We need not, I think, quarrel with Kant either about his
terminology or about his reasons for it. It is true that his
Postulates, like the mathematical postulates (if his account
of the latter is correct), are concerned with the activities of
1 Compare A 148-9 = B 188.
2 A 234 = B 287. This action is the synthesis of the mind which
imposes form or unity on the given matter and is necessary for know-
ledge of the object. It produces the concept in the sense that the concept
is the principle at work in the synthesis, and to be conscious of the
principle of the synthesis is to know the concept. Compare
A 220 = B 267.
3 The concept is produced through the act in the sense explained
by the previous note.
370 THE POSTULATES [L § 6
the mind through which an object is constructed and a concept
produced. This resemblance is not destroyed by the presence
of differences in the two cases, differences which are obvious
enough, since the mathematical postulate determines the
character of the object through and through, whereas Kant's
Postulates determine the inner character of the object not at
all. Yet even this difference is by no means so profound as
it appears ; for the synthesis of form and matter, in whose
different subjective aspects Kant finds the origin of possibility,
actuality, and necessity, is also, when viewed from another
angle, the synthesis which imposes the categories of quantity,
quality, and relation upon the matter given to sense, and so
determines through and through the character of 'an object
in general'. The term 'postulate' in Kant's sense may be said
— as he himself said both of the term 'anticipation'1 and of the
term 'analogy'2 — to apply in some degree to all Principles of
the Understanding, but to apply in a preeminent degree to
one particular group of Principles, in this case to the Principles
of Modality.
§ 6. The Competence of Kant's Exposition
Kant's exposition of the Postulates is, as I have already
suggested, comparatively simple and straightforward. I do not
say that it is elegantly written, or that it is well arranged, or
that it is a model of exact and careful expression — such merits
are not to be found in the later works of Kant. Again I admit
that difficulties can be found in the doctrine and that these
difficulties are real — it has not been my good fortune to discover
any philosophical writing of which the same could not be said.
But I do say that Kant's exposition can be understood by any
intelligent reader of good will who has mastered the arguments
for the preceding Principles and is prepared to assume —
provisionally — that these Principles have been proved.
When I turn to the Commentary of Professor Kemp Smith,
1 A 166-7 — B 208-9. Compare A 210 = B 256.
2 A 180-1 = B 223-4.
L § 6] ACTUALITY AND NECESSITY 371
I find here, as elsewhere, that on almost every page he applies
to Kant's exposition words like 'ambiguous', 'one-sided',
'misleading', 'obscure', 'confused', perverted', and 'perverse';
that on his view the 'so-called' principles are not really prin-
ciples at all — in spite of the admitted fact that they state
characteristics which necessarily belong to every object of
experience in its relation to the mind; and even that the 'com-
plicated and hazardous' patchwork theory of Adickes receives
at least a qualified approval. Such an estimate, the more
striking because of the comparative clarity of the passage in
question, seems to me, like so much of Mr. Kemp Smith's
writing, to do less than justice to the ability of Kant : so far
from helping the student, it places additional difficulties
in his way. The impression which I get throughout — I do not
know whether it is the impression which Mr. Kemp Smith
intended to give — is that Kant was grossly incompetent; that
he had a wholly imperfect grasp ot what he was trying to say ;
and that the Critical Philosophy, which in the Kritik is partly
embedded in a mass of non- Critical doctrine and partly not
even expressed at all, is known in its full stature only to a
few choice spirits of whom Kant certainly was not one. For
such an attitude in a Hegelian like Caird — although Caird
seems to me to do greater justice to the merits of the Kritik —
some justification could be found; for a Hegelian is in the
happy position of knowing that all other philosophies are
imperfect attempts to express the philosophy of Hegel, and
that Kant in particular only marks an important stage on the
way towards the final goal. But Mr. Kemp Smith is no Hegelian ;
and his account of the philosophy which Kant was unsuccess-
fully trying to expound, for me at least, carries no conviction
and awakens no response. The modern tendency to treat
Kant with condescension seems to me based on no rational
grounds ; and, paradoxical though it may appear to the present
age, I will venture to express the opinion — an opinion which
grows ever firmer the more I study the Kritik — that Immanuel
Kant had a far better understanding of the Critical Philosophy
than any commentator who ever lived.
BOOK XII
TRANSCENDENTAL IDEALISM
CHAPTER LI
EMPIRICAL REALISM
§ i. Problems of the Critical Philosophy
We have now — to borrow Kant's expression — explored
and surveyed the land of pure understanding or of truth,1
and I do not at present propose to embark with him upon the
stormy sea of illusion. Nevertheless as we look, on his sug-
gestion,2 at the map of the area we have left, we cannot but be
conscious that the character of certain regions is still regrettably
vague, or at any rate that we have concentrated more upon the
physical features than upon the spiritual life of the country.
More simply, we have dealt in some detail with the objects of
outer sense, but the study of inner sense and its objects has
been comparatively slight. Kant himself was obviously con-
scious of this weakness, for in the second edition he attempts
to deal more fully, although not fully enough, with the problem
of inner sense and with the cognate problem of the relation
between inner and outer sense.
These two problems, together with a third, namely the
meaning of the distinction between phenomena and noumena,
must be touched upon before our task is finished. All of them
raise fundamental questions as to the nature of Kant's trans-
cendental idealism and its combination with what he calls
empirical realism. In the second edition the emphasis on
empirical realism becomes much stronger, because his con-
temporaries tended, naturally enough, to assimilate his idealism
to doctrines which they already knew, such as the idealism of
Berkeley. In reply to such a tendency Kant is forced to insist
that objects in space are for him as real as the succession of
our ideas ; they are not known by an uncertain inference from
the succession of our ideas in inner sense; for apart from
knowledge of bodies in space we could not be aware of the
1 A 235 = B 294. 2 A 23$ = B 295.
376 TRANSCENDENTAL IDEALISM [LI §2
succession of our ideas. This doctrine is set forth in the Refu-
tation of Idealism, and before we examine inner sense itself,
we must first examine the Refutation.1
§2. Descartes and Berkeley
The idealism which Kant wishes to refute is what he calls
material idealism as opposed to his own formal or Critical
idealism.2 It might also be called empirical idealism3 as opposed
to transcendental idealism. This material or empirical idealism
is of two types — the problematic idealism of Descartes and the
dogmatic idealism of Berkeley. The former view regards the
existence of bodies in space as doubtful and incapable of proof;
it is essentially a kind of representative idealism which admits
the certainty of self-knowledge, but accepts the existence
of bodies only by a kind of faith. The latter view explicitly
denies the existence of bodies, and asserts (according to
Kant) that things in space are only fictions or products of
imagination.4
As Kant is clearly not a believer in representative idealism,
it was natural that his doctrine should be regarded as akin
to Berkeley's. His anxiety to deny this perhaps explains a
certain animus which he shows against that philosopher,
whom he refers to as 'the good Berkeley',5 while other thinkers
are referred to as 'the illustrious' so and so.6 It may be
doubted whether Kant had a very exact knowledge of Berkeley's
philosophy ; for he appears to suggest that Berkelcyan idealism
rests on the alleged impossibility of space and therefore of
1 B 274 ff. The Refutation is a substitute for the Fourth Paralogism
of the first edition, which, in dealing with the existence of bodies in
space, laid itself open (by its insistence that we know the existent
equally through outer and inner sense) to mistaken charges of sub-
jective idealism. It is introduced into Kant's discussion of the Second
Postulate, inasmuch as idealism is opposed to the doctrine of the
Second Postulate — that on the basis of sense-perception our thought
can know objects actually existing in space. 2 B 274.
3 A 369, A 371. In B XXXIX n. it is called psychological idealism.
4 *Einbildungen.y This assertion suggests that Kant's knowledge of
Berkeley was very imperfect.
5 See B 71. fl E.g. (der beruhmte Locke' in B 127.
LI § 3] EMPIRICAL REALISM 377
things in space. Kant maintains that this is an inevitable
result of taking space as a quality of things-in-themselves ;
to treat space in this way is to make it a non-entity or 'unthing',1
whose contradictions infect all spatial things with unreality.
He therefore holds that this type of idealism is refuted by the
doctrine of the Transcendental Aesthetic, which showed that
space is neither a thing-in-itself nor a quality of things-in-
themselves, but only a form of intuition. Whether this is
really relevant to a refutation of Berkeley, we need not here
consider.2
For the view of Descartes he has a much greater respect. He
believes that it is the inevitable consequence of transcendental
realism, that is, of the view which starts by holding that our
knowledge is of things-in-themselves which are independent
of our senses ;3 for on such a theory we can never pass from
our sensuous ideas to their supposed corresponding, but
independent, objects. The great merit of Descartes's position
is that it refuses to assert the existence of objects in space
until adequate grounds have been shown for doing so. It is
a scandal to philosophy that such a proof has not yet been
given,4 and this proof Kant now proposes to supply. He will
show that the inner experience which Descartes regarded as
indubitable is itself possible only under the presupposition
of outer experience.
§3. The Refutation of Idealism
The theorem5 which Kant seeks to prove is stated as follows :
The mere, but empirically determined, consciousness of my
own existence proves the existence of objects in space outside me.
There are two points to be noted in regard to the meaning
of this theorem. The consciousness of my own existence, since
1 'Undmg.' The concept of such an object is self-contradictory; see
A 291 = B 348.
2 The same type of argument is used against Berkeley in B 71.
3 A 371. 4 B XXXIX n. 6 'Lehrsatz.*
378 TRANSCENDENTAL IDEALISM [LI § 3
it is said to be empirically determined, is not pure apperception,
but involves consciousness of the succession of thoughts, ideas,
feelings, desires, and volitions present to inner sense.1 The
existence of objects in space outside me can mean only phe-
nomenal objects, and not things-in-themselves. The words
'outside me* are indeed ambiguous2 — they may refer either
to a thing-in-itself different from, and independent of, the
knower, or they may refer to phenomenal things in space —
but here there is no doubt that they refer to phenomenal
things in space.3
I. Kant's argument starts from two premises: (i) that I am
aware of my own existence as determined in time\ and (2) that
all time-determination presupposes something permanent in
sense-perception. Of these premises the first is taken for granted
by Descartes and by idealists generally;4 the second we must
assume to have been proved by the First and Third Analogies.
II. Now this 'something permanent' cannot be an intuition
in me? An intuition in me is simply one of the ideas which
are grounds for determining my existence in time, one of the
events in my changing mental history. If the succession of
my ideas can be determined — as is implied by our second
premise — only by reference to the permanent, it is obvious
that the permanent cannot be one of the ideas whose place in
the succession has to be determined.
Kant is assuming that in inner sense we have only a succession
of ideas and nothing permanent in relation to which the
1 Compare A 357-9 and B XL n. 2 A 373.
3 This is one of the few points on which there seems to be general
agreement among modern commentators. Professor Pnchard does
indeed urge (Kant's Theory of Knowledge, p. 321) that the argument
implies spatial objects to be things-m-themselves, but he recognises
that Kant himself is unaware of this implication.
4 It is taken for granted by Berkeley also. This doctrine could not
be attributed to Hume, but I think that Kant's argument would apply
equally to any view which holds, as Hume did, that we are aware of a
succession of ideas in time.
6 I follow the correction given by Kant in B XXXIX n.
LI § 3] EMPIRICAL REALISM 379
succession can be determined. This doctrine he holds con-
sistently— it is indeed at the very root of his argument in the
Paralogisms. I think that the doctrine is true, but the grounds
for holding it ought to have been stated.1 We ought to be told
whether the absence of the permanent from inner sense is
only an empirical fact or whether it rests on a priori grounds.
If Kant had rested his proof of substance on the nature of space,
his position would have been stronger.
III. His conclusion is that the sense-perception* of the per-
manent (which is necessary if we are to be aware of a succession)
is possible only through a thing outside me in space, and not
through the mere idea of a thing outside me? By a 'thing' Kant
means a permanent phenomenal substance in space (substantia
phaenomenon). Such a 'thing' is not to be regarded as one
idea among other ideas and, like them, present in our mind
at one time and absent at another. It is the permanent substratum
in space to which we refer all the changing states perceived by
us in succession, and as such it is a necessary condition of our
experience of objects in one space and one time ; but it is none
the less phenomenal.
Whatever difficulty may be found here is certainly not
new : it is simply the difficulty of the First Analogy ; and this
again is only a particular example of the general difficulty
that for Kant an object — though it is not one idea among
1 Such grounds as are stated by Kant are to be found in Note 2
(B 277-8). There he insists that all time-determination depends on
motion in relation to the permanent in space (compare B 291); that
the only permanent given to us in intuition is matter; that the per-
manence of matter is not known by mere generalisation, but is an
a priori condition of time-determination; and that there is no per-
manent ego in inner sense known through intuition as matter is
known through our intuitions of impenetrability.
2 It should be noted that the permanent in sense-perception which
was said in the premise to be 'presupposed' is here said to be 'per-
ceived*. There are difficulties as to the sense in which the permanent
is perceived. See Chapter XLII § 5.
3 The same doctrine is stated in A 197 = B 242, where it is said
that an idea cannot have objective significance merely by being related
to another idea, the idea 'object'.
380 TRANSCENDENTAL IDEALISM [LI § 3
other ideas — is a combination of our ideas in a necessary
synthetic unity. If we cannot accept this possibility, we must
say with Mr. Prichard that Kant's argument really implies
the existence of things-in-themselves ; and we can then accept
the argument (Mr. Prichard himself accepts it) only if we
consider ourselves entitled to hold that the existence of per-
manent substances in space as things-in-themselves is a condition
of our awareness of change. On Kant's view, however, the
existence of permanent substances in space can never be
proved unless these permanent substances are phenomenal
substances dependent, like time and space, on the constitution
of the human mind. Hence he is not departing in the slightest
degree from his own doctrine ; and we must, I think, recognise
this, even if we hold, with Mr. Prichard, that his doctrine is
untenable and that a permanent phenomenal substance (or a
phenomenal object which can be distinguished from our
ideas) is a contradiction in terms.
IV. The rest of the argument offers no difficulty. It follows
at once that the determination of my own existence in time (or
knowledge of the succession of my ideas) is possible only through
the existence of actual things*- which I perceive in space.
V. My consciousness (or my existence — for I exist as con-
sciousness) is essentially consciousness (or existence) in time?
and so knowledge of my existence necessarily involves the possi-
bility of determining existence in time.
VI. Hence knowledge of my existence is necessarily bound
up with the existence of permanent spatial things; or in other
words knowledge of my own existence is at the same time an
immediate* knowledge of the existence of permanent spatial
things.
1 These actual things must here be permanent substances.
2 Here again we may note a clear statement that for Kant knowing
is not timeless or noumenal.
3 I feel some difficulty as to the use of the word immediate'. See
§ 4 below.
LI §4] EMPIRICAL REALISM 381
§ 4. Turning the Tables on Idealism
Kant insists that the usual argument ot idealism is here
turned, with greater justification, against itself.1 Problematic
idealism rested its case on the certainty of immediate experi-
ence, and assumed that the only immediate experience is inner
experience? On this view our knowledge of things in space
is inferential : it depends upon an inference from our ideas as
supposed effects to bodies as their supposed causes. Such an
inference from given effects to determinate causes is always
uncertain, although we can know a priori that every effect
must have some cause. In this particular case it is possible
that we are ourselves unconsciously the cause of our ideas when
we perceive,3 just as we are consciously the cause of our ideas
when we indulge in arbitrary imagination. Hence the existence
of bodies in space is a matter, not of knowledge, but of faith.
Kant has turned the tables on this argument by proving (as
he believes) that outer experience is really immediate experience,
and that inner experience is possible only if we have immediate
experience of bodies in space. This proof depends on the
assumption that inner experience is more than pure apper-
ception, more than the 'I think' which must accompany all
our ideas of objects. The sense in which Kant believes that this
*I think' — here identified with 'I am' — immediately includes
in itself the existence of a subject cannot be discussed here.4
Knowledge of my existence in time requires more than pure
apperception, more than the mere thought or concept that
something or some subject exists. We must have intuition,
1 Note i, B 276.
2 Inner experience is experience of the self and its states, these
states being thoughts, feelings, and volitions.
3 This possibility is recognised by Descartes himself, as is also the
hypothesis of Berkeley — that God, and not bodies or matter, is the
cause of our ideas; see Meditation III and Meditation VI.
4 It involves consciousness, not of how I appear to myself or how I am
in myself, but only that I am. This consciousness is conception and
not intuition, a mere intellectual idea of the activity of a thinking sub-
ject. See B 278 and compare B 157 and B XL-XLI n. as well as
the Paralogisms. Compare also Chapters LI I and LI 1 1.
382 TRANSCENDENTAL IDEALISM [LI § 4
and, indeed, inner intuition under the form of time, if we
are to have determinate empirical knowledge of the existence
of the subject in time.1 In short, inner experience is empirical
knowledge of the succession of my ideas or states in time, and
we have proved that such knowledge is impossible apart from
immediate experience of permanent objects in space.
Kant insists in a footnote that he has proved, and not merely
presupposed, the immediate consciousness of the existence of
spatial things. This proof holds whether we have insight into
the possibility of this consciousness or not.2 Kant's discussion
of this possibility might suggest that he believes us to have
such insight,3 but this does not appear to be the case.4
I confess I always find difficulty in proofs that knowledge
of some particular kind is immediate ; for if the knowledge is
immediate, what need, and indeed what possibility, is there
of proving its immediacy ? I confess also that I think Kant is
1 Compare also B 135. In B XL n. we are told that if apperception
were itself intellectual intuition, the argument would not hold.
2 Compare A 171 = B 213, where 'insight* is said to fail us m
many cases of a priori knowledge. Insight ('einsehen9 or 'perspicere')
belongs to reason, not understanding, and we possess insight in regard
to very few things. See Log. Eml VIII (IX 65).
3 B 276-7 n. The question as to the possibility of such immediate
outer experience Kant identifies with the question whether we could
have an inner sense and no outer sense, that is, whether objects of
outer sense could be products of mere imagination. He answers that
our imagination of objects of outer sense would be impossible, and
that we could not 'exhibit' such objects imaginatively in intuition,
unless we already had an outer sense. He even suggests that we must
distinguish immediately the receptivity of outer sense from the
spontaneity of imagination ; for merely to imagine an outer sense
would be to destroy the very power of intuition which we were trying
to determine by means of imagination. I do not understand how the
immediacy of this distinction is established by this obscure reason, nor
how it can be reconciled with Kant's general doctrine. Compare § 6
below, and ProL § 13 Anmerk. Ill (IV 290), where Kant deals with
the cognate problem of the distinction between truth and dream.
4 In B XLI n. we are told that it is as impossible to explain how the
existence of a permanent spatial thing different from all my ideas is
necessarily involved in the determination of my existence ('m der
Bestimmung meines eigenen Daseins notwendig mit eingeschlossen wird')y
as it is to explain how we think the permanent in time.
LI §4] EMPIRICAL REALISM 383
carried away by his zeal when he asserts, not only that inner
experience is impossible apart from outer, but also that it is
itself possible only mediately — does he intend to deny that
inner experience is as immediate as outer experience? If so,
he must, I .think, be using 'immediate' as equivalent to 'self-
sufficient'. He does appear to hold that outer sense is possible
apart from inner and not vice versa, for he attributes outer
sense, but not inner, to animals j1 but animal consciousness
(Erlebms) is not strictly experience (Erfahrung). Experience
of bodies in space certainly involves thought and imagination ;
and even although consciousness of thinking (or pure apper-
ception) is not experience of our existence in time, I find it
hard to believe that pure apperception (which is a condition
of outer experience) can, on Kant's view, be found apart from
experience of our existence in time and of the succession of our
ideas. Furthermore experience of bodies in space is experience
of bodies moving ; and since this is impossible apart from time,
inner experience would seem to be the condition of outer,
just as much as outer experience is the condition of inner,
unless we are to abandon the doctrine of the Aesthetic that time
is the immediate condition of inner appearances and the mediate
condition of outer appearances.2
I would suggest that (granted the validity of the argument
in the First Analogy) Kant has shown inner experience to be
conditioned by outer experience, but not that outer experience
can be independent of inner experience. The two types of
experience cannot be separated from each other ; and although
an element of immediacy must be allowed to both in so far as
both involve direct intuition, neither can be regarded as imme-
diate in the sense of being self-sufficient.
I would suggest also that Kant is right in saying that the
Refutation of Idealism does not add anything new to his
doctrine, but only to his method of proof.3 He has already
proved that all awareness of change presupposes the existence
1 See Metaphysiky p. 129.
2 See A 34 — B 50. To abandon this doctrine would, I think, be
inconsistent with the doctrine of the Analogies. 8 B XXX IX n.
384 TRANSCENDENTAL IDEALISM [LI § 5
of permanent substances in space. What he now adds is only
that awareness of subjective change presupposes the existence
of permanent substances in space. Furthermore he has always
insisted that consciousness of the objective is inseparable
from consciousness of the subjective and vice versa ; and although
consciousness of the subjective was, in the Transcendental
Deduction, primarily a consciousness of the synthetic activity
of the self rather than of its changing states, I do not think
that these two aspects of self-consciousness can exist apart
from one another, and I see no reason to believe that Kant
ever thought they could.
§ 5. Empirical Realism and Transcendental Idealism
The strength of the expressions which Kant uses in his
desire to distinguish his doctrine of transcendental idealism
and empirical realism from problematic idealism must not
mislead us into thinking that he is going back upon his doctrine
that the world we know is a world which (although it is an
appearance of things-in-themselves) is essentially relative to
human minds. I do not think we need feel any difficulty when
he says, with obvious truth, that the idea of something per-
manent is not the same as a permanent idea,1 but may be very
variable like all our other ideas (including the idea of matter).2
We may feel more doubt when he asserts that this permanent
must be an external thing which is different from all my ideas,
but I think that on reflexion we shall see that this is only a
particular application of the doctrine which Kant has always
preached in regard to the nature of the object.3
1 In B 412 Kant speaks as if we required *a permanent intuition for
knowledge of substance', but this seems to be a loose phrase for 'intui-
tion of the permanent'. There are not the same objections to the phrase
'a permanent appearance' in A 364. In Chapter XLII § 5 I have dis-
cussed the difficulty of Kant's repeated statements that we not only
presuppose, but also observe or perceive, the permanent.
2 B XLI n.
3 The object is indeed only a totality of ideas (possible and actual)
— compare A 191 — B 236 — but it possesses a necessary synthetic
unity, and one condition (or manifestation) of this necessary synthetic
LI § 6] EMPIRICAL REALISM 385
Consciousness of my own empirical existence is more than
consciousness of an idea of my existence; it is consciousness,
not of a present idea, but of that succession of thoughts, feelings,
and volitions in time1 which constitutes my existence as a
thinking being; and I can determine or know such existence
only in relation to a permanent spatial world. Hence Kant
holds — and surely he is right — that consciousness of my exis-
tence is impossible apart from consciousness of a spatial world
of substances which are permanent amid change; and such
consciousness in turn is consciousness, not of a present idea, but
of a world spread out in space and time. The fact that the self
we know and the world we know are to be distinguished from
our momentary idea of them does not mean that either the self
or the world ceases to be phenomenal — Kant is still a transcen-
dental idealist. But he is also an empirical realist; and he
believes, not that we have ideas to which the world and the self
correspond,2 but that the phenomenal world and self are
directly present to our minds through thought and sense. The
fact that they are so present is compatible with (and indeed
on Kant's theory inseparable from) the doctrine that they are
determined by the forms of thought and intuition.
§ 6. Sense and Imagination
We must not suppose Kant's doctrine to involve the absurd
consequence that every idea of spatial objects which bears the
character of intuition involves the existence of these objects.3
Such an idea, for example in dreams or in madness, may be
the product of imagination. It is nevertheless possible only
through the reproduction and combination of past perceptions
of spatial objects; and what has been shown is that these
unity is that these ideas must be regarded as states or accidents of a
permanent substance in space. We must also remember that the inner
nature of the object is the thing-m-itself, but is to us unknown.
1 Compare B XL n.
2 Although Kant uses the word Correspond' sometimes rather
loosely, it is only the concept considered in abstraction from its
object which corresponds to the object presented to us in intuition
and thought. 3 Note 3, B 278-9.
VOL. II N
386 TRANSCENDENTAL IDEALISM [LI § 6
past perceptions were possible only through the existence of
actual spatial objects. Kant's argument is quite general; it
asserts only that inner experience in general presupposes outer
experience in general. Whether a particular supposed experi-
ence is experience or mere imagination must be decided in
accordance with the ordinary criteria, or in other words by
means of the Analogies. These Analogies (and especially the
Second Analogy) are the rules by which we distinguish ex-
perience in general (including experience of the self) from mere
imagination.1
Kant appears to assume, and with justice, that we have
usually no difficulty in distinguishing the products of our
waking imagination from actual objects in space. The chief
difficulty for sane men is to be found in the case of dreams.
Kant's clearest statement in regard to them is to be found in
the Prolegomena? The difference between truth and dream
does not lie in the character or constitution3 of the ideas in the
two cases, for the ideas are of the same character in both.
We deny that dream-objects are real, because they do not
conform to the rules necessary for determining an object,
and because they cannot cohere with other objects in an
experience which rests throughout upon causal law.
1 B XLI n. Compare A 201-2 = B 246-7. In A 376 Kant applies the
same principle to the 'illusion of sense' (Betrug dcr Sinnc). The rule
which he there gives is the Second Postulate — 'What is connected
with a sense-perception in accordance with empirical laws is actual'.
The empirical laws in question are, however, primarily causal laws.
In ProL § 13 Anmerk. Ill (IV 290-1) Kant again discusses illusions
of sense, and maintains that strictly speaking illusion is due, not to
the senses, but to the understanding which makes false judgements
on the basis of given appearances.
2 § 13 Anmerk. Ill (IV 290). 3 'Bcscliqffenlicit.9
CHAPTER L I I
INNER SENSE AND SELF-KNOWLEDGE
§ i. The Paradox of Inner Sense
After a period of comparatively easy going we must unfor-
tunately turn to one of the most difficult aspects of the Critical
Philosophy — the nature of inner sense. I have deliberately
kept this topic to the end.1 Kant's primary concern throughout
the Kritik is with physical objects ; and if we can first of all
understand his account of our knowledge of the physical world,
we may at least hope that we shall be in a better position to
understand his acco\mt of self-knowledge. Nevertheless it
cannot be too strongly insisted that the Kritik professes to give
an account of all knowledge and all experience, not merely
of the knowledge or experience of physical objects ; and indeed
that the account of time as the form of inner sense is an integral
and essential part of the whole Critical Philosophy.
The full treatment of this question demands a detailed
discussion of the Paralogisms, which is outside the scope of
this book. Here we must be content to examine only what
Kant calls the 'paradox' of inner sense, as it is expounded in
the Transcendental Deduction of the second edition.2 I feel
far from confident that I have mastered this doctrine, and
I am not sure whether my difficulties are due to my own
incapacity in following Kant's complicated expressions, or
whether they are partly due to a real obscurity in his thought ;
but at least it may be possible to bring out certain aspects of
his teaching which are implicit in what we have already learned.
Kant takes the paradox to be that by inner sense we know
ourselves, not as we are in ourselves, but only as we appear
to ourselves. In view of his doctrine that time, like space, is
only a form of our sensibility, this paradox may seem not to
1 Inner sense has been discussed briefly in Chapters II § 3, IV § 4,
and VII § 2. For the discussion of apperception see the Transcendental
Deduction, especially Chapters XXI-XXXI. 2 B 152 fT.
388 TRANSCENDENTAL IDEALISM [LII § r
be so very great. Kant himself has dismissed an analogous
objection somewhat lightly — perhaps too lightly — in his
first edition.1 The special difficulty of his theory seems to be
found in the reasons which lie behind it — namely that we can
intuit ourselves only as we are affected internally. This appears
self-contradictory ; for it means that we stand to ourselves in
a passive relation.2 This difficulty may, I think, be put more
clearly by saying that the self both affects and is affected by
itself. Inner sense, since it is sense, must be passive — that is
the differentia of sense. Yet to give us knowledge of the self,
it must be affected by the self.3 More precisely, inner sense,
which is a passive capacity of the self, must be affected
by apperception, which is an active power of the same
self.4
For this reason Kant carefully distinguishes inner sense
from apperception, although they are commonly identified.5
It does appear a trifle paradoxical that the self should have
two powers of self-consciousness, one active and the other
passive ; and that it should have to act upon, or affect, its own
passivity in order to produce a self-knowledge which in the
end will be knowledge of the self only as it must appear, not
as it really is.
Part of the difficulty lies, I think, in the fact that when Kant
speaks of the self as 'affecting* inner sense, he is not using the
word 'affects' in the same way as when he speaks of physical
objects, or things-in-themselves, as affecting outer sense. The
self affects itself through the transcendental synthesis of
imagination, and this kind of affection is clearly necessary even
for our knowledge of the external world. The difference
1 A 36 — B 53 ff. Compare Chapter VIII § 9, and also B 155-6.
2Bi53. 3B 15611.
4 I take this to be the implication of Kant's distinction between
inner sense and the active faculty or power (Vermbgcn) of apperception.
It is, I think, confirmed by the fact that he goes on to speak of under-
standing as determining inner sense. This of course takes place
through the transcendental synthesis of imagination.
5 Compare A 107 when what is commonly called inner sense is
equated with empirical apperception. Compare also B 139-40.
LII § i] INNER SENSE AND SELF-KNOWLEDGE 389
between outer and inner sense appears to lie in this — that outer
sense might receive external impressions (though it could
never give us knowledge of an external world) apart from
the transcendental synthesis of imagination and the unity
of apperception ; but apart from the transcendental synthesis
of imagination and the unity of apperception nothing could
be received by inner sense at all, and there could be no con-
sciousness of the stream of our ideas under the form of time.
This seems to be implied by Kant's references to the con-
sciousness of animals, who are said to have outer sense but not
inner, intuitions but not concepts.1 Yet it may also be held
that outer sense is really in the same position as inner sense,
if we take Kant's view to be that in order to intuit any line
however short there must be a successive synthesis of the parts,
and consequently a transcendental synthesis which holds
together the past and the present.2
In any case, if inner sense involves a direct awareness of my
ideas as succeeding one another in time, and if a transcendental
synthesis holding together the past and the present is necessary
for such awareness, then clearly the mind must 'affect' itself
by this transcendental synthesis, and only so can there be
inner sense at all. Such 'affection' does not supply a matter
to inner sense as the affection by objects (whether phenomenal
or transcendental) supplies matter to outer sense ; for the ideas
of the outer senses are said to constitute the proper stuff
or matter of inner sense.3 On the contrary, the affection of the
self by itself seems to be concerned rather with determining
inner sense as regards its form, which is time.
Once we have grasped this principle, the paradox of Kant's
doctrine will be diminished, and his account of self-knowledge
will approximate, in spite of real differences, to his account of
knowledge ot physical objects. I take it for granted that however
1 See Metaphysiky p. 129, and compare Chapter XVI § 13.
3 This is the commonly accepted view, but I think that Kant
holds it only for experience or measurement, not for mere intuition.
Compare A 426 n. -- B 454 n.
3 B XXXIX n. and B 67. Compare Chapter IV § 4.
390 TRANSCENDENTAL IDEALISM [LII §z
unsatisfactory the terms 'inner' and 'outer' may be, what
Kant attempts to describe is really an element in our experience :
we have a direct and immediate awareness, which must there-
fore be intuitive and not conceptual, of what is present to our
minds at any moment j1 and our immediate awareness is always
awareness of the time at which a sensum or idea is given, not
awareness of the time at which objects exist and change.2
Such immediate awareness is called by Kant (whether appro-
priately or not) inner intuition, and is ascribed to inner sense,
the form of which is time. Pure apperception, on the other
hand, is consciousness of the necessary unity of our thought
and of the necessary forms in which this unity is manifested.
In abstraction this implies the necessary unity of some sort
of intuition (intuition in general)} for thought apart from
intuition is empty. It does not imply any particular kind of
intuition, and it has in itself no reference to time.3
§ 2. Understanding, Imagination, and Inner Sense
Understanding is said to determine inner sense.4 'Determine
inner sense' seems to mean here 'hold together the manifold
of inner sense in necessary synthetic unity' ; for understanding
performs this task in virtue of its original5 power to combine
the manifold of intuition, and to combine is to bring under
an apperception,6 which always implies necessary synthetic
unity.
1 See Chapter IV § 4.
2 See Chapter VII § 2. An object may change as our scnsa do (when
we perceive an objective succession), but it may not; for we may per-
ceive successively the coexistent states of the object. The time of the
states of the object we must determine by thought, not by intuition;
but the time of our own ideas is known as immediately as anything
can be. 3 Compare B 150-1. 4 B 153.
5 * Original' in the sense of being wholly independent of anything
else and particularly of intuition.
6 Apperception appears to be the act here rather than the power ;
see Chapter XXI § i. As a power appeiception and understanding
appear to be identical (though 'apperception' indicates, not only a
power of thinking, but a power of thinking which is in some degree
self-conscious). Apperception in B 154 is the source of all combination,
LII §2] INNER SENSE AND SELF-KNOWLEDGE 391
The question then arises, as usual, how understanding, as a
po\ver of thinking by means of concepts, can be said to combine
the manifold of intuition. It is not itself a power of intuiting;
nor, even if intuitions are given, can it take them up directly
into itself (as a power of conceiving) and make them, as it were,
its own intuitions.
If we consider the synthesis of understanding in complete
abstraction from what is synthetised, all we are left with is
the unity of the act of thought. Of this act understanding
is said to be conscious even apart from sensibility, but this is
only by abstraction; for without sense-data there could be
no such thing as thought.1 The unity of the act of thought, it
may be added, manifests itself in the forms of judgment, which
are the same whatever be the matter thought. The act of
thought (with its necessary unity and its necessary forms),
although having a nature in no way determined by sensibility,2
is able to determine sensibility inwardly in regard to the mani-
fold which may be given to understanding ; but this determina-
tion is concerned with the manifold only so far as it is given in
accordance with a form of intuition, namely time.3 The under-
standing can impose the principles of synthesis native to itself
upon the pure manifold of time, and so upon all appearances
to inner sense.4
How can it do so ? It can do so only through a transcendental
synthesis of imagination which combines, as Kant has all
along insisted, the pure manifold of time, and consequently
while in B 130 (and indeed in the present passage) all combination is
ascribed to understanding.
The possibility of understanding is said to rest on apperception.
I do not know whether this means more than that understanding is
manifested only in acts of apperception. In A 97-8 the three subjective
sources of knowledge are said to make understanding possible (as a
power of knowing), but I am not sure whether this is relevant.
1 Compare A 96 and A 86 - - B 118.
2 In the sense that it is always the same whatever be the nature of
given intuitions — the differences in acts of thought are here irrelevant,
3 Compare B 150 and A 99. Space may be involved as well — perhaps
must be involved ; sec B 155.
4 Compare A 76-7 -- B 102 and A 79 = B 104-5.
392 TRANSCENDENTAL IDEALISM [LII §2
the empirical manifold given in time, in accordance with the
unity or apperception.1 Indeed Kant speaks here as if the
transcendental synthesis of imagination were the work of
understanding at a lower level (or of understanding considered,
not as a power of pure thinking, but as a power of a priori
knowledge).
In this way the understanding can be said to exercise its
activity on the passive or receptive self of which it is an active
faculty ; and thus the active faculty may be said to affect inner
sense.
There is therefore a complete contrast between apperception
and inner sense.
Apperception and its synthetic unity is the source of all
combination.2 As involving the forms of judgment it applies to
a manifold in general \ for whatever manifold may be given, if
it is to be judged and known, it must be combined in accordance
with the forms of judgment or the categories. And this means
that the categories, as principles of synthesis involved in the
very nature of understanding, arc independent of all differences
in sensuous intuition, and apply a priori to all objects in general.
Inner sense, on the other hand, if we eliminate the given
impressions which are its matter, contains only the form of
time, which is the form of all inner intuition, and so of all
intuition without exception.3 Such a form, however — and this
is a doctrine stressed specially in the second edition4 — contains
in itself no combination of the manifold, and so contains no
determinate intuition. This is obvious, if combination is due
1 We must remember that conception is always consciousness of the
general principle at work in a synthesis of imagination, and that the
categories are ultimate principles of synthesis necessary to all concep-
tion and imposed upon imagination by understanding itself.
2 I would again remind the reader that Kant is speaking of the
ultimate principles of combination which condition empirical com-
bination. We must always combine the given as accidents of a sub-
stance, for example, but it is a matter of empirical observation that
the accidents of sugar are to be hard and white and sweet.
3 Every intuition 'taken up* into consciousness is thereby an inner
intuition (whatever else it may be). 4 Compare B 160 n.
LII § 3] INNER SENSE AND SELF-KNOWLEDGE 393
only to understanding working through the transcendental
synthesis of imagination; but apart from such combination
the form of time is a mere abstraction.
In order that time may be, not only a form of intuition, but
also a pure and determinate intuition, there must be a deter-
mination or combination of the pure manifold through the
transcendental synthesis of imagination (which Kant has called
the synthesis speciosa1 as opposed to the synthesis intellectualis}.
There must also be a consciousness of this determination (or
of the principle of this determination), and such consciousness
is a conceptual consciousness of the understanding. Indeed
the ultimate principle of this determination is not merely one
which the understanding finds in the transcendental synthesis
of imagination, but one which it imposes a priori upon the
transcendental synthesis of imagination.2 Hence we are entitled
to speak of the synthetic influence of the understanding upon
inner sense.3
§3. Illustrations of Kant's Doctrine
Kant goes so far as to say that we always perceive this in
ourselves.4 Such an assertion is an overstatement; for our
knowledge of the synthetic activities of the self may be what he
calls 'obscure'.5 It nevertheless serves to bring out sharply
how far Kant was from regarding the transcendental synthesis
as necessarily unconscious. His subsequent statement that the
act of synthesis successively determines inner sense shows
also how far he was from regarding the transcendental synthesis
as timeless. There could be no more explicit contradiction
of the fantastic and, in my opinion, baseless interpretation
of Vaihinger so widely accepted at the present time.
Kant's illustrations are interesting, and they bear out the
view that the matter of inner sense is derived from outer sense.
1 See B 151. 2 Compare Chapters XIV § 3 and XXXIV § 3.
3 This is another way of saying that inner sense is affected by the
synthetic activity of understanding. 4 B 154.
6 Compare A 103, A 117 n., and B 414-15 n.
VOL. II N*
394 TRANSCENDENTAL IDEALISM [LII § 3
We cannot think a line without drawing it in thought.1 We
cannot think a circle without describing it. We cannot repre-
sent the three dimensions of space save by setting three lines
at right angles to one another from the same point. How little
are these illustrations concerned with the unconscious, the
timeless, or the noumenal ! Here indeed we are concerned with
the synthetic influence of understanding by means of mathe-
matical concepts, though at least the category of quantity is
necessarily involved. It may seem strange that the illustrations
are concerned with the objects of outer sense, if we forget
that the matter of inner sense is derived from outer sense;
but Kant goes on to explain how the determination of outer
sense is a determination of inner sense as well, and indeed how,
in accordance \vith the doctrine of the second edition, the
determination of inner sense must also be a determination of
outer sense.
In order to think time— and here, as in the previous cases,
the thinking is manifestly a knowing, and involves intuition
as well as concepts — in order to think time we must draw a
straight line (which has to serve as the spatial image of time).2
Kant's main point, however, is that we must attend only to
the act of synthesis whereby we determine inner sense succes-
sively (or successively combine the manifold in inner sense).
In other words we must attend to the succession of our acts of
combining the manifold and so determining inner sense.3
1 Here thought is manifestly equivalent to imagination.
2 Compare B 156. I suppose other spatial representations might be
possible, but they would be less appropriate; for a straight line alone
has one dimension. I am not so sure as Kant seems to be that we
could not adequately represent time coneretely hy a tune; but if all
change is relative to the permanent in space, his doctrine is not
groundless.
3 Kant says we must attend 'to the succession of this determination
in inner sense' rather than 'of inner sense' (which we should expect). I
suppose that the act of determination, so far as it is an act of adding a
new manifold to what we already have, may be said to be in inner sense.
Strictly speaking, I take it, it is the new manifold or the combined
manifold which is present in inner sense through our act. For aware-
ness of the act in the full sense, I should imagine that we require, not
only inner sense, but also empirical as well as pure apperception
LII § 3] INNER SENSE AND SELF-KNOWLEDGE 395
The act of combination or synthesis is here regarded as a
synthesis of the manifold in space. It is again seen to be suc-
cessive; for it is described, perhaps a little misleadingly, as
'motion' — motion as an act of the subject, not as the character
of an object. The subject may be said to 'move' only in the
sense that it successively describes a spatial figure in imagina-
tion: this is a pure act of successive synthesis of the manifold
in outer intuition in general, an act of the productive imagina-
tion. When we regard this act in abstraction from the spatial
elements involved, when we consider it, in short, only as deter-
mining inner sense in accordance with the form of time — then,
and apparently then only, have we the concept of succession.
This concept, it should be noted, is a concept of a mode of
time1: it should be sharply distinguished from the concept
of change, which is empirical.2
The concept of succession, on Kant's view, is the concept of
a principle at work in the synthesis of imagination. In this it
resembles other concepts ; for in concepts we conceive a prin-
ciple at work in the synthesis of imagination whereby an object
is produced.3 Kant is attempting, whether successfully or not,
to connect our concept of time with that of space; and even
the mere attempt was, I imagine, an advance on the accepted
views of his own period. The subject is, howrever, full of
difficulty. It is not altogether clear why for our concept of suc-
cession, and apparently even of time,4 \ve must have in mind
the synthesis of a spatial manifold in a straight line ; for we must
immediately consider the synthesis in abstraction from the
spatial elements involved. Partly no doubt it is in order to have
an image whereby we can indicate that time is of one dimension ;5
but is this due to more than the accidental prominence of
(consciousness of the special as well as the universal nature of our
activity); unless indeed, which seems to me very unlikely, acts of
imagination (as opposed to acts of thought) are themselves known
through inner sense. Compare Chapter XXI § 3.
1 See Chapter XXXIX §3.
2 B 3, A 171 = B 213, A 206-7 -= B 252.
3 The exceptions to this rule, if any, need not be here considered.
4 B 156. 5 Ibid.
396 TRANSCENDENTAL IDEALISM [LII § 3
sight in our experience? Partly perhaps it is that we may be
able to understand the successiveness of time as against the
non-successiveness of space.1
Furthermore the successiveness of our act of synthesis
seems already to presuppose time. On the other hand, there is
no time apart from the act of synthesis whereby past and
present are held together before the mind. Hence Kant can
speak of producing time itself in apprehension,2 and can say
that the ideas of a determinate time (or space) are produced
through the synthesis or combination of a homogeneous
manifold.3 It is a little surprising that he here makes no refer-
ence to the synthesis of the pure manifold of time itself; but
perhaps he thinks it unnecessary to do so, since in the pre-
ceding paragraph he has said that there is no determinate
intuition of time apart from the transcendental synthesis of
imagination.4 The successive synthesis of the manifold of space
in the imaginative construction of a straight line must also be
a successive synthesis of the manifold of time in which the
parts of the line are successively present to inner sense.5
Otherwise we could not be aware of the line (as a determinate
quantity).6
Kant may have this point in mind when he adds that under-
standing does not find in inner sense such a combination of
the manifold,7 but produces it, in that it affects that sense.
It must be remembered that in all apprehension of appear-
ances in space and time there must be present a transcendental
synthesis of the space and time in which these appearances
1 This is suggested by the statement that we can be conscious of
inner changes only against a permanent in space; see B 292.
2 A 143 - B 182.
3 B 202. Compare also A 210 -= B 255. 4 B 154.
5 There is no question here of a synthesis of points or instants. The
synthesis is continuous.
6 Compare (in spite of differences) A 99-100, A 102, and A 103.
The reader may also be referred again to the difference between
a determinate, and an indeterminate, quantity (or quantum) in
A 426 n. = B 454 n.
7 It is perhaps possible that the combination of the manifold
referred to is the combination of the manifold in space.
LII § 3] INNER SENSE AND SELF-KNOWLEDGE 397
are. Nevertheless I should have liked to see here a few of the
empirical illustrations which Kant so sternly denies himself.1
It is, however, clear enough that — leaving aside the question
of desires and volitions which are also present to inner sense —
the appearances given to inner sense are the same as the
appearances given to outer sense. All appearances, so far as we
are conscious of them, or at least so far as we are conscious of
them as present to our minds, are appearances to inner sense —
even a line or a circle which we construct a priori in imagination.
Understanding, through the imagination, affects inner sense
by bringing these appearances successively before the mind,
and by holding them together before the mind in one time.2
This, I presume, is true, whether we are imagining objects
like mathematical circles or are actually perceiving physical
bodies.
I cannot think that Kant is nearly so confused or so obscure
on this side of his doctrine as is commonly alleged. Many of
the confusions attributed to him arise, as it seems to me, from
reading into his words meanings which they cannot possibly
have. And I believe that, however much his account requires
expansion and modification, he is at least dealing with a very
real problem, and that he is right in saying that all our ideas,
whatever their origin, may be regarded as modifications of the
mind and so as belonging to inner sense.3 Kant always dis-
tinguishes our own mental history from the history of the world
we know. Indeed we can regard our own mental history — and
I think Kant does so regard it — as only a part of the history of
the world which we know. But from another point of view we
can regard the whole world known to us as a succession of
appearances revealed to us in inner sense under the form of
time.4
Nevertheless Kant's doctrine requires a much fuller working
out than it has received. Our knowledge of time, like that of
1 See A XVIII. 2 Compare B 156 n. 3 A 98-9-
4 The effort to do this seems to me rather like the effort to see a
picture (or the contents of a mirror) in one plane. When we do this we
are not looking at anything different from what we were before.
3p8 TRANSCENDENTAL IDEALISM [LII §4
space, is primarily intuitional and not conceptual.1 We do
not make time out of nothing either by understanding or by
imagination. Time, like space and even like sensation, is
something given, however much it may be given through
the nature of our own sensibility. Our concept, as opposed
to our intuition, of time is derived by abstraction as are empirical
concepts, although like them it presupposes a synthesis in
accordance with the categories. It does not, like the pure
categories, have its origin in the understanding; and its content
is a given manifold, although that manifold is pure and in this
respect unlike the contents of empirical concepts. All this
seems to me to suggest that Kant's theory must be supple-
mented by something like the modern doctrine of the specious
present, though I do not think that that doctrine, even as
expounded by the most able modern philosophers, is wholly
immune from criticism.2
§ 4. Inner Sense and the Phenomenal Self
Having attempted to explain the way in which the mind is
internally affected by itself Kant returns to the paradox that
in this way we can know the mind only as it appears to itself,
and not as it really is in itself.3
The problem is this. How can there be one and the same
self or subject, if we distinguish the I which thinks4 (apper-
ception) from the I which intuits itself (inner sense)?5 If I
1 See Chapter V § 8.
2 Compare my article in Mind, Vol. XXXVIII, N.S. No. 151.
3 B 155.
4 It seems to me unnecessary to change, as Vaihinger does, sdas Ichy
der ich denke* into ldas Ichy das denkt*. This is the ordinary Kantian
idiom; see B 407 and B 429. Other examples could be found in
other works.
6 Kant adds in parenthesis 'for I can think of another kind of
intuition as at least possible*. Strictly speaking, we have on Kant's
view no means of deciding whether another kind of intuition is possible,
and it is at least doubtful whether we can even conceive another kind
of intuition; compare A 230 - = B 283. Setting aside this difficulty in
terminology, I find it difficult to see the point of the observation, unless
he means that the self which thinks might be identical with a self
LII § 4] INNER SENSE AND SELF-KNOWLEDGE 399
am an intelligence and a thinking subject, how can I know
myself as a thought object, so far as (in addition to being a
thinking subject) I am given to myself in intuition P1 And how
can such knowledge be knowledge of myself only as I appear
to myself "in intuition, and not as I really am in myself for
understanding ?2
Kant answers that this question — and he appears to have
in mind especially the last question — has no more and no less
difficulty than the question how I can be an object to myself
at all, and indeed an object of intuition and of inner perception.3
That I can know myself only as I appear to myself in intuition,
can, he claims, be shown clearly, provided only we accept the
view that space is merely a pure form of appearances to outer
sense. His argument rests primarily on the contention that time
is on the same footing as space. This doctrine he develops
in a sentence of very great length.
Time, he insists, while it is no object of outer intuition,4
cannot be represented by us except under the image of a line,
in so far as we produce it; for apart from this we could not
know that time has only one dimension. Similarly, we can
determine the periods, and even the moments, of our inner
intuitions only in relation to changes in spatial objects. Con-
sequently we must order or arrange the determinations of
inner sense as appearances in time in precisely the same way
that we order or arrange the determinations of outer sense as
appearances in space. Now we have admitted that we know
objects through the determinations of outer sense only so far
as we are externally affected (presumably by things-in-them-
which intuited itself in some other way (for example, by intellectual
intuition), and so would be different from a self which intuited itself
sensuously under the form of time ; compare B 68.
1 I think Kant must mean this, though the language is obscure. I am
here differing from Kemp Smith's translation.
2 Understanding involves a kind of self-consciousness or apper-
ception, but this (as Kant shows in the Paralogisms) does not give us
determinate knowledge of the self except in so far as the form of our
thinking receives a content from the intuitions of inner sense.
3 Compare B 68. 4 B 156; compare A 23 = B 37.
400 TRANSCENDENTAL IDEALISM [LII § 4
selves). We must also admit that we can know ourselves through
the determinations of inner sense only so far as we are inter-
nally affected by ourselves. And just as we can know objects,
not as they are in themselves, but only as they appear to us in
space, the form of our outer intuition ; so we can know ourselves,
not as we are in ourselves, but only as WTC appear to ourselves
in time, the form of our inner intuition.
I have pointed out above1 that there is a difference between
the two cases, since the affection by outer objects gives us the
matter of intuition, whereas the affection by ourselves does not
give us a new matter, but merely combines the given matter
under the form of time. This Kant himself seems to support
in a footnote ;2 for he mentions attention as an example of the
kind of affection or influence he has in mind. This would be
simple enough, if he had merely said that by attention we
bring new objects or appearances before the mind, and so add
to the content of inner sense, not indeed by giving something
new (as is done in sensation), but by bringing into conscious-
ness what is already gi\en in sensation. Kant himself gives a
much more complicated account of attention. In attention,
he suggests, the understanding always determines inner sense
to inner intuition. That is to say, in attention understanding,
through the transcendental synthesis of imagination, combines
a given matter under the form of time, and does so in accordance
with the categories of thought.3 In so doing it gives rise to an
inner intuition ;4 and this intuition corresponds to the manifold
thought5 in the synthesis of the understanding (or, as I should
prefer to say, corresponds, as regards its combination, to the
synthesis of the manifold of intuition in general which is
thought in the pure category of the understanding).6
I can hardly help thinking that Kant weakens the effect of
his illustration by describing it in such highly abstract and
1 See § i above. 2 g T^ n
3 Kant says According to the combination which it thinks'.
4 Intuition here is a combination of form and matter.
6 I have introduced the word 'thought'.
6 It is perhaps possible for Kant to have in mind empirical concepts
as well as (or in place of) categories.
LII § 5] INNER SENSE AND SELF-KNOWLEDGE 401
general terms; but I suppose that the allusion to an activity
with which the plain man is familiar may perhaps help him to
understand what is being talked about, even if he fails to under-
stand what is being said about it.
§ 5« Apperception and Self-Knowledge
Kant has now shown that inner sense as affected by apper-
ception gives us knowledge of the self, not as it is, but only
as it appears. He proceeds to show that apperception, taken
by itself, does not give us knowledge of the self either as it is
or as it appears.1 In apperception we are conscious only of the
necessary synthetic unity of thought.2 This consciousness
Kant describes — perhaps in reminiscence of Descartes — as a
consciousness that I am. It is not, however, consciousness
of what I am (either in myself or as an appearance). It is a
mere thinking and not an intuiting: it gives us no object.
For knowledge of the self as an object we require more than
the act of thought which brings the manifold of every possible
intuition (or of intuition in general) to the unity of apperception
— even although this act is in some ways transparent to itself or
self-conscious. We require a definite kind of intuition, intuition
given under an assignable form, such as time ; and this must take
the place of the manifold of intuition in general, which is all
that we can combine in pure thought.
Hence my own existence as known through thinking is not
appearance, and still less is it illusion. We may be tempted to
imagine Kant means by this that consciousness of thought
presupposes the I as a thing-in-itself, just as an appearance
presupposes the thing-in-itself of which it is the appearance.3
I am inclined to believ^ he means that, by thinking, my o\\n
existence is known only as an act of thinking,4 or perhaps even
1 I* i57.
2 I have simplified the statement here. What I am conscious of is
said to be myself in the transcendental synthesis of the manifold of
ideas in general (that is, in the intellectual synthesis, not the synthesis
speiwsa). 3 Compare B XXVII and A 251-2.
4 He asserts in B 422 n. that *I am* cannot be inferred, as Descartes
maintained, from the proposition 'I think', but it is identical uith it.
402 TRANSCENDENTAL IDEALISM [LII § 5
that it is known only as a form of thought.1 In any case my
existence as known through thinking is completely indeter-
minate : in order to determine my existence I must know, not
only that I think, but what I think, and this is impossible
apart from inner sense.2 'The determination of my existence
can happen only in conformity with the form of inner sense,
according to the special way in which the manifold which I
combine3 is given in inner intuition.' I can know my own
existence, not as a thinking subject in abstraction, but only as
thinking this and that concretely in a temporal succession. If
so, then (granting that time is a form of my sensibility) I can
know my existence determinately only as I appear to myself in
time, and not as I am in myself.
The self-consciousness of thought, considered in abstraction,
is far from giving us knowledge of the self. It involves indeed
thought of the categories ; for the categories are the necessary
forms of thought in which the unity of apperception is mani-
fested. As Kant says, they constitute the thought of an object
in general: they are indeed concepts of the combination of a
manifold of intuition in general in one act of apperception, and
it is this combination which constitutes the essential nature
of an object qua object. But in themselves the categories do not
give us knowledge of any object. To know an object different
from myself, I require more than the concept of an object in
general (which I think in the categories): I require also an
1 Compare B 133 and B 138. In B 423 n. 'existence* in this sense is
said not to be a category, it is related, not, like the category, to an
indeterminately given object, but only to an object of which we have
a concept without yet knowing whether such an object is also 'posited*
apart from the concept. A form of thought has no objective validity
apart from the known possibility that there may be a corresponding
intuition.
2 I take it that for Kant we cannot, except by pure abstraction, be
conscious of the nature of our thinking apart from what is thought;
and there is no awareness of what is thought apart from inner sense.
3 In pure thought I may be said to combine the manifold of intuition
in general; but in order to determine my existence, a corresponding
combination of the manifold in time must be given to inner sense
through the transcendental synthesis of imagination.
LII § 5] INNER SENSE AND SELF-KNOWLEDGE 403
outer spatial intuition to give content and determination to my
concept. Similarly for knowledge of myself, besides self-
consciousness or the mere thought of myself (as a subject
thinking in accordance with the categories) I require an inner
temporal 'intuition to give content and determination to the
thought of myself. I exist indeed as intelligence, which is
conscious only of its own power of synthesis (in accordance
with the categories) ; but for the manifold that I must thereby
combine in order to have self-knowledge I am subject to a
limiting condition, namely, that the manifold must be given
to inner sense under the form of time. Hence the combination
or synthesis in question can be a combination of intuitions
only if it is in accordance with relations in time which lie
entirely outside the pure concepts of the understanding.1 Such
an intelligence can know itself only in relation to an intuition
which is not intellectual (or which cannot be given through
understanding itself). Consequently it can know itself only as
it appears in intuitions given under the form of time. It cannot
know itself as it is, nor as it would know itself if it were possessed
of intellectual intuition.
1 The text seems to he corrupt : I give the general sense.
CHAPTER LIII
SELF-KNOWLEDGE AND KNOWLEDGE OF OBJECTS
§ i. The Existence of Self
We have now seen that self-knowledge is more than con-
sciousness of the universal nature of thought. To know ourselves
A\e must not only think and be conscious of thinking: our
thought must, through the transcendental synthesis of imagina-
tion, 'affect* inner sense in respect of its form, which is time.
In this \\ay alone can our thinking receive a content, or
manifold, without which there can be no determinate exist-
ence or knowledge of determinate existence. But such
existence is existence in time, and therefore is phenomenal.
Consequently we can know our existence determinately only
as we appear to ourselves in time, and not as we are in
ourselves.
Such is the essence of Kant's doctrine, but we have still to
consider some of its further implications. These concern, not
only the existence and knowledge of the self, but also the
existence and knowledge of objects ; for apart from objects the
self could neither exist as a thinking being nor be aware of its
own existence.
We must first of all examine the difficult footnote1 in which
Kant summarises his general doctrine in regard to the existence
of the self.
The judgement 'I think* expresses the act whereby I deter-
mine my existence. Therefore in this judgement existence,
Kant maintains, is given.2 But such existence is indeterminate,
and the way in which I am to determine it is not given; for
the way in which 1 am to determine it is not merely a way in
which I think, but a way in which I have to posit or arrange
1B 1 57-8 n.
2 * I think' expresses, it may be noted, the act whereby any existence
is determined; but apparently it is only my existence that is given in
the act. Ib this because 1 can think without knowing?
LIII § i] SELF-KNOWLEDGE 405
in myself a manifold1 belonging to my existence. This manifold
is not given to thought in abstraction, but to inner sense or
self-intuition ; self-intuition presupposes time, as a form which
is given a priori; and this form is sensuous, not intellectual, a
form, not of the active thought which determines, but of the
passive sensibility which receives the manifold to be determined.
For knowledge of self (as for knowledge of anything else)
we require a determining activity of thought and a determinable
manifold. We have an intellectual conceptual consciousness of
the nature of our determining activity in abstraction from
what it determines, but we must not imagine that we have an
intellectual intuition of it. We should have such an intellectual
intuition only if all the manifold in the nature of the subject
were given by the mere activity of thought.2 Kant even implies
here that intellectual intuition would give us not a mere con-
sciousness of the general character of our activity — we have
that in any case — but the actual determining factor itself; and
it would give us this determining factor prior to the act of
determination,3 just as time gives us the determinable manifold
prior to its actual reception.4 The precise character of this
intellectual intuition is obscure, but Kant's main point is
clear enough: there is no such intellectual intuition in human
experience. That is to say, my consciousness of my thought
(or of my activity of determining) is purely conceptual ; it is not
intellectual intuition ; it gives us no manifold, and consequently
no determinate existence. By such conceptual consciousness of
my thought I cannot determine the existence of myself as a
1 Kant is assuming that existence cannot be determined by mere
conception, but only through connexion with a manifold; compare
A 218 =^ B 266. 2 Compare B 68.
3 I am not sure what Kant means by this, unless he means that it
would give us understanding in its real nature as a thmg-m-itself
independently of its manifestation in successive acts of determination
or thought.
4 I have added 'prior to its actual reception*. I take Kant to mean,
not that time gives us a pure manifold to be determined, but that
time, in virtue of containing a manifold of pure intuition, enables us
to know a priori (in its necessary temporal relations) the empirical
manifold of which time is the form.
4o6 TRANSCENDENTAL IDEALISM [LIII § 2
spontaneously active being. I can determine my existence as a
thinking being only by reference to a given manifold: I can,
in short, determine my own existence only so far as my thought
determines under the form of time a manifold given passively
to sense. Hence my existence cannot be determined other than
sensuously; and this means that it is determinable only as the
existence of an appearance in time. The fact that I can call
myself intelligence in virtue of my conceptual consciousness of
my own activity does not mean that thereby I can determine
my existence as it is in itself for understanding alone.
All this is complicated and difficult, as Kant puts it ; but I
am inclined to think he is trying to state something which is
both simple and true. If we are to know the existence of the
self we must pass beyond a mere conception of the formal
nature of thought. The self is known to exist only as thinking
something given to it in time ; and we cannot have knowledge
of our own existence apart from our knowledge of our existence
as a succession of definite thoughts, with definite objects, in
time. But if time is the form of our sensibility, it follows that
we can know ourselves only as an appearance in time, not as a
thing-in-itself.1
§ 2. The Existence of the Object
In all this we have little more than a restatement of what
we have already learned. The determination of my own existence
cannot take place by a mere thinking which is conscious only
of the nature of thought: it must always have reference to a
manifold given to inner sense under the form of time. But this
manifold, although it is given as a manifold of inner sense in
time because of the synthetic activity of the imagination, is not
itself given through that activity. The activity of imagination
merely takes up and combines in time what is given, according
to Kant, from without.2 The given which is thus taken up and
combined is given, primarily at least, to outer sense under the
1 Compare A 37 -- B 54.
2 This statement may require some modification in regard to
emotions and desires.
LIII §2] SELF-KNOWLEDGE 407
form of space ; and even the synthesis whereby it is combined
in time as a modification of inner sense is also (or at any rate is
accompanied by) a successive synthesis of the manifold in
space.
Whether I am observing physical objects, or constructing
mathematical figures in space, or determining the past history
of the physical universe, or of the human race, with the aid of
present evidence supplemented by causal law, I am always, not
only successively synthetising a manifold in space, but also
determining inner sense; for I am successively bringing a
manifold before the mind, and I am immediately aware of the
presence of this manifold to the mind.1 Hence in being aware
of physical objects and their changes I am also — from another
point of view — aware of a succession of ideas in my mind, this
succession of ideas being (as we have seen from the Analogies)
by no means necessarily identical with the succession of changes
in the objects which we know.2 Kant also holds that we can
make such a succession of ideas in inner sense intelligible only
by representing time imaginatively as a line, and representing
inner change through the drawing of a line: in fact we can
make the successive existence of the self in different states
imaginatively comprehensible only through outer intuition.
The reason for this is that we can be aware of changes, and
consequently of change in our ideas, only over against something
permanent; and the permanent is given to us only in space.3
This permanent, as we have seen in the Refutation of
Idealism,4 cannot be an intuition in me. I can determine the
change in my ideas, and consequently can determine my
existence during the time in which these ideas succeed one
another, only by reference to a permanent which is different
from my ideas.5
There is an obvious objection to this theory. I am supposed
1 Compare A 210 = B 255.
2 The identity between the succession of our ideas and the succession
of changes in the objects takes place only when we are directly observ-
ing an objective change. 3 See B 292 ; compare Chapter LI I § 4.
4 Compare Chapter LI § 3, II. 6 B XXXIX n.
4o8 TRANSCENDENTAL IDEALISM [LIII §2
to be immediately aware only of what is in me, namely, my
idea of outer things. It must therefore remain uncertain whether
there can be anything corresponding to my idea, and in par-
ticular whether there can be in space permanent substances
which can be distinguished from my changing ideas. This
objection Kant endeavours to meet.1
Through inner experience, he says, I am aware of more than
my ideas. I am aware of my own existence in time, and con-
sequently I am aware that my own existence can be determined
in time — by which I take him to mean that my existence can
be known to be, not merely at some time or other, but at a
definite time.2 Such determination of my existence in time is
possible only in relation to something which, while it is bound
up with my existence, is nevertheless external to myself. To
be conscious of my existence in time is to be conscious of a
relation to something which is external to myself; and only so
is it experience and not invention, sense and not imagination.
This implies that what is external to myself is inseparably
bound up with inner sense.
As we have seen,3 the words 'inner' and 'outer', 'internal' and
'external*, are by no means clear in such a context. If we are
speaking of an empirical or phenomenal object, to say that it
is an outer or external object is to say only that it is in space.
To say that it is an inner or internal object is to say that it is
only in time or possesses only temporal relations.4 The word
'outer' is, however, sometimes employed to indicate something
which exists as a thing-in-itself and is different from us. Since
such a thing-in-itself cannot be known at all, and still less can
be known to be permanent, there can be no question of such
a usage in the present context. Kant does indeed speak here of
the permanent as 'external to myself ; but by this he appears
to mean only that, as permanent, it must be different from the
successive and transitory ideas in which it is temporarily
1 BXLn.
2 Compare A 145 — B 184 for the schema of actuality.
3 Compare Chapter IV § 4.
4 A 372-3. Compare for space Chapter VII § i.
LIII §a] SELF-KNOWLEDGE 409
revealed: it is in short the permanent spatial substance to
which we refer our changing ideas as states or accidents. Kant
doubtless believes that the inner nature of such a substance is
a thing-in-itself which is different from me and wholly inde-
pendent of my knowing; but this inner nature is unknown to
me, and I have no ground whatever for regarding it either as
spatial or as permanent.
The phenomenal character of the permanent substance
external to myself is shown, not only by the statement that it is
inseparably bound up with inner sense, but also by the further
implication that it is revealed to outer sense. Unfortunately
what Kant says about outer sense in this connexion is obscure.
He appears to be giving a further reason why what is external
to myself is inseparably bound up with inner sense.1 The reason
is that what is external to myself is revealed to outer sense,
and outer sense depends for its reality (presumably its objective
reality or validity) upon the fact that it (as outer sense and not
mere outer imagination) is a condition of inner experience.
This argument, which I have simplified and abbreviated,
offers considerable difficulty in detail. Kant says that outer
sense is — I should prefer to say 'involves' — in itself a relation
of intuition to something actual outside me. He must, I think,
mean that a spatial intuition is distinguished from a mere
spatial image (such as we can invent in imagination) by the
fact that it is regarded as a state, or accident, of a permanent
substance in space.2 In this way a spatial intuition given to
outer sense has a reality, or an objective validity, which a mere
image has not. In the Analogies Kant claims to have shown
that spatial intuitions must be referred to permanent substances
in space, if \ve are to have experience of objects in one time
Here he asserts that spatial intuitions must be referred to
permanent substances in space, and so must have objective
reality, because this is a condition of the possibility of inner
1 B XL n. As often in Kant, this appears both to be a conclusion
from what precedes, and to receive support from what follows.
2 The fact that it is also the appearance to us of a thmg-m-itself
is, I think, here irrelevant.
4io TRANSCENDENTAL IDEALISM [LIII § 3
experience as an experience of change or succession in our
ideas. In other words — if there is to be inner experience at all,
outer sense must be genuine outer sense (not mere imagination) :
it must, that is to say, reveal to us permanent substances in
space, and so possess reality or objective validity.
Whatever be the difficulties of Kant's argument in detail, his
general position is clear. We can be aware of the succession of
our ideas in inner sense only if we set this succession over
against something permanent in space. Permanent spatial
substances are presupposed as a condition of outer and inner
experience alike. We therefore know a priori that there must be
such permanent spatial substances ; but their nature must be
revealed empirically to outer sense, and even their permanence
must, I think, find some confirmation in what is revealed
empirically to outer sense.1
§ 3 . Reality of Innw and Outer Sense
Kant adds some further considerations, which are com-
paratively simple.2
If the intellectual consciousness of my existence, in the
thought 'I am' (or 'I think'), were an intellectual intuition by
which my existence could be determined, consciousness of a
relation to something external to myself would be unnecessary.3
In human experience such intellectual consciousness, while
independent of inner intuition, requires to be supplemented
by inner intuition, and only so can my existence be determined.
Inner intuition is sensuous (or passive) and subject to the form
of time. The determination of my existence, and consequently
inner experience itself, is therefore a determination in time;
and since determination in time is impossible except by reference
to something permanent over against myself, inner experience
depends on the existence of such a permanent something or
substance. Apart from the curious statement that because the
permanent something is not in me, it must be in something
1 Compare Chapter XLII § 5. 2 B XI^-XLI n.
3 There would be no need to introduce inner sense and time and
the permanent. Compare Chapter LII§ 5.
LIII§4] SELF-KNOWLEDGE 411
outside me, all this adds nothing to what we are already
supposed to know.
Kant's conclusion is that for the possibility of experience
in general the reality of outer sense is necessarily bound up
with the reality of inner sense. In other words, I can know that
I exist determinately in time only if I know that there are
permanent substances in space which are revealed to outer
sense. Both of these kinds of knowledge — knowledge of the
self as thinking and knowing (as well as feeling and willing)
in time, and knowledge of physical objects existing permanently
in space — are equally necessary to what we call experience.
This seems to me to be true ; and it is a refutation of what is
ordinarily called idealism — the view that we have an immediate
knowledge of our own ideas or our own states, but that our
knowledge of spatial objects is at best inferential. It is not,
however, a refutation of transcendental idealism, which holds
that the existence of physical objects and the self is alike
phenomenal and is only an appearance to finite minds of a
deeper reality which lies beyond.
Two minor points are added. We have still to distinguish the
images and illusions of imagination from genuine intuitions of
objects (not only physical objects but also ourselves): this we
do by means of the Analogies.1 And we must not confuse our
idea of something permanent in existence with a permanent
idea. We have no permanent idea.2 Our idea of the permanent
and even of matter is liable to change ; but it always refers to
something permanent in space, whose existence is necessarily
involved in the determination of my own existence. Inner and
outer experience constitute only one experience; and there
could be no inner experience unless it was at the same time
also partly an outer expeiience, that is, an experience of
permanent objects in space.
§ 4. Ideality of Inner and Outer Setisc
The doctrine we have just examined may be described as
Kant's empirical realism. It establishes what he calls the 'reality'
1 Compare Chapter LI § 6. 2 Compare B 292
4i2 TRANSCENDENTAL IDEALISM [LIII § 4
of inner and outer sense.1 The one experience which we have
consists of more than mere ideas : it reveals to us both a pheno-
menal self whose ideas succeed one another in time and a world
of permanent phenomenal substances in space. We must now
turn to that aspect of his doctrine which may be described as
transcendental idealism, the doctrine that the self and the
world so revealed are only phenomenal: we cannot penetrate
into their inner nature as they are in themselves. With this
doctrine and its grounds we arc familiar; but we have still to
consider some additional arguments which he added in the
second edition in order to confirm the theory of the 'ideality'
alike of inner and of outer sense.'2
If we set aside feelings of pleasure and pain and also the
will, and consider only knowledge, everything that belongs to
outer intuition is said to contain nothing but relations. These
relations are identified with extension (relations of place),
motion (or change of place), and moving forces (described
rather strangely as la\\s in accordance with which change of
place is determined). In this obviously more than mere intui-
tion is involved. What Kant has in mind are the primary
qualities revealed by means of outer intuition, and it is these
primary qualities which he reduces to mere relations.
Although we know these relations, \\e do not know what it is
that is present in a place3 or what (apart from change of place) is
really at work in the things as they are in themselves. Position,
motion, and force, in so far as they are bound up with space,
which is only a form of our sensibility, can reveal reality only
as it appears to us, not as it is in itself; but Kant reinforces
his established doctrine by the further contention that these
things are all relational, and through mere relations we cannot
know a thing as it is in itself. In order to do this we should
require to know what it is that is related: we should require
to know the inner character of the object itself.
If Kant's premises are correct, the conclusion seems to
J Compare B XLI n. 2 B 66 ff.
3 Strictly speaking, a thing-m-itself is not piesent in a place, though
it appears to us as present in a place.
LIII§s] SELF-KNOWLEDGE 413
follow. He may, I think, even be right in saying that if outer
sense gives us only relations (and not the inner nature of the
thing which appears in these relations), then it gives us only
the relation of the object to the subject ; for this seems to mean
that it gives the object only as it appears to the subject, or as
it is in relation to the subject, not as it is in itself.
If this is true of outer sense, it must equally be true of inner
sense ; for in the first place the ideas of outer sense constitute
the proper stuff of inner sense; and in the second place we
may assume that if outer sense gives us only relations which
are in some way spatial, inner sense will give us only temporal
relations, and the same general argument will apply.
The second contention Kant expresses in a very elaborate
form, and his reference to relations is not developed in the
same direct way as it is in regard to space. Instead it is used to
support the view that time is only a form of intuition, and
from this the required conclusion follows. But \\e must examine
the argument in more detail.
§ 5. Time and Inner Sense
According to Kant we 'posit' the ideas of outer sense in
time. I am not sure whether he means only we must take up
and combine these ideas successively and be aware of the suc-
cession in our minds, or whether he means also (as the word
'posit' suggests) that we must assign to these ideas a position
in what we take to be the development of the physical world.
In any case he insists that time is a prior condition of our
consciousness of spatial ideas in experience — though apparently
it is not so in a purely animal Erkbnis. As such a prior and
formal condition, time conditions the way in which \\e posit
spatial ideas in the mind j1 and it contains in itself the relations
of succession, simultaneity, and permanence — the permanent
being what coexists with a succession.2 These relations are
1 B 67. The words 'in the mind' perhaps support the former
alternative mentioned above.
2 The reference to the permanent (which is not in the mind) supports
the second alternative mentioned above.
4H TRANSCENDENTAL IDEALISM [LIU § 5
identical with what he calls elsewhere the 'modes' of
time.1
Instead of going straight on to assert that inner sense, as
concerned only with temporal relations, cannot give us reality
as it is in itself, Kant proceeds to (what I take to be) a descrip*
tion of time. That which as an idea can be prior to all activity
of thinking any object2 is intuition; and if it contains only
relations, is the form of intuition.3 The inseparability of such
a form from the matter of which it is the form is shown by
Kant's statement that this form represents nothing except in
so far as something, presumably outer intuition, is posited in
the mind.4
From this last assertion Kant makes an inference which is
curiously expressed. This intuition or this form of intuition
(which, I take it, can only be time) is nothing other than the
way in which the mind is affected through its own activity,
namely, through this positing of its idea,5 and therefore through
itself. He further describes this 'way' in which the mind is
affected through itself as 'an inner sense in respect of the form
of that sense'.6 This seems an unnecessarily elaborate method
of saying what we know already — that time is the form of
inner sense.
1 A 177 — B 219. Compare A 182-3 =~= B 225-6 and Chapter
XXXIX §3.
2 Sueh priority need not be, and probably is not, temporal priority;
but it is less objectionable to ascribe temporal priority to intuition
than it is to ascribe temporal priority to thought (or to the form of
intuition in relation to intuition itself). For Kant intuition is given
independently of thought (A 90 ^- B 122).
3 Compare B 160-1 n., where the form is said to contain only a
manifold without unity. Incidentally this passage also suggests that if
unity is necessary for intuition, then intuition cannot be given apart
from thought. This would not imply that the manifold of intuition
could not be given apart from thought. Sec also A 107.
4 Compare A 452 n. = B 480 n.
5 B 67-8. I should have expected 'ideas' in the plural.
6 This seems to mean that the mind is affected passively from
within, and that such affection is necessarily under the form of time :
it necessarily produces a succession of ideas. A little later he says
that the way m which the manifold is given in the mind apart from
spontaneity must be called sensibility.
LIII§6] SELF-KNOWLEDGE 415
Kant's main point appears to be that inner sense, or at least
time as the form of inner sense, can arise only because the
mind is affected by the activity which posits ideas in the mind.1
But if he is adding anything to what we have already learned,
I must confess I do not know what it is. I am not even certain
what he means by 'positing/ unless he means 'taking up' and
'combining'.
§ 6. Inner Sense and the Phenomenal Self
Kant insists that everything known through sense is so far
always appearance.2 The reason for this I take to be that sense
is always conditioned by a form of sensibility. In any case, if
we accept the premise, we must either deny inner sense, or
else admit that the subject known through inner sense can only
be the subject as an appearance or phenomenon — not the subject
as it really is, and as it would be knowrn to itself if it possessed
an intellectual or active (as opposed to a sensuous or passive)
intuition. Assuming that we do not possess an intellectual
intuition, Kant insists that the only difficulty is to understand
how a thinking subject can have an inner sensuous intuition of
itself. This we cannot explain ;3 but it is simply a fact, and so
is a difficulty common to every theory.
On Kant's view we admittedly possess an active intellectual
consciousness of the self in apperception, which he identifies
here with the simple idea T (equivalent to 'I am' or 'I think').
If through this idea alone all the manifold in the subject were
given by means of its own activitity, we should have an inner
intellectual intuition, and nothing more would be required. In
human beings, and indeed in all finite beings, determinate
knowledge of the self (which always involves a manifold)
requires, in addition to apperception, an inner perception of
a manifold which is given in the subject independently of
thought.4 Such an inner perception must therefore be sensuous
1 Compare A 2 10 = B 255. 2 B 68. 3 Compare B XLI n.
4 This is, I think, already implied in the fact that the manifold is
not given in thought.
4i 6 TRANSCENDENTAL IDEALISM [LIII § 7
and passive; or (in Kant's elaborate terminology) the way in
which the manifold is given in the mind apart from spontaneity
must (because the manifold is given apart from spontaneity) be
called sensibility.
All this is common form and offers no difficulty. His method
of stating his conclusion is not so simple. If the active intel-
lectual faculty of self-consciousness (here manifestly including
imagination as well as thought) is to seek out, that is, to appre-
hend or take up, what lies in the mind, it must so far affect the
mind, and only in this way can it produce an intuition of itself.
The form (or a priori condition) of this intuition, however,
has its origin in the mind as passive, and it determines, in the
idea of time, the way in which the manifold is together in the
mind.1 Hence the mind intuits itself, not as it would if it
knew itself by an active intellectual intuition, but in accordance
with the way in which the mind is affected by its own activity
from within. In other words, the mind intuits itself, not as it is
in itself, but only as it appears to itself.
Kant's conclusion is obvious enough on his premises; but
the details of the \vay in which the mind affects itself, I am
sorry to say, still elude me, though I have no doubt that he is
trying to say something of real importance. The general direc-
tion of his thought is clear enough.
§7. Appearance and Illusion
We must guard against a possible misunderstanding of all
this.2 We have seen that by outer intuition we know spatial
objects only as they affect the mind, and by inner intuition we
know the self only as it affects the self. That is to say, since
such affection is conditioned by space and time, which are only
forms of our sensibility, we know objects, and we know the
self, only as they appear, and not as they are in themselves.
1 I think the togetherness of the manifold in the mind must be the
result of the activity, not (like the manifold and the form of time)
given in the mind as passive ; but the kind of togetherness (as temporal)
is conditioned by the fact that the nature of time depends on the
passivity or sensibility of the mind. 2 B 69.
LIII § 7] SELF-KNOWLEDGE 41?
This must not be taken to imply that objects and the self, as
known, are alike illusions.1 In appearances, as opposed to
illusion or mere seeming, the objects are regarded as something
really given ; and this is true even of the characteristics which
we attribute to them, but with this qualification — that in the
relation of the given object to the knowing subject the charac-
teristics in question depend (for their universal form) upon the
kind of intuition possessed by the subject. That is to say, the
characteristics of the object are transmuted in so far as they
must be intuited by a subject, the forms of whose sensibility
are space and time. For this reason we must distinguish the
object as appearance from the same object as it is in itself.
There could hardly be a clearer statement of Kant's view
that an appearance is not a mere product of our own mind taken
as a reality; if it were, it would be an illusion.2 An appearance
is always the appearance of a thing wholly independent of our
mind and existing in its own right. Even the spatial and temporal
characteristics which it possesses are appearances of real
characteristics of the thing as it is in itself. Because of the
nature of our mind things must appear to us as spatial and
temporal ; but it is because of the character of the thing-in-itself
that we see one object as round and another as square.3 We do
not know what this character is, but we cannot regard it as
roundness or squareness, because we cannot regard it as spatial
at all. Indeed we know the thing only as it appears to us, or
as it is in relation to our minds ;4 and consequently we do not
know whether we can rightly speak of it as 'existing' or possess-
ing 'characteristics/ since for us these terms must imply a
reference to time and space.
Hence Kant does not say that bodies merely seem to be
outside us, or that the soul merely seems to be given in my self-
consciousness. This would imply that a body and a soul might
be a mere illusion, and not the appearance ot an independent
reality. For Kant such a doctrine is unthinkable. What he holds
is this: that the spatial and temporal character of bodies and
1 Compare B XL n. and A 396. 2 Compare A 396.
3 Compare Chapter Vi § 8. 4 Compare B 67 and B 70 n.
VOL. II O
4i8 TRANSCENDENTAL IDEALISM [LIII § 8
souls, the 'quality' of space and time in accordance with which,
as a condition of their existence for me, I must posit the one
and the other — this lies wholly in the nature of my intuition,
and not in the thing as it is in itself. It would be my own fault,
if out of that which ought to be reckoned as appearance, I made
a mere illusion.
Such an error is not the result of recognising the ideality of
space and time, and so of all our sensuous intuitions. On the
contrary, this error arises from regarding space and time as
characteristics of things-in-themselves — a doctrine producing
so many absurdities and contradictions that the whole world of
space and time becomes a mere illusion, as Kant imagined
that it did in that philosophy of the 'good' Berkeley of which he
appears to have had so little exact knowledge.
§ 8. Difficulties of Inner Sense
It will be observed that our examination of inner sense rests
primarily on passages added in the second edition. This is
partly due to the fact that in the first edition this problem was
treated chiefly in the Paralogisms, which lie outside the scope
of the present book. It is also partly due to the fact that in the
second edition Kant was attempting to dispel misunderstandings
of his theory, and felt obliged to articulate more fully his doctrine
of inner sense and its relation to permanent substances in
space. These two doctrines are closely bound up together. A
fuller discussion of them is impossible without trenching upon
the argument of the Dialectic. Here I can only register my
opinion that both these doctrines are essential to the Critical
Philosophy,1 and that what is added in the second edition is
not a correction, but a development, of what Kant has held
all along.
When I say this, I have no wish to deny that Kant's whole
theory is difficult, and in some of its details very difficult. But
I find in it no trace of the contradictions and the muddle so
commonly attributed to him by his critics. Kant suffers from
1 I am glad to have at least the partial support of the Master of
Balhol on this point; see Lindsay, Kant, p. 53.
LIII § 8] SELF-KNOWLEDGE 419
the weakness common to all human thinking, especially where
that thinking is not content to achieve clarity at the expense of
being superficial. Some of the difficulty in his thought is due
to the fact that he is dealing with a difficult problem, and I am
far from suggesting that he has given a final solution. I think
it is true to say that a fuller working out of his doctrine is
urgently required. But the alleged muddle seems to me largely
the invention of critics, who too often continue to repeat charges
which rest on little or no evidence and sometimes on complete
misunderstanding.
If we are to know our own thinking and thereby to determine
our existence as thinking beings, it is not enough that we should
conceive the necessary unity of thought or even the necessary
forms of judgement in which that unity is manifested. The
universal nature of our thinking, if we separate it from what
we think, does not by itself give us grounds for describing the
kind of existence which we as thinking beings possess: it is
only by Paralogisms of Reason that we claim on this basis to be
substances, immaterial, incorruptible, personal, and therefore
spiritual.1 We can determine the existence of our thought, and
of ourselves as thinking beings, only as we have a direct aware-
ness of what we think and know — a direct awareness that such
and such is present to our minds. Such a direct awareness is
inner sense, and what is present to our minds is thereby revealed
to us under the form of time as a succession of ideas.
On Kant's view all our thinking involves, at least ultimately,
an imaginative synthesis of a manifold passively received by
sense.2 So far as this thinking can claim to be knowing and
to have an object which is more than its own creation, there
must be a transcendental synthesis of the imagination which
combines the given manifold in one space and time. This
combination, on Kant's theory, must always be in accordance
with the categories of the understanding ; but the crucial con-
1 Compare A 345 = B 403.
2 Compare A 19 = B 33, A 51 = B 75, A 77-8 = B 103. We need
not here consider the complications involved in highly abstract thinking
such as Kant's own thinking in the Kritik.
420 TRANSCENDENTAL IDEALISM [LIII § 8
tention for our present purpose is specially concerned \vith the
category of substance. If we are to know a world in one time
and space, our outer intuitions must be referred to permanent
spatial substances as their accidents. This we are doing at
every moment: Kant insists that our awareness of our own
thinking and knowing is always an awareness of ourselves as
thinking and knowing a permanent spatial world ; and indeed
that it must be so ; for if it were not so, we could not even be
aware of the succession of our own ideas . This is the precise con-
trary of an idealism which claims that we know only the succes-
sion of our own ideas and make doubtful inferences to a world
of bodies in space.
Taken thus, Kant's doctrine seems to me to be true. He is
also surely correct in saying that what is directly revealed to
us as before our minds and so as our idea is, and must be,
revealed successively in time (just as the objects which we
distinguish from ourselves are, and must be, revealed to us as
external to one another in space). We know immediately only
the time at which objects appear to us or are our ideas: the
time which we ascribe to them as objects we know, not imme-
diately, but as a result of thought. I have immediate knowledge
of the fact that I am thinking about the Critical Philosophy now.
I can have no such immediate knowledge of the fact that the
Critical Philosophy was produced before I was born.1
If Kant is right in holding that because time is necessary
and universal, it is therefore only a form of our sensibility, his
conclusion immediately follows that the self (and indeed any
object) revealed to us as temporal cannot be revealed to us as
it is in itself.2
1 The fact that when I watch a moving body, the motions take
place in the same time (at least approximately) as I perceive them is
no exception to this principle. It is only by thought I can know that
what I experience is an objective succession ; for the succession of my
perceptions is equally compatible with objective coexistence.
2 Or, more strictly, we cannot know that it is in itself as it is revealed
to us ; but the possibility that time should be both a form of sensibility
and a character of things-m-themselves is not worth considering, when
there can be no grounds whatever known to us why this should be so.
Compare Chapter VIII § 8.
LIII § 8] SELF-KNOWLEDGE 421
The most difficult part of Kant's doctrine is his account of
the way in which the self is affected by itself from within.
The self in its direct awareness of its own thinkings and
knowings — it is not the place here to consider its feelings and
volitions — must be passive, though it must also have, in the
act of thinking itself, an active conceptual awareness, however
obscure, of the necessary unity and form of thought. The
manifold or content of our thought must be given to a mind
which receives it passively and perceives it immediately: our
awareness of what we think and know is not a creating of what
we think and know. It is here that the complications begin ; for
the manifold must originally be given to outer sense. If the
manifold is given to outer sense, docs not this imply that we
are aware of it ? And if we are aware of it, are we not aware of
it as before our minds ? And if so, is it not given to inner sense
as well ?
On this point Kant gives us, so far as I know, no clear
statement; but his account of animal Erlebnis (which cannot
strictly be called experience) suggests that awareness of spatial
intuitions is possible apart from inner sense. Such an awareness
would be, I take it, momentary: it would not be awareness of a
succession, and still less of an object distinct from the self. To
be aware of a succession I must take up, run through,
reproduce, and hold together, or in one word synthetise, the
manifold. This synthesis must be also a synthesis of space and
time, and it is so far a transcendental synthesis of imagination
without which there could be for us no succession and no
time, and perhaps (though this is more doubtful) no space.1
According to Kant, when the mind is affected by itself, inner
sense is affected by this transcendental synthesis of imagination
and so ultimately by the understanding; for the transcendental
synthesis of imagination combines the manifold in accordance
with the principles of synthesis involved in thinking itself.
The general direction of Kant's thought seems to me sound,
and there is nothing arbitrary or unreal about his problem, but
there are many difficulties. Time is not a product of the trans -
1 There could certainly be no physical measurable space.
422 TRANSCENDENTAL IDEALISM [LIII § 8
cendental synthesis, but is the form of inner sense. It originates,
like space, in the nature of the mind, but of the mind as passive :
in this respect it is given to thought and imagination, not
created by them. Yet without the synthetic activity of thought
and imagination, it could not have unity, and it could not be an
intuition (or object of intuition). Furthermore, since the synthetic
activity of thought and imagination is itself successive, it clearly
presupposes time ; and this is perhaps another reason why time
must belong to inner sense. Kant will certainly not allow us on
this ground to maintain that time must be something real.1 If,
on the other hand, we suggest that our synthetic activity is
timeless, unconscious, and noumenal, we not only contradict
Kant's express statements,2 but \ve contradict ourselves; for
we are claiming to describe in detail what we assert to be
unknown and unknowable ; and we are describing as timeless a
synthesis \\hich is intelligible to us only because it is, and must
be, successive.3
Whatever be the difficulties in regard to time — and these are
not peculiar to Kant — he is surely right both in maintaining
that time, like space, must be given, and yet that we can be
aware of it, and of succession in it, only by an act of synthesis
which holds together the past and the present.4 We can also,
I think, understand how the synthetic activity of the mind
working upon a given manifold, not only constructs the
phenomenal world which we know (a world extended in space
and lasting through time), but also gives to our inner sense
that whole world as a succession of ideas in us ; for all awareness
of that world is also an immediate awareness of it as present
to our own minds.
In this again there are difficulties of which Kant gives no
detailed discussion. In knowing the world we are, so to speak,
1 See Chapter VIII § 9.
* The mere fact that our thoughts are said to be objects of inner
sense — compare A 342 = B 400 and A 357 — shows how far Kant is
from regarding our thinking as timeless or unconscious. Compare also
B 154 and B 156. See Chapter XXXI §§ 4-6. 3 Compare B 292.
4 This certainly holds for any determinate measurable time, and I
am inclined to think that it holds even for the specious present.
LIII § 8] SELF-KNOWLEDGE 433
making our own mental history; and nothing that we know,
or have known, is without its place in that history. Furthermore,
since knowing is conscious, in knowing our world we are aware
of our mental history. Nevertheless we can turn back and reflect
upon our mental history, and treat it as only a part, and a very
small part, of the world which we know. This is recognised by
Kant, and is indeed regarded by him as an essential element in
all experience ; for he holds that all consciousness of the succes-
sion of our ideas, and still more all determination of the time
at which our ideas occur,1 is possible only in relation to a world
of permanent substances, whose accidents change in an objective
time which must be distinguished from the time in which we
perceive them.
In the Analogies Kant has given an account of the principles
in accordance with which we determine the time of objective
events. He has omitted to give a similar account of the way in
which we determine the time of our own thinkings and per-
ceivings. No doubt he holds that there too the same principles
are at work;2 but in the absence of greater detail some critics
have thought that the categories cannot apply to the self. This
seems to me to be a mistake except in regard to the category
of substance ; and here, although the question is full of difficulty,
I am inclined to think that from one point of view Kant must
regard our thoughts as the accidents of our body ; but this is a
conclusion which, for whatever reason, he certainly fails to make
explicit.3
The difficulties which we have to face may legitimately raise
the question whether it is possible to think out Kant's system
consistently. An attempt to solve these difficulties would demand
a book to itself; and I must be content if I have made com-
paratively clear what his problem is. I should like to think that
1 Sec B 156 and Chapter LI I § 4.
2 See Chapter LI § 6 and § 3 above.
3 The best discussion of the application of the categories to the self
is to be found in Ewmg, Kant's Theory of Causality, Chapter VI.
This is perhaps the most valuable, as it is the most independent, part
of a too much neglected book, which has the great merit of being
clear even where (m my opinion) it is mistaken.
424 TRANSCENDENTAL IDEALISM [LIII § 9
I have shown it to be a real problem, and that the difficulties
in his doctrine are at least partly difficulties which arise from
the very nature of human experience itself.
§ 9. A Rough Analogy
It is no part of the philosopher's task to substitute images
or parables for thinking. Such images and parables are bound
to be inadequate, and likely to be misleading. Nevertheless it
may perhaps help the beginner, at least a little, if I develop
very briefly the analogy of which I have already made use.1
I suggested2 that Kant probably regarded reality as made
up of monads. The mind of man is, however, not a windowless
monad, but looks out through its windows at reality. We may
consider the colour or distortions in the glass of these \\ indows
as imposing certain universal characteristics upon the objects
we see ; and this is parallel to the imposition of a spatial character
on all objects by the nature of our sensibility.
We have now to add that for experience it is not enough that
our windows should be affected from without: they must also
be affected from within. There is, as it were, a film of steam
continually forming on our windows ; and it is only as we remove
this film, now from one part and now from another, that we
can see different parts of the outside reality. It is this internal
action on our part which makes us see the outside reality as a
succession ; and it is also this internal action which enables us
to see our own inner nature, and to regard the appearances of
the outside world as, from one point of view, changes on the
surface of the windows of our own mind.
We might perhaps also, and in some ways better, regard the
windows of our mind as photographic plates. They must be
acted upon from without, if anything is to be seen on them.
But they must also be treated chemically trom within; and
this successive affection from within brings out successively
the different results of the affection from without. This image
1 Sec Chapter VIII §§ 3, 8, and 10.
2 Chapter VIII § 10.
LIII § 9] SELF-KNOWLEDGE 425
perhaps does more justice to Kant's use of the word 'affection';
but it fails to bring out what I believe to be the heart of Kant's
doctrine — that what we are aware of in intuition is no mere
effect of an outside reality, but is a direct appearance to us,
through the medium of our own sensibility, of that very
reality itself.
VOL. II
CHAPTER LIV
THE TRANSCENDENTAL USE OF CONCEPTS
§ i . Empirical Realism and Transcendental Idealism
The philosophy of Kant is always to be conceived as empirical
realism and transcendental idealism. These two main aspects of
his doctrine are so closely inter-related that neither is intelligible
apart from the other; but in the last three chapters we have
considered primarily his empirical realism — the theory that
we have direct knowledge both of a self \\hich thinks and feels
and wills in time and of permanent physical bodies which
interact in space. These two kinds of knowledge constitute one
single human experience. We must not imagine that our
knowledge of bodies is merely inferential: if we had no direct
knowledge of permanent physical substances in space, we could
have no knowledge of our own successive mental states.
We have now to consider the other side of Kant's doctrine —
his transcendental idealism. The self and the bodies which we
know are in themselves realities which are not created by our
knowing: Kant never doubts that they are what they are,
whether we know them or not. On the other hand we do not,
and we cannot, know them as they are in themselves. We know
them only as they are in relation to us, or as they must appear
to finite minds whose knowledge, or experience, is made up of
two elements — thought and intuition. All objects known to us
must be given to intuition under the forms of time and space,
and must be thought by means of categories which spring from
the nature of thought itself. Things as objects, or as known to
us, have therefore a universal form1 imposed upon them which
has its origin in human sensibility and human understanding.
Hence Kant's doctrine may be called formal idealism — the
universal form of the objects we know is due to the human
1 It is only the universal form which is imposed. All differences
between objects are due to differences in the matter, and the matter is
not imposed but given.
LIV§2] TRANSCENDENTAL USE OF CONCEPTS 427
mind, and not to things. The self and the world as known to
us is therefore only phenomenal : apart from human experience
there would be no space and time, and no spatial and temporal
world. What would remain would be the thing as it is in itself,
but we have no reason to regard this as spatial or temporal, and
consequently no reason to describe it as either changing or
permanent.
The limitation of our knowledge to phenomena and our
ignorance of the thing-in-itself is the one problem which has
still to be discussed. This problem Kant claims1 he has already
solved in the course of the Analytic. All we require now is a
summary statement of our solution, a bird's-eye view which
may strengthen our conviction. We shall see that we can, and
must, be content with our knowledge of the phenomenal world,
since we have no means of other knowledge; and we shall
understand more clearly the title under which we possess what
knowledge we have.
To any one who has understood Kant's argument the present
exposition, if wre except the passage omitted in the second
edition, is so easy that it hardly requires a commentary. The
first part especially2 is, as he says, little more than a summary
of his previous argument ; but he gives in it a clearer indication
than he has yet given, at least in the first edition, of what he
means by a pure category, and he also deals with the nature
of the pure categories separately. In the second part,3 although
he is still working out the implications of his doctrine, he
breaks what is to some extent new ground in his discussion of
phenomena and noumena, although here also there is more
preparation for this discussion in the second edition than there
was in the first.
§ 2. The Empirical Use of Concepts
We have seen that the understanding derives from itself
certain pure concepts or categories.4 These are not, like
1 A 236 -- B 295 ff. 2 A 235-48 = B 294-305.
3 A 248-60 = B 305-15. 4 A 236 = B 295.
428 TRANSCENDENTAL IDEALISM [LIV §2
empirical concepts, merely borrowed from experience by
abstraction. Nevertheless they can be applied only in experience.
That is to say, they are only of empirical use or application:
they have as objects only what is given to intuition under the
forms of space and time.
The universal application of the categories to all objects of
experience is formulated in the Principles of the Understand-
ing. These Principles, whether mathematical or dynamical, are
said to contain, as it were, only the pure schema of possible
experience. They state the general framework into which the
given manifold must be fitted (or, less metaphorically, the
principles of combination to which the manifold must conform),
if experience is to be one. The unity of experience is that
necessary synthetic unity which the understanding, from its
own nature, contributes to the synthesis of imagination so far
as that synthesis is determined by apperception and not by the
given manifold.1 The unity of thought, without which there
could be no experience, demands that the given manifold,
whatever it may be, must be combined by the transcendental
synthesis of imagination in one space and time; and Kant
claims to have proved that such a combination of the manifold
in one space and time must be in conformity with the pure
categories of the understanding. Hence appearances, as data
for a possible experience, must possess the necessary synthetic
unity which is thought in the categories and articulated in the
Principles.
It may be suggested that all this is of comparatively little
importance. No doubt these Principles express the rules by
which understanding is actually guided. They are not only a
priori truths themselves, but the source of all truth. Apart
from them there can be no truth, that is, no correspondence
between knowledge and its object, since apart from them there
can be no object; in Kant's language they contain the ground
of the possibility of experience (as the totality of all know-
ledge) in which objects can be given to us.2 Yet when all is said
1 Compare A 118. The synthesis of imagination as so determined
is transcendental. 2 A 237 — B 296.
LIV § 3] TRANSCENDENTAL USE OF CONCEPTS 429
and done, we have learnt no more than we actually presuppose
and apply in our ordinary empirical thinking. Has it really been
worth all the trouble we have taken ?
Kant protests — apparently forgetting that the reader has
followed him all this weary way — that no kind of inquisitiveness
is more detrimental to the extension of human knowledge than
that which1 asks what is the use of an enquiry before we have
undertaken the enquiry, and before we are in a position to
understand that use, even if it were clearly explained. There is,
however, one use of our transcendental enquiry which can be
made intelligible, and even important, to the most reluctant
student. An understanding which occupies itself only in
ordinary empirical thinking, without reflecting on the sources
of its knowledge, can get on very well in its own way; but it
can never determine the limits of its own knowledge. It can
never know what is inside and what is outside its own sphere.
Consequently without the difficult enquiries \\e have made, it
can never be sure of the soundness of its claim to possess
knowledge; and it must expect to meet humiliating reproof
when, as is inevitable, it steps beyond its own boundaries and
wanders in error and illusion.
Hence the doctrine that the Principles of the Understand-
ing, and indeed all concepts without exception, have only an
empirical application is one which, when it is really known and
understood, carries with it the most important consequences.
§3. The Transcendental Use of Concepts
Against the empirical use of concepts we must set their
transcendental use.2 In the empirical use the concept is applied
only to appearances, that is, to objects of a possible human
experience. In the transcendental use it is applied to things in
general, that is, to things-in-themselves. These things-in-
themselves may be described, in accordance with one of Kant's
1 I differ here from Kemp Smith's translation.
2 A 238-9 = B 297-8. Compare A 56 =* B 81 and ; Chap-
ter XI § 4.
430 TRANSCENDENTAL IDEALISM [LIV § 3
own notes in his copy of the Kritik, as objects given to us in
no intuition, and consequently not sensible objects.1
It is commonly held that Kant should have termed this use
'transcendent' rather than 'transcendental'. Such terminology
would, however, be at variance with his own distinction between
a 'transcendent' and a 'transcendental' use.2 The point is of no
great importance, and Kant may mean by a transcendental use
merely one which transcends the limits of experience by accident
or by lack of criticism, whereas a transcendent use is one which
transcends the limits of experience by a kind of necessity. But
it seems to me possible that by a transcendental use he means
one in which, not only the origin of a concept, but its actual
application, may be entirely a priori. Such an application is
always illegitimate, and strictly speaking there is no trans-
cendental use of concepts at all.
If a concept is to give us knowledge of objects, two things
are necessary. First, the concept must have the logical form of
a concept in general, and this Kant identifies with the form of
thought. By this, I think, he means more than that the concept
must not be self-contradictory. He means that it must possess
universality ; and this it can possess only as the predicate of a
possible judgement.3 To conceive is to judge, and if so every
concept must have the form of thought.4
The important point, however, is the second one: we must be
1 Nachtrage CXVII. 2 Sec A 296 -= B 352. 3 A 69 = B 94.
4 Hence it must either be a category or presuppose the categories.
This is the reason why all concepts are a source of necessity: see
A 105-6 and compare B 142.
Kant also says that every concept must contain the logical function
of making a concept out of some kind of data — data in general. The
function (or form) here looks like the function of making concepts
by analysis and abstraction: see A 68 = B 93, A 76 = B 102,
A 78 — B 104. But we have seen that the same function which gives
unity to different ideas (or objects) in a judgement by that act of analysis
whereby concepts are made also gives unity to the bare synthesis of
different ideas in an intuition : see A 79 — B 104. Hence every concept
is the concept of a synthesis, and the categories are concepts of the
universal synthesis which is present in, and presupposed by, all
empirical synthesis and all empirical concepts.
LIV§4] TRANSCENDENTAL USE OF CONCEPTS 431
able to show that there can be given an object to which the
concept may be related. Apart from this the concept contains
only the form of thought and nothing more. But for human
beings an object can be given only to sensuous intuition.
We haVe indeed pure sensuous intuitions (of time and space)
which arc logically prior to given objects; but even they can
have objective validity, or application to an object, only if the
object is given to empirical intuition.1
It follows that all concepts, and consequently all Principles,
however a priori they may be, must in the last resort be related
to empirical intuition. Without this they have no objective
validity, but arc a mere play of imagination, or of understanding,
with the ideas that belong to them respectively.2
A transcendental use of concepts, therefore, inasmuch as it
affects to have no need of empirical intuition, is quite incapable
of giving us knowledge of any object.
§ 4. Mathematical Concepts
This doctrine is illustrated by examples. Let us consider
the case of mathematical concepts, taking them first of all 'in
their pure intuitions'.3 This phrase is difficult, unless Kant
means that they have a secondary reference to empirical
intuitions.4
Space has three dimensions : between two points there is only
one straight line. Such are the principles, or axioms, on which
1 Strictly speaking, I think it is the concepts of spatiahty and
temporality, rather than the intuitions of space and time, which have
objects given to empirical intuition.
2 The elements or marks in empirical factitious concepts are
arbitrarily combined by imagination. In applying the categones to
things-m-themselves, we have an arbitrary play, not of imagination,
but of understanding. J A 239 = B 298-9.
4 The examples given seem to be what Kant calls axioms ; com-
pare A 163 = B 204 and A 31 = - B 47. This may not have any par-
ticular significance, and I do not see that it can have any special
:onnexion with the phrase 'in their pure intuitions*. It shows, how-
ever, clearly enough that Kant believes a combination of thought and
ntuition to be necessary, if we are to know space and time as objects.
Compare Chapter V § 8 and also B 160 n. and A 107.
432 TRANSCENDENTAL IDEALISM [LIV § 5
Euclidean geometry rests. Their object I take to be space as
such, and according to Kant our idea of it is produced a priori
in the mind. Yet although these principles are thus entirely
a priori, they would have no significance — that is to say, we
could not know that they referred to a possible object — unless
we could exhibit their significance in appearances (or empirical
objects).
Hence if we take a concept in abstraction from its object, and
wish to make certain whether it is the concept of an object, we
must make the concept sensuous;1 that is, we must exhibit an
object corresponding to it in intuition. Apart from this, a
concept is without sense2 or objective significance.
This requirement mathematics fulfils by the construction of
a figure. Such a figure is constructed a priori in accordance
with a concept; but it is nevertheless, whether constructed in
imagination or on paper, an appearance present to the senses.
In mathematical reasoning we attend only to the elements in
it which are the necessary consequences of construction in
accordance with the concept: its merely accidental features are,
or at least ought to be, entirely ignored.3
§ 5. The Categories
Kant's main concern is with the categories. He turns naturally
to the category of quantity,4 the fundamental category of mathe-
matics, and so makes a transition to categories in general.
The category of quantity finds its sense and significance in
number, which is its schema. Number is employed in arithmetic,
1 Compare A 51 -- B 75.
2 It seems to me quite clear that Kant is playing on the ambiguity
of the word 'sense*.
3 Compare A 713-14 •- B 741-2. It is commonly said that in the
first proposition of his first book Euclid failed to do so ; for he assumed
from looking at the diagram that two circles could intersect only in
two points, and this requires to be proved. If this cannot be seen
directly to follow, without proof, from the very nature of a circle as
defined, then he made the mistake of mixing up empirical with a priori
evidence. The fact that he made this mistake is taken by modern
mathematical theorists to show that Euclidean geometry is empirical.
This appears to me to be an error. 4 A 240 = B 299.
LIV § 5] TRANSCENDENTAL USE OF CONCEPTS 433
and Kant seems to regard it as the basis of all mathematics.1
Number in turn finds its sense and significance in the fingers,
in the beads of the abacus, or in strokes and points written
on paper.
In all 'this Kant is very insistent that however much a
concept may be a priori (and however much the universal syn-
thetic principles — that is, axioms — or the individual formulae2
based upon it may be a priori), its use or application, and its
reference to objects, can be sought, in the last resort, only in
experience: indeed these a priori concepts are said to 'contain*
the possibility of experience in the sense that they are concepts
of its form or necessary conditions.3
The same principle applies to all the categories.4 This is
shown by the fact that we cannot give a real definition to any
category (that is, a definition showing that it applies to a
possible object) without a reference to its schema, and so to
space and time as conditions of sensibility, or forms of
appearances.3 Consequently the categories must be limited
to appearances. If we remove the reference to conditions of
sensibility, the whole significance of the concept, that is, its
reference to an object, disappears. We cannot give any example
which would enable us to grasp what kind of thing could
possibly be thought by such a concept.
In a passage omitted in the second edition, this contention is
further elaborated.6
In his earlier discussion7 Kant stated that although he had
in mind definitions of the categories, he deliberately omitted
them on the ground that they were not required for his limited
purposes and might rouse doubt and opposition. He promised
to articulate them later so far as was necessary, but not in the
detail demanded by a complete system of pure reason, of which
1 Compare its relation to spatial figures and temporal durations as
described in A 724 B 752. 2 Compare A 165 — B 205-6.
3 Compare Chapter XL1X § 5. 4 A 240 = B 300.
5 The phrase 'forms of appearances' suggests that Kant means
space and time by 'conditions of sensibility'; but 'conditions of
sensibility' might equally mean the transcendental schemata (see
A 140 - B 179). 6 A 241-2. 7 A 82-3 = B 108-9.
434 TRANSCENDENTAL IDEALISM [LIV § 5
his work is only an outline.1 He now asserts that there was a
deeper reason for his procedure.
The earlier discussion, strictly speaking, is concerned only
with pure categories, though the names applied to them are,
in some cases at least, the names of schematised categories.
If we remove — as for pure categories we must remove — all
reference to those conditions of sensibility which mark out the
categories as concepts whose use is empirical, if in short we
regard the categories as concepts of things in general and so
as having a transcendental use,2 what are we left with? Only
the logical forms of judgement considered as somehow con-
ditions of the possibility of things themselves.3 But in such a
case we have not the slightest idea of how they could apply to
any object, and consequently we are unable to give any real
definition of them.
It will be observed that for Kant — and we shall see this
more clearly in the sequel — the pure categories, as having
their origin in the understanding, are so far not restricted to
sensible objects, but have zprima facie claim to apply to things-
in-themselves. It will also be observed that there is no difficulty
in saying what a pure category is. Kant himself has just done
so, and he is about to explain the nature of the separate pure
categories. The only reason why this is not regarded as a
definition is that such a description cannot show that there is
any possible object to which a pure category can apply. A little
later4 Kant adds as a further reason that the forms of judgement,
and so the pure categories, cannot be defined without a circular
definition; for the definition would itself be a judgement, and
therefore would already contain these forms.5 This does not
prevent us from recognising that every pure category is a
form of judgement considered as determining the combination
of a manifold of intuition in general, and so as the concept of
an object in general* Kant would have made the Kritik much
1 Compare A 13-14 = B 27-8. 2 Sec A 238 = B 298.
3 Compare Chapter XIV § 8. 4 A 245.
5 This suggests that all the forms of judgement are for Kant, as
they ought to be, present in every judgement. fl Compare A 245-6.
LIV § 6] TRANSCENDENTAL USE OF CONCEPTS 435
easier to understand, if he had given this explanation at the
beginning of the Analytic, instead of at the end. He himself
does so, if not too clearly, in the second edition.1
Kant's discussion of the separate categories, both as pure
and schematised, has already been examined and elaborated
in my account of the transcendental schemata.2 I need add no
more here.3
§ 6. Kant's Conclusion
It follows that the use of the categories is always empirical,
and never transcendental.4 The Principles of Pure Under-
standing must apply only to objects of the senses, and never to
things in general or things-in-theinselves ; for apart from the
universal conditions of a possible sensuous, and indeed human,5
experience, the categories have for us no reference to any object
known to be possible.
Kant's conclusion is therefore that understanding can antici-
pate only the form of a possible experience in general. In so
doing, it can never go beyond the limits of sensibility, within
which alone can objects be given to us. We must give up the
proud name of Ontology — a science which professes to give
us a priori synthetic knowledge of things in general, and so of
things-m-themselves. This supposed science must give place
to a modest Analytic of the pure understanding.
Kant reinforces his conclusion by referring to the doctrine
of the transcendental schema, a doctrine which lies at the
root of all his arguments throughout this chapter.
Thinking, he says, is the act of relating a given intuition to
an object.6 This may seem to contradict his view that there is
a kind of thinking which gives us no knowledge of an object
1 B 128-9. 2 See Chapter XXXIII.
8 The passage omitted in the second edition (A 244-6) is repetitive,
and is probably omitted for this reason. 4 A 246 = B 303.
6 The pure categories would apply to any finite experience which
had a manifold given to it under forms of intuition other than time
and space ; but of such an experience we have no real conception.
6 A 247 — B 304. Compare the definition of judgement in B 141.
436 TRANSCENDENTAL IDEALISM [LIV § 6
but is merely problematic, the entertaining of a possible
concept without enquiring whether its object is also possible.
Even such thinking, however, has for him a vague reference to
some sort of object — how otherwise could we ask whether its
object is possible ? It has even a vague reference to some sort
of manifold of intuition in general — though we do not ask
ourselves how such an intuition could be given. Indeed, as
we shall see, it is this kind of problematic thinking which he
has here primarily in view,1 although his description is intended
to cover all thinking, including problematic thinking.
This is borne out already by his statement that if the kind
of intuition in question is in no way given,2 then the object is
merely transcendental : it is just an unknown something — X.3
The concept entertained must be a concept of the understand-
ing, since all other concepts have reference to some sort of
intuition or combination of intuitions; and its use must be
transcendental in the sense that the application of the concept
so far makes no claim to rest on an intuition which could be
described as given to sense.
At this stage Kant, rather loosely, identifies the transcendental
use with 'the unity of the thought of a manifold of a possible
intuition in general'.4 He must, I think, mean that the concept
in this transcendental use can 'contain' only the unity imposed
by thought on a manifold of intuition in general.5 This mani-
festly is no determinate object, and such thinking by itself
1 Compare A 255 == B 310.
2 He may mean 'if the form of this intuition is in no way given', but
perhaps his statement is meant to be more general.
3 Compare A 104 and A 109.
4 I follow Kant's own obvious emendation (Nachlragc CXXV).
Kemp Smith translates the actual text thus: 'The concept of the
understanding has only transcendental employment, namely, as the
unity of the thought of a manifold in general'. I am not sure whether
the cas' can thus be understood without amending the German, but
the general sense seems right. Incidentally the transcendental object
itself might almost be defined in the same way; see A 105.
6 If so, this accords with the doctrine of A 105 and A 109, and
indicates the only way in which we can give any sort of definite
meaning to the transcendental object.
LIV § 6] TRANSCENDENTAL USE OF CONCEPTS 437
gives us no knowledge. As Kant says, through a pure category
(in abstraction from every condition of sensuous intuition — the
only kind of intuition that is possible to us) no object is deter-
mined, and nothing is known.1 All we have is the thought of an
object in' general expressed according to different forms of
judgement.2
For the use of a concept — if it is to give us knowledge — we
require more than conception or problematic thinking: we
require also, as we have seen in connexion with the trans-
cendental schemata,3 a function of judgement (in the technical
sense). Only so can an object be subsumed under the concept.
For such judgement we must have at least the formal condition
under which something can be given in intuition. The formal
condition in question is the transcendental schema.
If we do not have this schema, which is the condition of
judgement, all subsumption under the category is impossible;
for there is simply nothing given which can be subsumed under
the category. Hence the transcendental use of the category,
which professes to have no reference to sense or conditions of
sense, is in fact no use at all; or at any rate no use whereby
anything can be known.4 It applies to no determinate object,
not even to the form (or schema) of an object which could be
determined.5
Kant therefore sums up his position as follows. Apart from
the formal conditions of sensibility — by which he might mean
1 Here again I follow Kant's own emendation (Nachtrdge CXXVI)
2 'naih vcruhiedenen modis.y
J A 132 - B 172 ff. There the power of judgement (Urteilskraft) is
opposed to understanding and reason.
4 Again I follow Kant's emendation (Nachtraqe CXXVI I).
5 Literally, *it has no even merely (as regards its form) determin-
ablc object*. This is obscurely expressed, but I ean hardly think Kant
means 'it has not even a determmable object in the sense of a manifold
of intuition which remains to be determined by being brought under
a form (or schema)'. I think he must mean that it has not even a
determmable object in the sense of a form (or schema) which could
be determined by receiving under it a particular manifold of intuition.
For Kant both the form and the matter, the concept and the intuition,
are 'determmable' in relation to each other.
438 TRANSCENDENTAL IDEALISM [LIV § 6
space and time,1 but more probably means the transcendental
schemata2 — the pure categories have a merely transcendental
significance:3 they profess to apply to an object given to no
sensuous intuition. They have no transcendental use. A trans-
cendental use is in itself impossible; for in it all the conditions
of using the categories in judgements disappear, namely the
formal conditions4 for subsuming an alleged object under the
categories. Hence if we take the categories as pure categories
alone, and not as schematised categories, they are not supposed
to have an empirical use, and they cannot have a transcendental
use. In short, they are of no use at all. That is to say, in abstrac-
tion from all sensibility they cannot be applied to any alleged
object. They are merely the pure form5 of the use of under-
standing (or the pure form of thought) in relation to objects in
general; but through this pure form alone they cannot think
(in the sense of 'determine') any object.
The whole of this elaborate discussion is little more than an
expansion of Kant's doctrine of the transcendental schemata.6
1 Compare A 138 = B 177. 2 Compare A 140 — B 179.
3 Yet Kant might equally have said they have no significance at all ;
see A 240 = B 299 and A 242. 4 Here clearly the schemata.
5 Perhaps it would be better to say 'concepts of the pure form*.
6 See especially A 139-40 — B 178-9.
CHAPTER LV
NOUMENON AND TRANSCENDENTAL OBJECT
§ i. Phenomena and Noumena
In their empirical use concepts are applied to sensible objects,
which may be described as appearances, or, more technically,
phenomena. In their transcendental use concepts are applied —
or such at least is the intention — to things as they are in them-
selves and as they can be grasped by understanding without
the aid of sense. Such objects are called 'noumena', that is,
understandable or intelligible (and not sensible) objects. Thus
the opposition between phenomena and noumena corresponds
to the opposition between the empirical and the transcendental
use of concepts.
We have now seen that there is no transcendental use of
concepts. It is therefore natural enough to conclude that there
are no such things as noumena, and even that there are no
things-in-themselves. A doctrine of this kind is often read into
Kant's discussion of phenomena and noumena:1 it chimes in
with certain idealistic predilections, and it has also been wel-
comed by minds of a more realistic tendency. To abolish the
thing-in-itself may be to improve Kant's theory, though I do
not feel so confident about this as I did when my ignorance
was greater than it is to-day. What seems to me to be certain
is that this improvement was never made by Kant himself.
His discussion of phenomena and noumena is an attempt to
show that things-in-themselves can never be known by human
minds. This is a very different thing from an attempt to show
that there are no things-in-themselves; and I doubt whether
Kant even envisaged a hypothesis so revolutionary. Belief in
the reality and independent existence of things-in-themselves
seems to me to be the presupposition of his present discussion,
1 I think this is roughly the view of Hermann Cohen and his fol-
lowers, but I find traces of it almost everywhere.
440 TRANSCENDENTAL IDEALISM [LV § 2
as it is of the whole Critical Philosophy.1 This is a complicated
and controversial question which can be settled only by careful
analysis. Unfortunately, for part of the discussion a new
version is substituted in the second edition, and this means
that we have to cover more or less the same ground twice
over.
The rest of this chapter will be an examination of the argu-
ment peculiar to the first edition. This argument is difficult,
mainly because it occupies itself with the distinction between
the noumenon and the transcendental object. It repeats some
of the complicated theories which we have already studied in
the provisional exposition of the Transcendental Deduction.
The reader who is anxious to grasp Kant's main doctrine
without the study of unnecessary detail will be well advised to
devote himself to the very much clearer account given in the
second edition, an account which will be examined in
Chapter LVI.
§ 2. Alleged Knowledge of Noumena
In the first edition2 Kant begins by explaining the ground
on which we may be tempted to claim that we have knowledge
of noumena.
He defines phenomena very clearly: they are 'appearances so
far as these are thought as objects in accordance with the unity
of the categories'. If he had only used the word 'phenomenon'
consistently for the appearance as an object (or for the pheno-
menal object), we should have been saved many difficulties of
interpretation; for he habitually uses the word 'appearance'
without making clear whether by that he means the whole
object or only a partial and temporary aspect of it.
Appearance for Kant is always an appearance to sensuous
intuition. We may suppose that there are things which are
not appearances in this sense, but are mere objects of the
understanding. Such objects, since they are not given to sense
1 On this point compare Adickes, Kant und das Ding an sich. This
work seems to me of great importance. 2 A 248-9.
LV§2] TRANSCENDENTAL OBJECT 44*
and cannot be given to discursive thinking,1 would have to be
given to some sort of active intellectual intuition. They would
then be called 'noumena'2 or 'intelligibilia\
It might be thought that the doctrine of the Transcendental
Aesthetic, justifies a belief in the objective reality of such
noumena. The doctrine of the Aesthetic limits appearances to
sensible appearances given to us passively under the forms of
our sensibility — space and time. Since it separates passive
sensibility from active understanding, the understanding is
manifestly in no way confined to sensible appearances; and
this suggests the possibility of a distinction between pheno-
mena and noumena, between a sensible and an intelligible
world.
This implication was accepted by Kant himself in the
Dissertation of 1770, though I am inclined to doubt whether
even then he was so confident about it as he appeared to be.
It was in any case a new possibility which had not been open
to the followers of Leibniz. According to Leibniz the same
object is known indistinctly by sense and distinctly by thought,
the difference between sense and thought being only a difference
between indistinctness and distinctness in our knowledge.3 This
means that the object as thought and the object as sensed differ
only in the degree of distinctness with which they are known :
there is no difference in kind. But if sense and understanding
are two fundamentally different powers, and if objects may be
given independently to these different powers, then there may
be a distinction in kind between the object as sensed and the
object as understood, between the phenomenon and the
noumenon.
The possibility that an object which is not given to sense
at all might be given to understanding4 is not here discussed
by Kant. He takes instead the case where the same object is
1 Discursive thinking is always a thinking about something given to
it from without, not given by the act of thinking itself.
2 The word 'vovc;' or 'rdj/ff/f* is used for the faculty whereby we
have direct intellectual vision of reality without any help from the
senses such as is present even in buivoia; compare Plato, Republic,
p. 51 id. 3 Sec Chapter XIX § 8. 4 Compare B 306.
442 TRANSCENDENTAL IDEALISM [LV § 3
given independently to sense and understanding. If, as Kant
has proved in the Aesthetic, the senses can represent something
only as it appears under the human forms of time and space,
the something which appears must be a thing-in-itself ;* and if
it is given to understanding, it must be an object of some kind
of non-sensuous intuition — Kant assumes that conception (by
which we merely think about given objects) cannot itself give
us an object to think about.
Hence we seem to have established the possibility of a kind
of knowledge in which there is no sensibility. This knowledge
has by itself, apart from sensibility, an absolutely objective
reality or validity: by it we know objects as they are, and not
merely as they appear.
If we use our understanding empirically, if we apply our
concepts only to appearances given under conditions of sensi-
bility, we can know objects only as they appear. This follows
at once from Kant's theory of space and time. But now we
seem to have a whole new field of knowledge opening before
us, a world of things-in-themselves which we can think by
means of our pure categories2 and in some sense apparently
intuit, a far nobler object for the exercise of our pure under-
standing.
If this were really true, it would contradict everything that
we have said before.
§ 3. The Transcendental Object
Kant discusses3 this difficulty in the light of his previous
account of the transcendental object.4
All our ideas are in fact referred by understanding to some
object. Appearances, since they are ideas, are thus referred to
a 'something'; that is, they are regarded as appearances of
something; and this 'something' may be described as the
transcendental object.5 It is called transcendental, because it
1 Compare B XXVI-XXVII.
2 All other concepts contain an element derived from sense.
3 A 250. * A 104 ff.
6 In a note Kant describes it as 'something as object of an intuition
in general1 ; see Nachtrage CXXXIV.
LV § 3] TRANSCENDENTAL OBJECT 443
manifestly cannot be given to sense ; for if it could, it would be
only another appearance. Hence it must be known a priori, if
at all.
Unfortunately, if our previous argument is correct, it is not,
and it cannot be, known at all. Kant therefore proceeds to
argue, exactly as he did in the Transcendental Deduction, that
it can only be a correlate to the unity of apperception: it has to
serve as, or to be identified with, that unity of the manifold
whereby the understanding unites the manifold in the concept
of an object.1
On this view the transcendental object, so far as it is known,
must be identified with that necessary synthetic unity which is
the only assignable and universal mark of objectivity, a unity
which is itself imposed upon the manifold of intuition by the
understanding.2 As Kant says, the transcendental object in this
sense cannot be separated from sensuous data — if it is, nothing
is left over by which it can be thought. It is no object of know-
ledge in itself. I take this to mean it is not an object which we
can know (by pure understanding) as it is in itself.
The double meaning of transcendental object is confusing,
though we can understand how one meaning grows out of the
other.3 The passage affirms that we cannot know the trans-
cendental object as a thing-in-itself. It might be interpreted as
asseiting that there is no transcendental object, and therefore
by inference no thing-in-itself. I do not see that this interpreta-
tion is necessary, nor that if it were necessary in regard to the
transcendental object, it would therefore hold of the thing as
it is in itself.
Kant adds that the transcendental object is 'only the repre-
sentation of appearances under the concept of an object in
general, a concept which is determinable through the manifold
of appearances'. I do not know what this means, unless the
transcendental object is being identified with the act of thinking
2 For this reason it would properly be called transcendental; see
Chapter XXII §2.
3 Compare Chapter XXII § 2.
444 TRANSCENDENTAL IDEALISM [LV § 3
or the unity of apperception.1 I do not think this is very
intelligible in itself; but if this is the meaning, it can apply only
to the transcendental object in its second sense. I should
require very much more evidence before I could accept the
view that Kant was here retracting his whole doctrine about
things-in-themselves.
The doctrine of the transcendental object is then applied to
the categories, which are concepts of an object in general, and
consequently, at least in their pure form, concepts of something
in general.2 We think the object in general, or the transcendental
object in its second sense, by means of the categories. This
does not mean that by them we have knowledge of some
special object given to the understanding by itself. The
categories merely serve to determine the transcendental object
— here apparently equated with the concept of something in
general — through what is given in sensibility in order thereby
to know appearances under concepts of objects.3
The ambiguity of so many of the terms makes the interpre-
tation of this difficult. The general sense is that the pure
categories give us no knowledge of things-in-themselves. Their
only use is empirical. How they determine the transcendental
object or its concept is not so clear ; but by their reference to
the transcendental schemata they supply a matter for the
ultimate concept of something in general, and so enable us to
apply this ultimate concept to an empirical manifold charac-
terised by the transcendental schemata. In this way we can
1 A 251. It would be much simpler to say that it is merely the
universal form of an object and can be determined only by receiving
an appropriate matter from sense. Kant later identifies it with the
concept of something in general, which complicates matters. Perhaps
this is what he means here — compare § 5 below — although if so, he has
expressed himself loosely.
2 It is not clear whether Kant intends to identify or to distinguish
concepts of an object in general and concepts of something in
general. Strictly speaking, an object in general should be an object
of sense, though the concept of it is not always confined to this
usage. Something in general' should be equivalent to 'a thing in
general', and the concept of it should be wider in its application than
the concept of an object in general.
3 A 251. 'Concepts of objects' here may mean 'empirical concepts'.
LV § 4] TRANSCENDENTAL OBJECT 445
know appearances through empirical concepts of objects,
empirical concepts which presuppose the categories and the
concept of the transcendental object itself.
This is a very elaborate way of describing phenomenal
objects and explaining the use of the categories in relation
to them.
§ 4. Origin of the Belief in Noumena
Kant endeavours to explain further why we refuse to be
satisfied with phenomena and insist on adding noumena thought
only by the pure understanding.1
The Transcendental Aesthetic has shown that since space
and time are forms of our sensibility, we can by means of
sensibility know things only as they appear to us, not as they
are in themselves. This means that, so far as concerns sensi-
bility, we are confined to knowledge of appearances only: it
consequently implies a contrast with things-in-themselves. But
even apart from this the concept of appearance itself implies
some correlative which is not an appearance. An appearance is
nothing in itself; it must be an appearance to something and an
appearance of something.2 The latter point is the one with
which Kant is especially concerned. The very word 'appearance'
implies a reference to 'something' in itself, that is, to an object
independent of our sensibility.3 The fact that the appearance
itself (or our immediate idea of the object) is sensible does not
affect this contention in the least.
From the limitation of our sensibility springs the concept
of a noumenon. This concept Kant in the first edition treats
1 A 251; he has already explained it in A 248-9. He says here
that we are not satisfied with the 'substratum* of sensibility. This is a
curious phrase for the transcendental object, yet I feel it hard to see
what else he can mean. Appearances possessing the unity thought in
the concept of the transcendental object are phenomena (or phenomenal
objects).
2 Compare B XXVI-XXVII. If the word 'appearance' is appro-
priately applied — a large question — this contention is true. And it
seems impossible to believe that an appearance can be an appearance
of an appearance, and so ad infimtum.
3 This is what distinguishes an appearance from an illusion.
446 TRANSCENDENTAL IDEALISM [LV § 4
as negative i1 it gives us no determinate knowledge of anything.
This concept is merely the thought of something in general,
and in this thought there is complete abstraction from any
reference to the forms of sensuous intuition.2 But if the nou-
menon is to be a genuine object distinct from phenomena, it is
not enough that in the concept of it there should be abstraction
from all the conditions3 of sensuous intuition. I must have a
positive ground for assuming a non-sensuous intuition to which
such an object could be given. Otherwise my concept, though
it may not be self-contradictory, will be empty — in the sense
that I cannot know that it applies to a possible object.
Now we cannot prove that sensuous intuition is the only
possible kind of intuition. But equally we cannot prove that
there is any other kind of intuition. The fact that in thinking
we can entertain a concept in abstraction from sensibility is
quite inconclusive. It still remains an open question whether
our concept is not the mere form of a concept, whether in
abstraction from sensibility it can have any object, and indeed
whether in such abstraction any possible intuition remains
at all.4
So far as words are concerned, this question may be still open ;
but for Kant it is really closed. The concept of a noumenon is
only the form of a concept, and we are quite unable, in abstrac-
tion from sensibility, to apply it to any object at all. This does
not necessarily mean that Kant is entitled to assert, or that he
wishes to assert, the unreality of noumena, and still less the
unreality of things-in-themselves. It may mean only that we
have no way of knowing them; and this is what I believe it
does mean.
1 In the second edition he distinguishes between positive and nega-
tive meanings of the word ; see B 307.
2 The concept of a thing in general or something in general stands
to the concept of an object in general as the pure category stands to
the schematised category; but unfortunately Kant does not always
adhere consistently to this usage, and at times his statements are
ambiguous. 3 'Conditions' are equivalent to 'forms'.
4 The last point is added from Kant's own note ; see Nachtrage
CXXXVII.
LV § 5] TRANSCENDENTAL OBJECT 449
§ 5. Kant's Conclusion in the First Edition
The last section has been comparatively straightforward, but
for the conclusion1 we must turn again to the complications of
the transcendental object.
The object to which I relate appearances is always the trans-
cendental object. This Kant identifies with the thought, the
wholly indeterminate thought, of something in general — I should
prefer to say it is the content of that thought. It cannot be
called the noumenon, by which we mean a thing known, by
pure understanding, as it is in itself. In the case of the trans-
cendental object we do not know what it is in itself.2 Our only
concept of it is the thought of the object of a sensuous intuition
in general, an object which is therefore the same for all
appearances.3
1 cannot think the transcendental object4 through the
categories; for these apply only to phenomenal objects: they
serve to bring empirical intuitions under the concept of an
object in general. No doubt a pure, or rather a transcendental,
use of the categories is logically possible; that is, it can be
thought without contradiction; but it has no objective validity,
for we cannot know that it has a possible object. More
elaborately, we cannot know that it has reference to any
non-sensuous intuition which could thereby acquire the unity
^253.
2 This at least leaves it an open question whether the transcendental
object (in the first sense) may not be a thmg-m-itself.
3 It is not clear in this statement whether Kant is thinking of the
transcendental object in its first sense (as the unknown something to
which any appearance must be referred) or in its second sense (as the
unity of the manifold of any phenomenal object). I incline to think
he means the latter. Compare A 109.
4 Here clearly the transcendental object in its first sense. In the
second sense the transcendental object is that necessary synthetic
unity which is articulated in the categories, and is * determined' by
them through what is given m sensibility (see A 251). In this second
sense we could, I imagine, be said to think the transcendental object
through the categories ; for it is through them that we think the neces-
sary synthetic unity of the phenomenal object.
TRANSCENDENTAL IDEALISM [LV § 5
which characterises an object.1 The category is a mere function
(or form) of thought. Through it no object is given. The object
which we think through the categories must be given as a
manifold of intuition and combined by the transcendental
synthesis of imagination in one time and space.
We must recognise that in the conclusions so stated there is a
certain amount of ambiguity due to the intrusion of the trans-
cendental object. As in the Transcendental Deduction, Kant
first of all treats the transcendental object as the unknown
'something' to which we refer the manifold of appearances,
and then reduces it, so far as it can be known, to the necessary
synthetic unity of the appearances themselves. This seems to
me to leave the question open whether we must still think that
there is an unknown 'something', a thing-in-itself, a reality of
which we know only the appearances to us. As I understand
Kant, he has no intention whatever of giving up his belief in
the unknown thing-in-itself or of the noumenon in this negative
sense. What he is anxious to assert is that by means of the pure
categories we can have no knowledge of such a thing-in-itself,
though even this he leaves as a logical possibility. If we take
the noumenon in a positive sense, that is, as a reality intelligible
by means of our pure categories alone, he certainly means to
deny that we are justified in claiming to know any such reality.
His position can be made clear only if we distinguish between
a positive and a negative sense of the word 'noumenon', and
this distinction is made explicit only in the second edition.
I need hardly add that Kant has no intention here, any more
than in the Transcendental Deduction, of giving up his doctrine
of the phenomenal object. The reduction of the transcendental
object to the necessary synthetic unity of the manifold of
appearances is in fact a way of insisting that the only objects
we know are necessarily phenomenal.
There is a further source of difficulty in Kant's habit of
identifying the concept with what is conceived, the thinking with
1 At times Kant says roundly that our categories could apply only
to sensuous or passive intuitions and not to intellectual or active
intuitions; see B 145.
LV § 5] TRANSCENDENTAL OBJECT
what is thought, the unity of thinking with the unity of the
object, and so on. There was a time when I believed that this
was due to mere carelessness and perhaps to confusion. I still
find it puzzling, but I have an uneasy suspicion that if I under-
stood Kant better, these difficulties might disappear.
VOL. II
CHAPTER LVI
PHENOMENA AND NOUMENA
§ i. Categories and Knowledge of Nonmena
The account given of the noumenon in the second edition
is more brief, and also more clear, than that given in the first.
Kant begins with the categories.1 These originate in the
understanding, not (like the forms of time and space) in sensi-
bility. Hence there seems no reason why they should be applied
only to sensible objects : they have a prima facie claim to apply
to objects other than those of sense.
This claim, however, is an illusion. The categories in them-
selves are mere forms of thought or of judgement. They contain
no matter or manifold in themselves, and so cannot by them-
selves give us knowledge of any object. All that they contair
is the logical power of uniting2 a priori in one consciousness
a manifold which must be given in intuition. If we considei
them in abstraction from the only kind of intuition possibk
to us — namely, sensuous intuition under the forms of time anc
space — then they are empty: they have no meaning, in tht
sense that they refer to no assignable object. They have ever
less meaning than the pure forms of sense (time and space)
for through these at least some sort of manifold, and so some
sort of object, is given.3 In the categories all we think is a waj
of combining the manifold, a way proper to understanding
and involved in the very nature of thought itself. If we se
1 B 305.
2 Kant here seems to be thinking of the categories as acts (sci
A$7 — B8i)oras forms (or functions) of acts of the understaiidmj
(see A 69 = B 94). If we take them as concepts, what they 'contain
(or what is thought in them) is necessary synthetic unity in one of it
aspects. This necessary synthetic unity is the unity of a manifold o
intuition in general', but it remains an empty form till we consider i
as the necessary synthetic unity of a manifold given under the forn
of time.
3 The object given is only the form of an object; see B 147.
LVI § i] PHENOMENA AND NOUMENA 45*
aside entirely the sensuous intuitions in which alone a manifold
can be given to us, then the mere way of combining by itself
has no meaning. We can still of course consider it as a form of
thought, but it tells us nothing about any object.
Hence, as has been said, the claim of the categories to apply
to objects not given to sense is an illusion. We must, however,
try to understand how this illusion arises.
The ordinary objects which we know may, as appearances
to us, be called phenomena (or sensible entities). This ter-
minology implies a distinction between the objects as they
appear to us (or are intuited by us) and the objects as they are
in themselves with a character independent of our sensibility.1
For example, the table which we know appears to us as occupy-
ing space and lasting through time; but this is only because
space and time are the forms of our sensibility, and so we must
distinguish the character of the table as it appears to us from
its character, or inner nature, as it is in itself.
Consequently if we regard tables and similar objects as
phenomena, we are bound to set over against them the same
objects in their own character as they are in themselves,
although in this character we cannot intuit them; for we can
intuit them only as they appear under the forms of time and
space. We are also bound to suppose that there may be other
things which have their own character in themselves, even
although they are never intuited by us as phenomena at all.
These things as they are in themselves, whether they are
intuited by us as phenomena or not, we are obliged to regard
as objects which we think by mere understanding apart from
sense. We call these objects noumena (or intelligible entities).
The question then arises whether the pure categories may
not be applied to these noumena ? Can the pure categories be
said to have meaning as applying to noumena, and can we
regard them as giving us knowledge of such noumena?2
1 Compare B XXVII and A 251.
2 B 306. Note that Kant does not even ask the question whether
we should give up our belief in these noumena. The only question is
whether we can know them.
,^2 TRANSCENDENTAL IDEALISM [LVI §2
§ 2. The Positive and Negative Meaning of 'Noumenon'
To answer these questions we must distinguish two different
meanings of the word 'noumenon'.1
The understanding when it thinks of an object as a pheno-
menon in its relation to our senses, also thinks of an object as
it is in itself apart from this relation. It supposes further — else
how could it think of them? — that it must be able to make
concepts of these objects as they are in themselves. The only
concepts which the understanding can produce out of itself
without the aid of sensibility are the pure categories. Hence it
is only natural to believe that by means of these pure categories
(if by no other concepts) we must be able to think objects as
they are in themselves.
In this argument we are misled. We are confusing the quite
indeterminate concept of a noumenon as a mere 'something in
general' which is what it is independently of our senses — we
are confusing this indeterminate concept of a noumenon with
the determinate concept of a noumenon as an entity that admits
of being known by understanding in a purely intellectual way.
Here then are clearly two different meanings of 'noumenon'.
If by 'noumenon' we understand a thing so far as it is not the
object of our sensuous intuition, this is a noumenon in the
negative sense. Its concept is derived by making complete
abstraction from our sensuous intuitions under the forms of
time and space.2 But if we understand by 'noumenon' a thing
so far as it is the object of a non-sensuous (or intellectual) intuition,
this is a noumenon in the positive sense. We are then not merely
making abstraction from our own sensuous intuitions: we are
supposing that there is another kind of intuition (an intellectual
intuition through which the noumenon can be known), although
we neither possess such an intuition nor have any insight into
the possibility of such an intuition.
The concept of 'noumenon' in the negative sense is an
1 B 306-7.
2 Such abstraction gives us the pure concept of an object in general,
or (better) the pure concept of a thing in general.
LVI § 3] PHENOMENA AND NOUMENA 45 $
indeterminate concept: it gives us no knowledge, unless a
manifold can be supplied for it.1 The concept of 'noumenon'
in the positive sense professes to be a determinate concept;
but in the absence of an intellectual intuition it must fail to
make good its claim.
§ 3. Can We Know the Thing-in-Itself?
We must now draw our conclusions from this distinction.
Kant does so in a passage which is one of the most important,
as it is one of the clearest, in the whole Kritik? In it he shows
beyond any reasonable doubt, not only that he holds the thing-
in-itself to be unknowable, but also that he has not the remotest
intention of giving up his belief in things-in-themselves. His
incidental account of our knowledge of phenomena is also one
of the most precise with which I am acquainted, and is in full
accordance with the interpretation which I have attempted to
give throughout.
The theory of sensibility as expounded in the Kritik is at the
same time a doctrine of noumena in the negative sense. It
implies that we must think of things as they are in themselves,
not merely as they appear to us, or as they are in relation to
our sensibility. Yet as we think of things in abstraction from
our sensibility, we understand that in considering them thus
we can make no use of the categories. The categories have
meaning (or objects) only in relation to the unity of our intui-
tions in time and space; and they can determine this unity
a priori, through universal concepts of combination, only
because of the ideality of time and space.
This seems to me to indicate — what I have argued for
consistently — that the transcendental synthesis of imagination
can impose unity on objects in accordance with the pure
categories only because time and space are at once pure intui-
tions and necessary forms of all appearances. And the categories,
as we have demonstrated, can have objective validity only
1 No manifold can be supplied for it, and it cannot become deter-
minate without a manifold. 2 B 307-9.
,454 TRANSCENDENTAL IDEALISM [LVI § 3
because all our intuitions, and all our objects, must be united
in one time and one space.1
If this unity of all intuitions in time (and space) is lacking,
as it must be ex hypothesi in the case of noumena, then the
whole use of the categories, and their objective validity or
meaning, entirely ceases. The very possibility2 of things to
which the categories might apply can never be comprehended3
by us. We can never determine the possibility of a thing from
the mere fact that the concept of it is not self-contradictory :
we can do so only by showing that there is an intuition
corresponding to the concept. If we wish to show that the
categories apply to objects otherwise than as phenomena, we
must base this on an intellectual intuition; and in that case
the object would be a noumenon in the positive sense. Since
such an intellectual intuition has no place in our cognitive
powers, our use of the categories cannot go beyond objects
of sensuous experience.
Nevertheless Kant does not doubt that corresponding to
phenomena there are intelligible entities : every appearance is
an appearance to us of a thing-in-itself . He does not even doubt
that there may be intelligible entities which never appear to us
in intuition at all.4 All he asserts is that our categories cannot
be applied to such entities; for our categories are mere forms
of thought awaiting a manifold given in sensuous intuition.
When we speak of a noumenon, we must interpret it only in
the negative sense as a thing which is no object of our sensuous
intuition.
We can see how this passage may be taken, by Hegelians
and others, as showing that Kant ought to have given up a
belief in things-in-themselves.5 On that point I offer no opinion,
beyond saying that if this is really so, Kant would have to
1 This applies especially to the Analogies, but also to the other
Principles.
2 B 308. Compare also, as Kant himself suggests, B 288 ff.
3 The word used is 'einsehen', which is especially connected with
reason. * B 309.
6 Fichte is perhaps to be regarded as the originator of this view.
LVI §4] PHENOMENA AND NOUMENA 455
re-write his entire philosophy. To assert that Kant has explicitly
given up his belief in things-in-themselves seems to me a
manifest contradiction of his express statements.
§ 4. Thought and Intuition
The rest of Kant's argument1 is little more than an amplifi-
cation of what has already been said; but it contains some
points which are of interest in themselves, and others which
are of interest because of the misunderstandings to which they
have given rise. The main contention may be said to be the
central contention of the Critical Philosophy — that although
we must always distinguish thought and intuition, neither can
give us knowledge of objects apart from the other.
Merc intuition by itself is blind.2 The fact that there is an
affection of sensibility in me — and even this could not be known
as a fact without thought — does not constitute a reference of the
idea so received to an object. To know that this appearance
given to me is the appearance of an object, I must think, and
think through the categories: I must, for example, regard this
appearance as the state of a permanent substance; and it is
only on this presupposition that I can apply empirical concepts
of objects.
Mere thought by itself is empty. If I leave out all intuition,
I am left only with the form of thought. Such a form of thought
is simply a principle of synthesis, a way of combining some
sort of manifold, and so a way of determining an object for
the manifold of a possible intuition. The categories, as such
principles of synthesis, contain, however, no reference to
sensibility as the special way in which the manifold (and con-
sequently the object) may be given. Elsewhere3 Kant appears
to suggest that the very nature of the categories implies that
the manifold must be given passively and therefore to a
sensuous intuition; but in any case the categories contain no
1 A 253 — B 309 fT. It is to be noted that this passage occurs in both
editions, and the passage peculiar to the first edition must be inter-
preted in the light of this.
2 A 51 =•= B 75. 3 Sec B 145 and compare B 149.
456 TRANSCENDENTAL IDEALISM [LVI § 5
reference to time and space as the only forms of human
sensibility. Therefore the categories, as concepts of objects in
general, do have a prima facie claim to apply beyond the realm
of sensuous intuition, or at least beyond the realm of human
sensuous intuition. Nevertheless they do not give us determinate
knowledge of any objects other than sensible phenomena ; for
we cannot assume that such objects would be given except by
presupposing a non-sensuous or intellectual intuition ; and this
we are not entitled to do.1
§ 5. The Concept of 'Noumenon' as a Limiting Concept
Kant next proceeds to examine the concept of 'noumenon',
and asserts that it is a limiting concept. This contention has
often been misunderstood.
The concept of a noumenon (or of a thing as it is in itself
and as it is known to be by pure understanding) is, in the
first place, not self-contradictory; for there is no contra-
diction in assuming a non-sensuous intuition, as is done in
this description of the concept. Secondly this concept coheres
with the rest of our knowledge as setting a limit to other
concepts, particularly the concept of sensibility: it is a concept
of what is beyond sensibility. Thirdly we have no means of
showing its objective reality or validity. On these grounds
Kant calls it a problematic concept.2
The concept of a noumenon is more than this : it is also a
necessary concept. It is necessary in order to limit the objective
validity of our sensuous knowledge, that is, to prevent us from
thinking that our sensuous intuitions give us knowledge of
things as they are in themselves.
It is hard to see how Kant could have held this unless he
believed in things-in-themselves, and unless he believed that
we must think — though we can never know — things-in-
themselves. Yet when all is said and done, we can, he insists,
have no insight into the possibility of noumena. The area
1 We arc not even entitled to assume sensuous intuitions with forms
other than time and space. 2A254 = I33io.
LVI § 5] PHENOMENA AND NOUMENA 4157
outside the realm of appearances is empty — empty, he is
careful to add, for us. Our understanding does extend prob-
lematically beyond the realm of appearances — how otherwise
could it know the limits of that realm ? But we have no intui-
tion— wt have not even any concept of an intuition — by which
objects beyond the range of sensibility could be given to us.
Hence our understanding cannot be used assertorically beyond
the limit of sensuous appearances.
All this seems to me to mean that we must think there really
are things-in-themselves beyond the realm of appearances (and
even perhaps — though the thought is empty — that these
things-in-themselves could be known only by an intelligence
different from our own). All Kant is denying is that we can
have any positive knowledge of such things-in-themselves. His
whole thought seems to me utterly remote from the doctrine
that the thing-in-itself is to be reduced to a mere concept of
the mind.
Hence he concludes that the concept of a noumenon is a
limiting concept.1 Its use is only to limit the pretensions of
sensibility, and is therefore negative, not positive. The concept,
however, is far from arbitrary. It is bound up necessarily
with the limitation of sensibility, although it can give us no
positive knowledge of the inner nature of that which lies
beyond sensibility. It is to me extraordinary that this passage
should be used to show that Kant is consciously reducing the
thing-in-itself to a mere concept. It should be noted that Kant
does not assert the noumenon to be a limiting concept — he is
sometimes quoted as saying this: he asserts only that the
concept of a noumenon is a limiting concept (or the concept of
a limit). To say this is to say only that it is a concept — an
indeterminate concept no doubt — of what lies beyond the
limits of our sensibility; for on Kant's theory that which limits
must be different from that which it limits.2 In the absence of a
non-sensuous intuition we can never know what lies beyond
the limits of our sensibility. But Kant does not doubt that
something which is not an object of sensuous intuition does
1 A 255 = B 310-11, 'GretusbegtiJT. 2 See A 515 = B 543.
VOL. II P*
4^8 TRANSCENDENTAL IDEALISM [LVI § 6
lie beyond these limits — otherwise there would be no sense in
talking about limits at all.1
§ 6. Understanding not Limited by Sensibility
In a further paragraph2 Kant elaborates his doctrine without
adding anything really new.
He insists that the division of objects into phenomena and
noumena, and the distinction between a mundus sensibilis and a
mundus intelligibility cannot be admitted in the positive sense.
The latter phrase is added in the second edition; and, I suggest,
it indicates that the distinction between noumenon in the
positive, and noumenon in the negative, sense has been
introduced mainly to guard against the interpretation that
Kant is giving up the thmg-in-itself instead of merely denying
that we have knowledge in regard to it.
His further distinction between sensuous and intellectual
concepts, and his insistence that the categories give us no
knowledge unless we can indicate a possible intuition to which
they can apply — all this calls for no comment.3 The same
applies to his contention that the concept of a noumenon as
a problematic concept4 is, not only admissible, but inevitable:
nevertheless we must not interpret the concept positively, or
suppose that thereby our understanding acquires a determinate
object known by means of pure thought. An understanding
which knew reality in this way, not discursively by categories
1 I think some commentators have been misled by the modern
associations of a 'limiting concept'. Kant does not mean by it the
concept of something to which we can get closer and closer approxi-
mations. He does not mean to imply by it — as has been suggested, for
example, by the Master of Balhol, Kant, p. 284 — that we can come to
know reality more and more as it is. He means to imply, on the con-
trary, that we can never come to know reality as it ib.
2 A255 = B 311.
8 Except perhaps the qualification that the intellectual concepts (or
categories) can be valid, and must be valid, of objects of empirical
intuition : Kant's language might suggest that this is not so. When he
says that we cannot determine any object for intellectual concepts, he
must mean 'so long as they remain purely intellectual' (that is,
.unschematised). 4 Sec A 254 — B 310.
LVI § 7] PHENOMENA AND NOUMENA 45$
which await an intuition given to sense, but intuitively in a
non-sensuous intuition, is for us itself a problem: we have no
means of showing that such an understanding is possible.
By the concept of a noumenon our understanding acquires
an extension that is purely negative : it is not limited by sensi-
bility, but rather limits sensibility; for it must think that
beyond sensibility and beyond appearances there is the thing
as it is in itself, which it calls a noumenon in distinction from
phenomena. But it also immediately sets limits to itself; for it
recognises that it cannot know these things-in-themselves by
any of its categories. It can only think them under the name of
an unknown something.
In all this there is no denial of the thing-in-itself. There is
only an insistence that while we must think things-in-
themselves, and thereby recognise the limits of our experience,
we must never delude ourselves into the belief that we can
know these things-in-themselves by pure understanding.
§ 7. The Union of Understanding and Sensibility
The distinction between the sensible and the intelligible
world is not to be identified with the distinction between the
world as known by observational astronomy and the world as
known by theoretical (or mathematical) astronomy.1 We can
of course apply understanding and reason to appearances ; but
the phrase 'an intelligible world* should be confined to a world
known by understanding alone. To ask whether we know such
an intelligible world is to ask whether there is a transcendental,
as well as an empirical, use of understanding ; and this question
we have answered in the negative.2
Therefore if we say that the senses represent objects as they
appear, while understanding represents them as they are, we
must use the latter phrase only in the empirical sense. To
know things as they are is simply to know them as objects
of experience — that is, as appearances bound together in one
system in accordance with the categories. We cannot know
1 A 256-7 = B 312-13. a A257 = 6313.
TRANSCENDENTAL IDEALISM [LVI § 8
them as they may be apart from their relation to possible
experience, and so we cannot know them as objects of mere
understanding apart from sense. We cannot even know whether
such a knowledge is possible — at least, Kant adds, if it is to
stand under our human categories.
The last phrase may suggest speculations always at the back
of Kant's mind, but never regarded as more than speculations.
A finite understanding must receive a given manifold from
without, and must combine it in accordance with the categories
which originate in itself — how then can it possibly know reality
as it is in itself? Surely this is the prerogative of an infinite
mind which would have no reality beyond itself. Such an
infinite mind might perhaps know all reality in its own intel-
lectual, and yet intuitive, activity. In such knowledge our
categories could have no place, but we have certainly no means
of knowing that such a divine knowledge is possible.
If we confine ourselves to experience which we know to be
possible, we must say that for us understanding and sensibility
can determine objects only in conjunction.^ If we separate them,
we may indeed have intuitions without concepts, or concepts
without intuitions, but neither of these by itself can give us a
determinate object. The Analytic ends as it began.2 The funda-
mental distinction and the necessary co-operation of sense and
understanding, intuition and thought, in all our knowledge —
this is the central and all-important doctrine of the Kritik.
§ 8. The Limits of Knowledge
If we are still unconvinced by this doctrine and reluctant to
give up the transcendental use of the categories, Kant asks us
to try the experiment of making synthetic judgements by means
of the categories alone.3 We may be able to make analytic
judgements by means of the categories alone, but in that case
we are only making explicit what is thought in the category:
we do not show that the category applies to an object, and it
may be merely a principle of synthesis involved in the nature
1 A 258 = 6314. 2A5i=B75. 8 A 258 ==6314.
LVI § 8] PHENOMENA AND NOUMENA 4<y
of thought. If we try to make synthetic judgements — if, for
example, starting merely from the concept of substance and
accident, we say that everything which exists, exists as substance
or accident — how can we justify our assertion ? Such a judge-
ment professes to apply to things-in-themselves as objects
known by pure understanding. Where then is the third thing,
or the necessary intuition,1 which alone can carry us beyond
our concept ? We can never prove such a proposition except by
appealing to something other than our original concept. This
third thing can only be possible experience ; but if we appeal to
possible experience with its necessary forms, we thereby
renounce our claim to make a priori judgements free from all
reference to sense.
We have therefore no principles2 by which we can apply the
concept of a merely intelligible object, if we regard that concept
as positive3 and as a source of possible knowledge; for we
cannot think of any way in which such objects could be given.
We must treat the concept as problematical or negative. It
then leaves open a place for such intelligible objects;4 but it
serves only, like an empty space, to limit the empirical Principles
of the Understanding. We can say that the Principles of the
Understanding (such as the law of causality), together with
the sciences based on them, can be applied only to the pheno-
menal world. We must not delude ourselves into the supposition
that this negative and necessary limitation is at the same time
positive knowledge of a world beyond.
In Kant's whole discussion of phenomena and noumena I
can see no suggestion that he gave up for a moment his belief
in things-in-themselves. The passages in regard to the trans-
cendental object might indeed with a certain plausibility be
interpreted in this sense ; but I do not believe that either here
1 Compare Nachtrage CXXXIX.
2 'Everything which exists, exists as substance or accident' would be
such a principle, if it could be established.
3 Compare Nathtrage CXL.
4 It is absolutely vital to Kant's philosophy that such a place should
be left open.
^62 TRANSCENDENTAL IDEALISM LVI § 8
or in the Transcendental Deduction such an interpretation is
necessary, nor do I believe that it could express the intention
of Kant's thought. These passages are in any case withdrawn
in the second edition, perhaps because they are susceptible of
this interpretation. There can at least be no reasonable doubt
that in the second edition Kant's position in this matter is
perfectly clear. Nor can there be any reasonable doubt that
without the presupposition of things-in-themselvcs — whether
we regard it as justified or not — the whole of the Critical
Philosophy falls to pieces.
EPILOGUE
As I look back on the long and difficult road that we have
traversed, I feel compelled to ask whether it has been worth
while. For myself at least I must answer emphatically, Yes.
I think I can now see Kant's theory as a whole, and even as a
comparatively simple whole, so far as a theory which deals
with the most ultimate questions possible to the human mind
can ever be called simple. I think I can see also that the intricacy
of his exposition is not due to incompetence, but mainly to
the complications of his subject ; and I have found not rarely
that my own first simplifications of his argument were erroneous,
and that his more intricate statement was the only one that
was correct. His exposition would have been clearer, if it had
been better arranged; and there are passages, unfortunately
too often crucial passages, where there is unnecessary obscurity
due presumably to excessive haste. Nevertheless on the whole
Kant seems to me both to have a consistent philosophy and to
have expressed it as it ought to be expressed. I have convinced
at least myself that the prevalent charges of pedantry, formalism,
incoherence, and confusion are wide of the mark: so far as they
are true at all, they deal only with the surface of things; and
they are bound to be set aside, in their present exaggerated
form, as soon as men can acquire that internal understanding
apart from which no great philosophy can be intelligible.
Such an internal understanding it is the business of every
commentator, within the limits of his own capacity, to acquire
and to communicate. In my belief this can be done only by a
patient study of the details, by an attempt to follow the
intricate workings of an author's mind, provided always we
remember that there is a whole which we seek to know and in
the light of which all the details are to be interpreted. This at
any rate is the method which I have tried to follow. I could,
I think, have written an easier, and certainly a shorter, book,
had I attempted only to set forth my own views of Kant's
philosophy. For such books there is certainly an urgent need,
464 EPILOGUE
and at times I have felt the desire to try my hand at writing
one of them. But, at the best, works of this kind do not enable
the student to check the statements which they make ; and no
book, however good, can be a substitute for the direct under-
standing of Kant himself.
My hope is that by the method I have chosen the student may
be helped in the reading of the Kiitik itself and may be enabled
thereby to form his own judgements. In no other way can Kant
be restored to his real position in the history of philosophy, a
position which, in my opinion, is generally misjudged at the
present time. This seems to me particularly important when
the modern idealisms to which he gave rise appear to have
worked themselves out, at least for the moment, and when
thinkers everywhere are approaching the same problems from a
different point of view. I believe that the attitude of Kant is
much nearer to the modern attitude than was that of his imme-
diate successors; and I believe that a real, as opposed to a
superficial, knowledge of the Kritih may help to save modern
philosophy from unnecessary errors and to keep it in the path
of progress.
The edifice which we have studied in detail is little more
than the portico of that extraordinary structure which is called
the Critical Philosophy. Nevertheless I believe that if we have
mastered the principles of its architecture, we have already
acquired the necessary clue for the understanding and apprecia-
tion of the whole. No philosopher is truly great whose work
does not cover the whole range of human experience ; and by
this negative test at least Kant's prima facie claim to greatness
cannot be questioned. I believe myself that Kant stands out
among the greatest thinkers by all the tests which can reasonably
be applied to men who share the common weaknesses of
humanity. If I can persuade others to acquire, by patient study
of the Kritiky some of that respect and admiration for Kant
which has grown upon me the more I have examined his work,
I shall feel that my long and at times depressing labours have
not failed to find an appropriate reward.
GENERAL INDEX
abgeleitet,.! 118 n. 2, 512 n. r.
abstraction, I 200, 200 n. 6, 267; see also comparison.
different kinds of, I 124-6.
accident, see substance.
accurate, I 266 n. 4.
acquaintance, I 334, 334 n. 9.
act, and function, I 413.
identity of, see function, identity of.
actio mutua, I 297 n. 4, II 294 n. 2.
action, II 215, 215 n. 3, 216, 282, 325.
activity, causal, see substance.
continuity of, II 287.
actual, see possible.
the, and the necessary, II 360.
actuality, II 57, 228 n. 4; sec also existence.
and necessity, II 341 ; see also necessity; possibility.
logical and real, II 361.
no wider than necessity, II 340, 343.
pure category of, II 58.
schematised category of, II 59.
sense-perception the mark of, II 359.
transcendental schema of, II 59.
Adam, I 15, 159 n. i.
Adickes, I 38, 40 n. 3, 41, 41 n. T, 42 n. i, 53 n. 2, 61 n. 2, 66 n. 4,
70 n. 2, 237 n. 4, 301 n. 2, 308 n. i and n. 2, 320 n. 2,
373 n. 2, 378 n. 3, 421, 421 n 2, 424 n. 3, 426 n. 6,
429 n. 2, 486 n. i, 490 n. 4, 492 n. 7, 520 n 6, II 60 n. 3,
66 n. 2, 165 n. 7, 224 n. 2, 287 n. i, 318 n. i, 339,
339 n. i, 346 n. 3, 371, 440 11. i.
Aesthetic, the Transcendental, I 52, 73, 93, 98, II 93, 96 n i, 445.
doctrine of the, II 121-4, 441.
principles of the, II 97.
affection, by ourselves, II 400.
by outer objects, II 400.
double, I 520 n. 6; see also causality, double.
of the self from within, II 421.
affects, meaning of, II 388.
affinity, I 366, 367, 369, 480 n. 6; see also appearances.
and association of ideas, I 448, 480.
and object, I 445.
association by, I 366, 367 n. 2.
transcendental, I 367-71, 395, 481-4.
transcendental and empirical, I 446-9.
*66 GENERAL INDEX
aggregate, II 152.
Alexander, S., I 49, 112 n. 4, 152 n. i, 175 n. i, 305 n. i, II 78 n. i,
107 n. i, 256 n. 3.
algebra, I 157-8.
Amphiboly, of Concepts of Reflexion, I 308.
Analogies, Principle of the, II 159-61.
proof of the, II 175-6.
the, regulative, II 178-9.
analogy, cognition by, I 67 n. 2.
mathematical, II 179.
Analogy, first meaning of, II 179-80.
second meaning of, II 180-3.
analysis, I 200-1, 250.
and conception, I 267.
and synthesis, I 81, 87, 266-9, 437, 505.
confusion between two kinds of, I 219.
of concepts, I 160, 172.
Analytic, the Transcendental, I 52, 73, 234, 236-8.
animals, I 330 n. i, 376 n. 3.
consciousness of, II 389; see also consciousness, animal;
Erlebnis.
Anschauung, I 94 n. 5, 477 n. i, II 284-6, 291.
Anticipations, of Sense-perception, Principle of the, II 134-9.
appearance, I 339, 339 n. i.
and illusion, II 416-18.
and phenomenon, I 96 n. 7.
meaning of, II 230, 445.
necessary synthetic unity of the, and necessary unity of
consciousness, I 419.
appearances, affinity of, I 444-6.
and objects, I 488.
change, or exchange of, II 216, 217.
forms of, I 102, 109, 131, 135.
given, I 476-8.
necessary synthetic unity of, I 369, 482.
outer, time the mediate condition of, II 383.
relation of, to reality, I 61-3.
substance, the permanent substratum of, II 191.
appercepho, I 332 n. 7, 333 n. i.
apperception, I 345-6, II 87, 415; see also imagination; self-
consciousness; sense, inner; space and time; unity.
ancj categories, I 432-4; and form of judgement,
I 521-3; and objects of knowledge, I 516-18;
and self-consciousness, I 398, 511, 512; and
self-knowledge, II 401-3; and space and time,
I 462; and synthesis, I 465; and transcendental
object, I 417-20; and understanding, I 469-71,
515 ; and unity of time, I 486.
GENERAL INDEX 4$7
apperception as an act, I 397; as the condition of experience,
I 408-11 ; as a power, I 397.
communion of, II 319.
empirical, I 402; and inner sense, I 399-403.
empirical and transcendental, I 379-81, 398-9.
1 inner sense affected by, II 388.
original, I 346, 397; and time, II 162.
pure, the act of, I 403, 408, see also experience, inner.
transcendental, I 403-5.
apperception, the unity of, I 207, 405-8, 458-9, 482, 483, 570-1,
II 161.
and timc ant} space, I 420, 462, 516;
and unity of the manifold, I 512,
515; sec aho interaction ; time ; under-
standing.
— analytic and synthetic, I 513; empirical,
I 519; objective, I 518-21, 522;
original transcendental, I 520; syn-
thetic, I 510-16; synthetic, ultimate
principle of, 1 517-18; transcendental,
I 512, 520.
apprehensio, or Aitffassung, I 359 n. 7.
brnta, I 333 n. i.
apprehension, I 262 n. 2, 355, 489, II 139, 168, 186, 232.
and inner sense, I 355, 360; and sense-perception,
I 361 ; and space and time, I 539-40.
continuity as the formal condition of, II 289-93.
mere, II 303, 312.
production of time in, II 396.
pure synthesis of, I 360.
reversible and irreversible order in, II 263; see also
sense-perceptions.
rule of, II 236-7, 242-3, 266.
successiveness of, II 192-5, 231, 239, 246, 250.
synthesis of, I 264, 354~5, 35&, 359~63, 447, 4?8-9,
538-9, 542-3, H 258, 352.
a priori, comparatively, II 358.
meaning of, I 76.
two senses of, I 154, 166, 191, 322 n. 2.
Archimedes, I 580.
architectonic, I 54, 235-7, 308, II 66 n. 2, 76, 121, 339.
argument, analytic or regressive, I 457.
indirect, II 198; see aho proof.
progressive and legressive, I 130.
synthetic and analytic, I 130.
synthetic or progressive, I 457.
Aristotle, I 159 n. i, 187, 190, 246 n. i, 257, 578, II 18 n. i, 130 n. 7,
187 n. i.
4,158 GENERAL INDEX
arithmetic, I 160; see also geometry.
formulae of, II 129-31.
association, I 367 n. 2, 368, 489; see also ideas; reproduction.
astronomy, observational and theoretical, II 459.
atomism, of Hume, I 138, 354 n. 3.
atoms, and the void, II 148 n. 2, 154, 318 n. 5, 365.
attention, II 400.
attraction, see repulsion.
attributes, I 85, II 163.
analytic and synthetic, I 86 n. i.
Auffassungy or apprehensio, I 359 n. 7.
axioms, I 127, 218 n. 6, II 101, 124, 130, 431.
Axioms, of Intuition, Principle of the, I 218, II in.
Balfour, Lord, II 217 n. 2.
Barker, H., I 20, 280 n. i.
Baumgartcn, I 47, 48 n. 2, 85 n. 3, 100 n. 2, 138, 204 n. 5, 257, 257
n. 3 and n. 4, 307, 332 n. 7, 365, 522 n. 2, II 294 n. 5,
295 n. 2.
begreifen, I 263 n. 4, 376 n. 2.
or comprehendere, I 334 n. 8.
Begnff9 I 94 n. 5, 108 n. i, 115 n. i, 376 n. 2.
Begnffe, usurpierte, I 197 n. 2, 315 n. i, II 364 n i.
Beloselsky, Prince von, I 332 n. 5, II 21 n. 4.
Berechtigiing, see Benchtigung.
Benchtigung, and Beretlitigung, II 217 n. 2.
Berkeley, 1 48, 67, 71, II 262 n. 2, 375, 376-7, 3?8 n. 4, 381 n. 3, 418.
Bestimmungeriy I 107 n. 4, 112 n. 3, 133 n. 6, 171 n. i.
Bewusstsein, I 332 n. 7, 333.
bezeichnen, II 232 n. i.
bezeichnety I 141 n. 5, 158 n. 2, II 123 n. 4, 170 n. i, 216 n. 3, 253 n. 3.
Bezeichnung, II 123 n. 4.
Blester, I 45 n. 4.
Black, II 119 n. i.
blind, I 96, 98, 170 n. i, 269, 270, 270 n. i, 321, 434, 455, 574-
bodies, I 561.
body, II 212.
the concept of, II 219.
Borowski, I 40, 46.
Bradley, I 252.
brain, phantoms of the, II 349.
Braithwaite, I 162 n. i.
Broad, I 514 n. 2, II 199 n. i, 329 n. i.
Brown, George, I 20.
Caesar, Julius, II 227 n. i, 228.
GENERAL INDEX 46^
Caird, E., I 17, 213 n. 5, 260 n. 3, 290 n. i, 300 n. 4, 349 n. 1,422 n. i,
513 n. 3, 560 n. 2, 581 n. i, II 27 n. 2, 51, 51 n. i, 361,
3?i.
canon, I 189, II 23 n. 3.
capacities, original or underivative, I 345.
capacity, -I 94, 345 n. 4.
Cassirer, Ernst, I 49 n. i, II 147 n. 4.
Cassirer, Heinnch, I 20.
casust I 197 n. 2, II 364.
categories, I 225, 226, 426, 488-91, II 432-5; see also apperception;
concepts; intuition; mind, infinite; revolution, Coper-
nican; space and time.
and formal conditions of sensibility, II 31; and forms of
judgement, I 259, 293-7, 299, 341, 475, 524; and
forms of thought, I 430-2; and the form of time,
I 532-5; and generic concepts, I 306-7; and human
experience, I 526-7; and knowledge of noumena, II
450-1 ; and the manifold, II 455 ; and non-human in-
telligence, I 531-2 ; and the self, II 423 ; and synthesis,
II 338 n. 5 ; and the transcendental object, II 444.
as acts of pure thought, I 224, II 450 n. 2.
as conditions of the unity of self-consciousness, I 426.
as predicates of possible judgements, II 25.
claim of the, II 450-1, 456.
clue to the discovery of, I 169, 239, 297-300.
completeness of list of, I 308-9.
Deduction of the, sec Deduction.
definitions of the, I 256-60, 303, II 433, 434.
derivation of the, II 75.
discovery of the, I 299.
limits of knowledge through, I 530-1.
names of the, I 298.
objective reality of, II 348.
objective validity of, I 321, II 453-4.
pure, I 260, 298, 304, 320, 325, 526, 532, 555, II 63, 343,
434-
pure, without sense and meaning, I 304 n. 2.
schematised, I 260-1, 304.
schematised and pure, II 82.
subsumption under, II 24-5; difficulty of, II 25-8.
table of, I 297.
trichotomy of the, I 305-6.
use of, empirical and transcendental, I 231, II 338.
use of, transcendental, II 438, 460.
category, and schema, II 42-4, 68-70, 76, 102, 182.
pure, II 42.
pure and schematised, II 41, 42, 67-8.
transcendental use of the, II 436-7.
470 GENERAL INDEX
category, two senses of, I 66 n. 4.
causa cognoscendiy II 363 n. i.
causa essendiy II 363 n. i.
c ausa fiendi , II 363 n. i.
causality, I 308, 445-6, II 106.
analysis of the concept of, II 281-3.
and time, II 273-5.
argument for, 'moments' of the, II 257; presuppositions of
the, II 262.
category of, I 544~5-
continuity of, II 292.
double, I 64, 96 n. i ; see also affection, double.
kinds of, II 278.
origin of the concept of, II 248-9.
predicables of, II 282.
Principle of, II 221-4, 283.
reciprocal, II 314; of co-existent substances, II 327; of
simultaneous states, II 327.
six proofs of, II 224-5.
subject of, II 216.
transcendental schema of, II 54, 236 n. i, 243 n. i.
vertical and horizontal, II 150 n. 2, 279n. i.
causation, and continuity of time, II 288.
streaky view of, II 297 n. i.
cause, and effect, I 326-8, II 70, 362-3; the law of, II 221; quanti-
tative equivalence of, II 179 n. 5; the schematised category
of, II 54; simultaneity of, II 283-4, 327; successiveness of,
II 283-4.
causality of the, II 284.
concept of, I 433.
determines effect, II 244.
efficient or effective, II 281
causes, final, II 278.
certainty, II 100 n. 2.
intuitive, II 125, 145, 147.
intuitive and discursive, I 545 n. 4, II 56, 100-3.
change, I 148, 152, II 188, 216, 226, 268 n. 2.
and exchange, II 216, 217.
and motion, I 101, 128.
and the permanent, II 407.
a way in which the permanent exists, II 202.
the concept of, II 217-18, 395.
the continuity of, II 153, 256, 284-7, 291-2.
experience of, II 196-7.
the form of, II 285, 290.
the law of continuity in, II 288-9.
subjective, awareness of, II 384.
changes, measurement of, II 196.
GENERAL INDEX 471
T/ •
chimaera, I 193.
Cicero, I 255 n. 3.
cinnabar, I 368.
Circe, II 229 n. 6.
clear, I 266 n. 4.
clock, ship's, I 197 n. i, II 349.
coexistence, see also interaction.
meaning of, II 297-8.
necessary, II 314.
objective, II 301, 305, 307, 309
objective and necessary, II 312.
objective, and causation, II 314.
objective, and objective succession, II 264, 301, 311-12.
cogmtio discursivay I 216.
cognition, different grades of, I 334.
subjective sources of, I 353.
cognitions, a priori, origin of, I 223 ; see also origin.
cognoscere, see erkennen.
Cohen, Hermann, I 84 n. 2, 422 n. i, II 130 n. 5, 439 n. i.
Coleridge, I 13.
colours, totality of, I 117.
combination, see also connexion.
or synthesis, I 503-10.
subjective and objective, I 504.
commeraum, I 297 n. 3, II 55 n. 3, 294 n. i, 316, 326.
communw, I 297 n. 3, II 55 n. 3, 294 n. i, 316, 319 n. 3.
communion, II 55 n. 3, 294, 294 n. 2, 309; see also apperception.
dynamical, II 326.
subjective, II 320.
subjective, objective ground of, II 320.
communion, pure category of, II 54-5.
comparison, reflexion, and abstraction, I 199, 249.
composition, Kant's method of, I 45, 53.
composituniy and totum, II 323 n. 2.
composition realey and compost turn ideale, II 323 n. 2.
comprehetiderey see bcgreifen.
comprehemiOy see Zusammenfassung.
comprehension, I 334.
conceiving, and judging, I 201-2.
form of, I 203.
concept, see also concepts; synthesis.
and existence, II 358; and imaginative synthesis, I 272, 465;
and intuition, I 94, 115, II 26; and rule, I 388-90; and
rule of imaginative synthesis, I 273; and schema, II 35.
a priori factitious, I 197.
arbitrary or factitious, I 196.
different types of, I 196-8, II 343, 346- 54.
empirical, I 196, 473.
^72 GENERAL INDEX
concept, empirical factitious, I 197.
form of the, I 196.
'in a', I 195.
intellectual, or notion, I 196.
limiting, II 457, 458 n. i.
logical form of a, II 430.
mathematical, I 197, 389, 473, II 26.
mathematical, and schema, II 33.
nature of the, I 94, 192, 249-51.
of body, I 391, II 219; of circle, II 26; of dog, I 273 n. 2;
of God, I 352; of object in general, I 417; of objec-
tivity, I 424; of spirit or soul, I 351 ; of tree, I 199; of
triangle, I 272, 388-9.
possibility in relation to different types of, II 346-54.
pure, two types of, I 317.
recognition in the, I 375.
'under a', I 195.
universality of the, I 196.
conception, II 344; see also analysis; intuition.
concepts, see also concept; imagination.
analysis of, I 160, 172, 238.
a prwny I 497; objective reality of, II 89.
bringing the pure synthesis to, I 278.
bringing the synthesis to, I 263, 271-3, 388.
clear knowledge of, I 200.
completeness in, II 336 n. 2.
complex, I 268.
construction of, I 160.
content or matter of, I 267.
empirical, I 197, 390-2, 430, II 26, 445 ; and universal, 1 139 ;
and necessary synthetic unity, I 430; and schemata,
II 35; objective reality of, II 347.
factitious, I 198, II 349.
• form of, I 198-203, 249, 267; made and not given, I 198.
general, I 1 1 5 n. i .
generic, see categories.
higher or wider, I 254 n. 4.
intellectual, or notions, I 197; see also concepts, sensuous.
logical origin of, as regards their form, I 199.
mathematical, I 161 n. 3, 197, 304 n. 2, II 347 n. i, 431-2;
and the categories, I 277; objective reality of, II 350.
matter of, I 192-6, 268.
origin and acquisition of, 1316.
partial, I 194.
predicates of possible judgements, I 251.
pure, I 225 ; see also intuition, pure.
pure, and acts of pure thought, I 224 ; see also categories.
sensuous and intellectual, II 458.
GENERAL INDEX 473
concepts, simple, I 194.
synthesis in accordance with, I 442.
unity in accordance with, I 429-30.
universal and particular, I 303.
usurpatory, I 197 n. 2.
.use of, empirical, II 427-9; empirical and transcendental,
II 439; transcendental, II 429-31.
Concepts, the Analytic of, I 236, 238-9.
conceptus communis, I 201.
conccptus dati, I 196 n. 5.
factitn, I 196 n. 5.
condition, see form.
confused, I 266 n. 4 ; see also distinct.
and distinct, I 133.
connexion, II 226, 335 n. 6.
and combination, II 159 n. 5, 173 n. 2.
necessary, II 159, 170; and existence, II 360; see also
experience.
objective, I 464.
teleological, II 278 n. i.
connotation, I 193 n. i, 195.
conscientia, I 332 n. 7, 398 n. i.
consciousness, I 332; see also synthesis.
animal, I 332-5, II 383; see also animals.
categories not the conditions of, I 334.
empirical, I 463.
empirical and transcendental, I 460-2, 483.
mediate and immediate, I 377.
possible, I 477-8.
consciousness, unity of, I 378-9; analytic, I 201, 202, 289 n. i, 514
n. 2 ; formal, I 385-7 ; necessary synthetic, 1 461-2 ;
subjective, I 519; see also appearance, unity of;
manifold, unity of; object, unity of.
conservation, the Cartesian doctrine of, II 197 n. 4.
constitutive, II 179.
construction, II 351, 432.
a priori, the necessity of, I 158-60.
symbolical and os tensive, I 158.
content, transcendental, I 289, 291-2, 301.
contingent, the, I 519 n. 5, II 102 n. 6.
continuity, the doctrine of, II 152-3; see also activity, causal;
causality; change; space and time; time.
the formal condition of apprehension, II 289-93.
Cook Wilson, I 405 n. i, II 214 n. 2.
co-operation, of mind and reality, I 581-2.
Copernicus, I 75.
copula, I 522.
correspondence, see truth.
474 GENERAL INDEX
counting, I 374.
Cousin, D. R., I 20, 280 n. i.
Croce, I 563 n. i.
crude, I 266 n. 4.
Darstellung, II 73 n. 4.
day, see night.
Dasein, I 297 n. 5, II 52 n. 3, 58 n. 2.
Dauer, II 45 n. 2.
deduced, meaning of, II 368.
deduction, meaning of, I 313.
Deduction, of the Categories, the, I 220.
Metaphysical, the, I 239, 280, 325 n. 5, 521, 538, 538 n. i,
553 ; divisions of, I 245 ; sec also Deductions.
Objective, the, I 240, 350-2, 523-5; method of, I 342-4;
summary of, I 502-3.
Subjective, the, I 240, 352~3> 54*-2; aim of the, I 537-8;
and the Objective, I 527 (see also Deductions);
framework of, I 529-30; method of, I 344-7.
deduction, transcendental, in general, I 314; necessity for, I 319-21;
principle of, I 344; principles of, I 313-14.
transcendental, of the categories, difficulty of, I 322-3 ; of
the categories, difficulty of, illustration of, I 326-7 ; of
the categories, difficulty of, reasons for, I 322-3.
transcendental, of space, I 321 ; of space and time, I 109,
319 n. 2.
Deduction, Transcendental, the I 316, 552, II 40, 275, 443; argument
of, I 558-61, II 265 ; authoritative exposition of, 1313,
348, 457-8; divisions of, I 313; in the first and second
editions, I 499-501 ; progressive exposition of, I 457;
provisional exposition of, I 53, 313, 322 n. 5, 348,
364, 365 n. 3, 457; regressive exposition of, I 476;
subjective and objective sides of, I 555-8.
deductions, empirical and transcendental, I 314-16.
Deductions, Metaphysical and Transcendental, I 239-41.
Subjective and Objective, I 241-2, 473, 501-2, 528-9.
definition, real, I 303-4, II 433.
definitions, in philosophy, 151.
degree, II 49~5°> i35> r4°, i49> 285; see also time.
Demonax, II 210 n. i.
demonstration, II 101 n. 3.
denotation, I 195.
derivative, I 118 n. 2.
Descartes, I 398 n. i, II 164, 165 n. 8, 184 n. i, 381 n. 3, 401, 401
n. 4; and Berkeley, II 376-7.
determmately, I 541.
determination, II 176; temporal, II 313; see also Bestimmung ; time-
determination.
GENERAL INDEX 4^
determine, meaning of, II 244, 252 n. 10, 254, 313, 319 n. 4, 338 n. 2,
342, 363 n. 2, 390-
deuthch, I 266 n. 4.
development, psychological, in time, I 317.
de Vleeschauwer, I 18, 53 n. 3, 365 n. 2, II 281 n. 3.
dialectic,. Hegelian, I 306.
Dialectic, Transcendental, the, I 74, 170 n. i, 235, 237, II 366.
dichotomy, I 306.
differences, empirical, due to things, I 140.
discontinuity, II 364.
discursive, I 216 n. 3.
distinct, I 266 n. 4; and indistinct or confused, I 377.
distinctness, see indistinctness,
doctrine, Kant's, novelty of, I 46-8.
rationalist, I 336.
DoktriHy II 23 n. 3.
dream, I 434.
dreams, 145911. i, 539 n. 9, 54*> II 121 n. 3,267,270, 359 n. 2, 385-6.
dunkely I 266 n. 4.
duration, II 45, 166, 188; see also permanence.
Eddy, Mrs., I 55.
effect, see cause.
empirical criterion of the, II 268 n. 3.
efficacy, real, II 282.
Eindrucky 1 97 n. 3, 477 n. 3.
etnfliessen, and Ewfluss, I 458 n. 5.
Etnfluss, see etnfliessen.
einsehen, or perspicere, I 334 n. 7.
Einstein, I 162 n. 2.
elements, heterogeneous and homogeneous, II 160.
Empfindungy I 477 n. i, 539 n. 2.
empty, I 222 n. 2.
energy, II 207, 209.
England, I 213 n. 5.
epigenesis, I 578.
equation, 7 + 5 = 12, I 160, II 129.
Erdmann, Benno, I 100 n. 2, 418 n. 4, II 24 n. 5, 99 n. 4, 141 n. 8,
186 n. 3, 200 n. i.
Erdmann, J. E., I 377 n. 2.
Erfahrungy II 383.
Erfahrungsbegnffy I 196 n. 4.
erkenneriy or cognoscere, I 334 n. 5.
Erkenntnisgrund, I 195 n. 3.
ErlebntSy II 383, 413, 421.
Erzeugung, II 221 n. i.
essence, I 85, II 163.
^6 GENERAL INDEX
essentialia, I 85, II 163.
Euclid, I 159, 432 n. 3.
events, the objective order of, II 169-71, 227.
evidence, intuitive, II 62 n. i ; see also certainty.
Evidenz, II 100 n. 2.
Ewing, I 398 n. 4, 529 n. 2, 573 n. 2, II 192 n. 2, 254 n. 8, 256 n. i,
276 n. 2, 294 n. 5, 423 n. 3.
exact, I 266 n. 4.
exchange, II 216, 217; see also change,
exhibition, II 73.
existence, II 169, 178, 298; see also actuality; concept; connexion.
and actuality, II 357 n. i ; and matter, II 359.
determinate and indeterminate, II 404.
my, consciousness of, II 385; my, determination of, II 402,
406, 408, 410; my, knowledge of, II 380-1.
of other men, I 179.
— necessary, II 362.
not restricted to the present, II 358.
E\istenz, II 58 n. 2.
experience, I 318, 331, 426, 431, 489, 531, II 169-71, 175; see also
science ; synthesis, pure.
advance of, in time, II 290.
analysis of, I 547~9> 575 » 579-
and necessary connexion, II 175.
conditions of, II 268-71, 272.
development of, I 577-9, II 272.
divine, I 178, 427, 559-
form of, II 90, 338.
formal conditions of, II 335, 337, 341, 345, 348.
formal and material conditions of, II 341.
human, I 178-80, 526-7; all-embracing system of, II 367;
empirical and a priori within, I 559.
immediate, II 381; see also inner experience; outer
experience.
inner, II 382, 408; and permanent substances in space,
II 410; and pure apperception, II 381; and outer,
I 147, II 386; immediacy of, II 383; space, mediate
condition of, I 147.
judgements of, I 270 n. 3.
material conditions of, II 335.
matter of, II 338.
matter and form of, I 78.
metaphysic of, I 72.
one all-embracing, I 427-9, 450-3 ; the phenomenal world
as, II 366 n. 3, 367.
outer, immediacy of, II 381.
possible, I 350, 531, II 89, 461 ; the pure schema of, II 428.
possibility of, I 472, II 90-5, i?5, 354-6.
GENERAL INDEX 47^
experience, process to, II 271-3.
unity of, I 427-9.
universal conditions of, II 336, 341-2.
experiences, of different individual men, I 428.
exposition, II 194 n. i.
»- Kant's method of, I 348, 382, 488 n. 4; the competence of,
II 370-1, 463-
metaphysical, I 108; see also space and time.
transcendental, I 108, 108 n. 4 ; see also space and time.
extension, II 412.
extension, see denotation,
extent, I 225, 228, 240.
Fdhigkeit, I 94 n. 4, 345 n. 4.
fate, I 197 n. 2, 315.
fatum, I 197 n. 2, II 364.
force, II 215 n. 3, 282.
forces, moving, II 135 n. 3, 137, 138 n. 3, 149, 212, 324, 326 n. i,
412; see also repulsion and attraction,
form, and condition, I 103, 103 n. 4, 137.
and matter, I 97, 137-43.
empirical, I 140, 142 n. 3.
intellectual, I 497.
freedom, I 66, 74.
function, I 250, 281, 413 ; see also mind.
and act, I 413.
and power, I 419.
definition of, I 247.
identity of, and identity of act, I 440.
meaning of, I 245-8, 434-8.
functions, see synthesis.
of unity, I 246, 247, 248.
Galileo, I 75.
Garve, I 45 n. 4.
Gegenstand, I 193 n. i.
Gegenwirkung, II 295 n. 2.
Gemeinsthaft, I 297 n. 3, II 55 n. 3, 294 n. i, 316, 319 n. 3.
Gemut, I 95 n. 4.
genau, I 266 n. 4.
general, and universal, I 77.
geometries, modern, I 160-3.
geometry, I 126, 319-20; and arithmetic, II 131.
axioms of, II 124-5 \ see a^so axioms.
— Euclidean, I 159, 161.
— pure, I 1 06, 127.
478 GENERAL INDEX
GesctZy and gesetzt, I 446 n. i.
gesetzt, II 228 n. 4; see also Gesetz.
Gestalt, II 45 n. 2, 127 n. 4.
given, I 506 n. i, 515, 541, 580, II 88.
ambiguity of the word, I 525.
Gtock, II 364 n. i.
gravitation, the law of, II 295, 324 n. 2.
gravity, the moment of, II 150 n. 4.
Green, T. H., I 386 n. 5.
ground and consequent, the pure category of, II 18, 53.
Grundkraft, II 350 n. i.
Hardy, I 155 n. i.
harmony, pre-established, I 181, 556, 574.
Heath, I 130 n. i.
Hegel, I 65, 386 n. 5, II 362, 371.
Herz, I 44 n. 6, 46 n. i, 321 n. i.
hiatus, II 364.
Hirngespinst, I 220.
Hirngespinste, II 349 n. 5.
history, mental, II 423.
homogeneous, synthesis of the, II 44.
Hume, I 43, 44, 46, 48, 67, 138, 354 n. 3, 373, 444 n. 3, 571, II 144 n. 3,
146, 168, 171, 219, 222, 226 n. 3, 248 n. 3, 262 n. 2, 270,
283, 378 n. 4.
'!', constant and unchanging, I 486.
— the idea, I 463.
idea, I 334; see also ideas; object; representation; thing; Vorstellung.
contained in one moment, I 358, II 193.
discursive, I 198 n. 4.
of the permanent, and permanent idea, II 411.
Idea, I 238 n. i ; see also reason,
idealism, and science, I 68-70.
Berkeleyan, and space, II 376.
dogmatic, II 376.
empirical and transcendental, II 376.
formal, II 426.
material and formal, II 376.
problematic, II 376, 381.
representative, II 376.
transcendental, I 143 n. 3, 144 n. 2, 453, II 411, 412; see
also realism, empirical.
turning the tables on, II 381-4.
Idealism, Refutation of, II 377-80.
idealisms, modern, II 464.
GENERAL INDEX 479
ideality, transcendental ; see reality, empirical,
ideas, a priori, I 80; and object, I 338.
association of, I 480; see also affinity; association.
clear and obscure, I 377-9, 463-4.
co-existence of, II 331.
empirical, I 337-8.
innate, I 377.
objective unity of, I 523.
of space and time not empirical, but a priori, I 110-14.
play of, I 434, II 245, 263.
Ideas, see reason.
illusion, see appearance.
image, I 477, 479, II 37.
image, and time, II 37.
imagination, I 263, 269, 345, 363, 536, II 87, 301,411; see also sense.
and concepts, I 465; and judgement, II 71-2; and sensi-
bility, I 488 ; and understanding, 1 269 n. 3, 488, 503,
536, II 392.
associative, I 366.
plastic, I 366.
play of, II 257, 259, 43i.
productive, I 484, II 395.
reproductive, I 114, II 89, 354 n. i.
reproductive and productive, I 365.
three kinds of, I 366-7.
transcendental, and apperception, I 486-8.
transcendental, and experience, I 484-5.
transcendental power of, I 364.
uncontrolled by thought, II 227.
imagination, synthesis of, I 572, II 257; formal unity in, I 490;
necessary aspects of, II 56 ; principle of the necessary
transcendental unity of the pure (productive), I 465 ;
pure, I 464-6; reproductive, I 464, 536 n. 2.
imagination, transcendental synthesis of, I 413, 431, 440-1, 467, 475,
4^3-5, 529, 535-7, 540, SS^, 558, 576, 581, II 71-2,
77, 174, 278-80, 388-9, 392; and necessary synthetic
unity, I 485; and time, I 536, II 421.
productive, I 536 n. 2; re-
productive, I 364; tran-
scendental unity of, I
468-9.
immanent, I 232.
immediacy, proof of, II 382.
immediate, meaning of, II 383.
impenetrability, I 391 n. 4, II 135 n. 3, 207.
impression, I 97, 477.
Indiscermbles, Identity of, I 180, 452 n. 2.
indistinct, T 266 n. 4 ; see also distinct.
480 GENERAL INDEX
«
indistinctness, and distinctness, II 441.
infinity, I 305.
influence, I 62, 65, II 143 n. 7, 294 n. 5, 295, 309; see also things-in-
themselves.
reciprocal, II 326.
influences, continuous, II 317.
Inhalt, I 195 n. 5.
inherence, II 203.
and subsistence, II 298.
inner and outer, meaning of, II 408.
inside, and outside, I 100.
insight, I 334, II 382.
intelligence, an infinite, I 527.
non-human, see categories.
intelligere, see verstehen.
intelligibilia, II 441.
intension, I 193 n. i, 195.
interaction, II 294, 294 n. 2, 295-6, 309, 317, 326.
and co-existence, II 324-9; and sense-perception, II 316-
18; and space, II 330; and the unity of apperception,
II 319-24.
concept of, II 324-5, 330.
dynamic, II 315.
matter in, II 317.
mediate, II 318.
mediate and immediate, II 315, 328.
Principle of, II 294-7.
proof of, II 329-31.
schematised category of, II 55, 323.
transcendental schema of, II 55, 315.
intuition, I 73, 93-8, 458; see also concept; intuitions; possibility;
thought.
and conception, I 122-4; an<i object, II 119-21; and
thought, I 431, II 460; and understanding, I 329-32.
by itself, blind, II 455 ; see also intuitions, blind.
categories independent of, I 122.
empirical, see validity, objective.
form of, I 101-3, H 4J4'
form of, and pure, I 104, 109.
in general, I 284 n.3, 287, 289-92, 528, 534, 538, 542.
in general, and human intuition, I 260.
intellectual, I 178, 217, 217 n. 3, 532, II 403, 405, 410,415,
441, 452, 454, 456.
matter of, II 138.
mere, II 113.
mere, synthesis of, II 341 n. i.
outer, see time.
outer, and relations, II 412.
GENERAL INDEX 481
intuition, permanent, II 384 n. i.
pure, I 103-6.
pure, in two senses, I 105.
pure, and the categories, I 262 ; and form of intuition, I 104,
109; and pure concepts, I 338-40.
intuitions, blind, I 96, 98.
in general, I 526 n. i.
intellectual, I 249, 5^7> 53°-
pure, I no.
space and time not concepts but, I 114-15.
unconscious, I 458.
investigation, psychological or physiological, I 200.
irreversibility, II 246 ; see also sense-perceptions.
'I think*, I 463, 518-20.
the idea, I 510.
Jachmann, I 349 n. i.
Joseph, I 204.
judgement, I 251-6, 548, II 337; see also imagination; judgements.
acts of understanding can be reduced to, I 251.
analysis in all, I 219, 283.
analysis and synthesis in, I 265, 269.
analytic, I 201, 549 n. i.
apodeictic, I 202 n. 3.
a priori synthesis in all, I 516.
definition of, I 206, 220, 522.
form of, I 288.
form of, one ultimate, I 207 ; see also apperception.
forms of, I 204-6, 209, 246, 248-9, 294, 435; see also
categories ; judgement, moments of.
forms of, and the categories, I 259, 260, 293-7, 299, 341,
475, 524.
forms of, as moments, I 211, 294.
forms of, classification of, I 204.
forms of, common to all judgements, I 215.
forms of, table of the, I 204, 568.
forms of, universal and necessary, I 206-8.
functions of, I 246.
hypothetical form of, II 223.
infinite, I 205, 208 n. 2, 212 n. 2.
metaphysical, I 89.
moments of, I 211, 294.
moments and forms of, I 208.
power of, II 21.
problematic, I 202 n. 3, II 344.
singular, I 205, 208 n. 2.
synthesis in every, I 220, 509.
VOL. II Q
f.te GENERAL INDEX
judgement, synthetic, different kinds of, II 84-6.
two aspects of, I 280, 287.
unity in, I 281-3.
Judgement, the Transcendental Doctrine of, I 236, II 21-4.
judgements, analytic, I 84-6, 189 n. 8, 214, 300 n. 5, II 84.
analytic, principle of, II 83-4.
analytic, truth of, I 214, 214 n. 3, II 84.
analytic and synthetic, I 81, 82-4, 220, 300-2, 508, II 460.
analytic and synthetic, analogy between, I 301.
copulative, I 204.
of physical science, I 89.
logical forms in all possible, I 213.
mathematical, I 87, 89, II 91.
matter of, I 206.
metaphysical, I 89.
modality of, I 205.
— problematic, assertonc, and apodeictic, II 57.
— quality of, II 51.
— simple and complex, I 204.
— - synthetic, I 86-7, II 86, 461.
— synthetic a posteriori, I 88, II 85, 94-5.
— synthetic a priori, I 81-2, 87, II 91.
— synthetic, different kinds of, 11 84-6.
— synthetic, form of, 1213-15.
— synthetic, principle ot all, II 94-6.
synthesis in all, I 509.
judging, see conceiving.
Kanthteratur, I 18.
Kemp Smith, I 19.
Commentary, I 37 n. i, 38, 43 n. i, 49 n. 2, 75 n. 3, 201
n. 4, 213 n. 5, 216 n. 2, 217 n. 5, 250 n. 6, 300 n. 4,
305 n. 4, 307 n. i, 323 n. 4, 329-30, 332~3, 339 n. 5,
345 n. 2, 346 n. 6, 382, 397 n. i, 413 n. i, 421-5,
421 n. 7, 423 n. i and n. 2, 424 n. 3, 425 n. 4
and n. 5, 490 n. 2 and n. 3, 516 n. 2, 529 n. 2,
573 n. 2, 583 n. i, II 21 n. 4, 24 n. 5, 25 n. 2,
66 n. 2, 69 n. 2, 165 n. 7, 182 n. 4, 224 n. 2, 282
n. 6, 289 n. 2, 294 n. 5, 301 n. 4, 335 n. 6, 339,
340 n. 3, 346 n. 3, 359 n. 3, 367 n. 3, 37<>-i-
Translation, 1 147 n. 2, 195 n. 6, 339 n. 5, 371 n. 3,
378 n. 2, n. 3, and n. 5, 391 n. i, 418 n. 4, 444 n. 4,
458 n. 5, 462 n. 3, 463 n. 2, 492 n. 7, 495 n. 2,
512 n. i, 528 n. 6, 531 n. 5, 534 n. 2, 537 n. i,
540 n. i, II 24 n. 5, 36 n. 3, 50 n. 3, 60 n. 3, 84 n. 4,
86 n. 6, 87 n. 2, 90 n. 5, 91 n. i and n. 3, 92 n. 4,
115 n. 4, 163 n. 4, 166 n. 5, 169 n. 3, 178 n. 5,
GENERAL INDEX 483
181 n. 5, 186 n. 5, 217 n. 7, 249 n. 4, 251 n. 2, 258
n. 6, 317 n. 2 and n. 3, 399 n. i, 429 n. i, 436 n. 4.
kennen, or nose ere, I 334 n. 4.
Kinkel, I 84 n. 2, 213 n. 5, 232 n. 3, II 130 n. 5.
klar, I 266 n. 4.
knowing, see thinking.
knowledge, I 334, 354, 582 n. i.
acquired and innate, I 78.
a priori, I 76-7.
a priori, comparatively, II 358.
a priori, conditions of, I 278-9 ; double character of, I 564 ;
types of, I 80-2 ; see also a priori.
empirical, an advance in time, II 289.
limits of, II 429, 460-2.
mathematical, I 170 n. i, 530.
mathematical, intuitive, I 218.
philosophical and mathematical, I 218, II 101.
pure a priori, I 76.
pure, synonymous with a priori, I 77.
subjective sources of, I 345, 354, 401.
synthetic a priori, I 561-3.
transcendental, I 226-30 ; see also theory, transcendental.
two factors in, I 269-71.
use of, transcendental, I 230-2.
Krdfte, bewegende, II 137.
Kntik, II 23 n. 3.
Laird, II 256 n. 5, 260 n. i.
Lambert, I 182 n. i.
language, Kant's use of, I 50-4.
Laughland, Miss Elizabeth, I 20.
law, see rule.
causal, and the transcendental synthesis of imagination, II 278-80.
definitions of, I 495.
laws, see rules.
causal, empirical, II 363; causal, particular, II 275-8.
empirical and universal, I 139-40.
of nature, I 450, 496, II 98 n. 2.
of nature, empirical, I 496.
particular empirical, I 494.
particular necessary, I 494.
ultimate and universal, I 496.
universal, I 546.
lecturing, Kant's method in, I 349.
Leibniz, I 43, 78, 107, 125, 125 n. 2, 138, 145, 161, 171, 173, 175, 183,
235 n. 2, 309, 359 n. 6, 377 n. 2, 398 n. i, 458, 477 n. 4,
562, 563 n. 4, 564 n. 2, II 295, 353, 366, 441.
^84 GENERAL INDEX
Leibniz, arguments against, I 171-5.
Lenzen, II 282 n. 4,
Levett, Miss M. J., I 20.
light, I 64, II 317, 328.
limitation, II 48, 149.
limits, I 228, 240.
Lindsay, I 135 n. 3, 138 n. 3, 142 n. 3, 576 n. i, II 128, 297 n. i, 418
n. i, 458 n. i.
line, intuition of a, II 389.
knowledge of a, I 372, II 193.
Locke, I 48, 100 n. 2, 315 n. 3, 317, 377, II 203 n. 5, 206 n. i, 376 n. 6.
Loewenberg, II 269 n. i.
logic, applied, I 1 88; general, I 187; mathematical, I 188, 210; modem,
I 172; philosophical, I 188; special or particular, I 187.
Logic, Formal, I 187-8, 521, 525.
Formal, divisions of, I 188-90.
Transcendental, I 223-6, 487 n. 5.
Transcendental and Formal, I 222-3, 232-3, 278, 293.
Transcendental, and time, I 261.
Transcendental, divisions of, I 233-5.
Lucian, II 210 n. i.
luck, I 197 n. 2, 315.
Maimon, I 321 n. i.
Malebranche, I 132 n. 7, 321 n. 5.
manifold, as a manifold, I 357, 359.
empirical, and pure synthesis, I 466.
given, and the categories, II 455.
homogeneous, II 115.
in general, I 507 n. 5.
necessary synthetic unity of the, I 462, 515.
synthetic unity of the, I 551.
transcendental principle of the necessary synthetic unity of
the, I 459-60.
unity of the, I 459-60, 512.
mark, I 125, 194.
marks, I 119 n. 2, 549.
mass, II 206, 209, 212.
conservation of, II 209.
mathematical theory, modern, I 155.
mathematicians, the intuitionist school of, II 119.
mathematics, I 73, 160, 218.
application of, to objects of experience, II 131-3.
principles of, II 97.
pure, I 81, 530 n. 4.
matter, I 96 n. 2, II 135 n. 3, 138 n. 4 and n. 6, 149, 210 n. 3, 317; see
also existence; form.
GENERAL INDEX 485
matter and substance, II 211.
- conception of, II 207.
- conservation of, II 197, 209, 213-14.
dynamical theory of, II 155.
— magnetic, II 357.
— mechanical theory of, II 155.
— permanence of, II 204.
quantity of, II 212.
Mattmgly, Miss Lilian, I 20.
meaning, II 31 n. 3.
mechanics, third law of, II 295.
three laws of, II 213.
Meier, G. F., I 47, 85 n. 3, 190 n. 3, 200 n. 5, 257 n. 3, 309, 332 n. 7,
522 n. 2.
Mellm, I 221, 247, 247 n. 6, 332 n. 7, II 86 n. 5, in n. i.
memory, I 401, II 171-2.
Mendelssohn, I 44, 45 n. 4, 182 n. i.
Merkmal, I 194 n. 2
McrkmalCy I 119 n. 2.
metaphysics, as a natural disposition, I 82.
as a science, I 82.
claim made hy, I 80.
first part of, I 76.
Meyerson, II 220, 362 n. i.
Milky Way, I 267 n. 2.
mind, infinite, and our categories, II 460.
common function of the, I 441.
object in relation to our, II 336.
windows of the, I 183, II 424.
minds, co-existence of, II 331.
modality, interdependence of categories of, II 339-42.
schema of the category of, II 61.
schemata of, II 56-60, 342 n. 3.
mode, II 163.
modes, I 85, II 164; see also sensibility, pure; space; time.
moment, I 211, II 287 n. i.
monads, I 183.
monogram, II 36.
Moore, G. E., II 225.
morality, I 72.
More, Henry, I 321 n. 5.
motion, I 148, II 210 n. 3, 288, 412; sec also change; synthesis.
and change, empirical, I 101 ; see also change, and motion.
general doctrine of, I 128.
movable, the, II 149, 210 n. 3, 211.
the, and substance, II 211.
Muirhead, J. H., I 20, 216 n. 3.
mundus sensibilis, and mundus intelhgibilis, II 458.
486 GENERAL INDEX
natura formaliter spectata, I 412 n. 4, 491 n. i, 545 n. 7.
natura materialiter spectata, I 412 n. 4, 545 n. 7.
nature, I 450, 491.
laws of, I 450, 496, II 98 n. 2.
uniformity of, I 445.
unity of, I 411-16, 449-50.
necessary, the, see actual, the, and the necessary,
necessity, II 57; sec also actuality; objectivity; possibility.
actuality no wider than, II 340, 343.
and substances, II 363.
ancj universality, I 77, 135, 146.
category of, II 340, 340 n. 2.
criterion of, II 363.
empirical, II 216 n. 8.
logical or formal, and real or material, II 362.
pure category of, II 58-9.
real, not absolute, but hypothetical, II 363.
schematised category of, II 59-60.
subjectivity and knowledge of, 1 169-71.
transcendental schema of, II 60.
negation, see reality.
neo-Kantians, English, I 65.
Newton, I 106, 113, 132, 144, 171, 174, 175, 176, 56711. i, II 13211. 4,
291 n. i.
arguments against, I 171-5, 176.
nexus, II 159, 170, 226.
Ntchtsem, I 297 n. 5.
night, and day, II 270, 270 n. 3.
non-contradiction, the law of, II 83-4.
noscere, see kennen.
nota, I 194 n. 2.
notion, see concept, intellectual.
notions, see concepts, intellectual.
noumena, II 441 ; see also phenomena.
alleged knowledge of, II 440-2; see also categories.
in the negative sense, II 453.
origin of the belief in, I 445-6.
noumenon, and the transcendental object, II 440.
concept of, II 445-6; as a limiting concept, II 456-8;
determinate, II 452; indeterminate, II 452; neces-
sary, II 456; problematic, II 456, 458, 461.
in the positive sense, II 454.
positive and negative meaning of, II 448, 452-3.
number, I 375, II 45-7, 114, 432.
numbers, II 127.
object, I 193, 325, 337 n. 2, 34°-i, 3 82-5* 5J6, II 235-6, 306; see also
affinity ; intuitions ; objectivity ; objects ; thinking ; thought.
GENERAL INDEX 487
object, actual, II 337.
and idea, I 337.
and its temporal relations, II 330-8.
as an unknown something, I 384, 418.
causality of the, II 150-1.
characteristics of the, II 417.
definition of, I 387, 396 n. 5, 516-17, II 235, 236.
determinate, I 341.
determinate and indeterminate, I 326.
existence of the, II 406-10.
form and matter of the, II 340.
immanent and transcendent, I 421.
indeterminate, I 51, 95-6.
in general, the concept of an, I 259, 341-2, 417, II 265, 402.
in relation to our mind, II 336.
knowledge of, II 265.
knowledge of, and knowledge of subject, I 361.
matter of the, II 138, 340.
meaning of, II 231, 250.
necessary, II 338.
phenomenal, I 51, 96, 151, 424, 425, II 234, 266.
possible, II 337.
reference of ideas to an, II 250.
succession m the, II 242.
transcendental, I 420-5, II 234, 237, 436, 442-5, 447~8, 461;
see also apperception ; categories.
transcendental, and thing-m-itself, I 420-5.
under all the categories, I 226.
unity of the, I 571.
unity of the, and unity of consciousness, I 386.
the word, I 50, 95.
objects, sec appearances and objects.
as they appear and as they are, II 459.
differences m, ignored by Formal Logic, I 191, 191 n. i.
in general, concepts of, I 342.
phenomenal, I 422.
Objektj I 193 n. i.
objective, and object, I 193 n. i.
objectivity, and necessity, II 270.
concept of, I 424-5.
obscure, I 266 n, 4.
obscurity, I 45.
Ontology, I 257, II 435.
handbooks of, I 307.
opposition, real and logical, II 149.
order, objective, II 173.
subjective and objective, II 172.
orders, subjective, II 227 n. i.
488 GENERAL INDEX
organon, I 189.
origin, I 223, 225, 227, 228, 316.
original, I 118 n. 2.
outer, I 99 n. 2.
outside, and inside, I 100.
'outside me1, meaning of, II 378.
Pacius, I 15.
Pappus, I 130 n. i.
Partialvorstellungcn, I H9n.2, 194 n. 3.
passion, II 282.
patchwork theory, the, I 38-40, 328-9, 498, II 346 n. 3.
the, consequences of, I 42-3.
Paulsen, II 196 n. 2, 282 n. 5.
perception, judgements of, I 270 n. 3.
perceptions, petites, I 477 n. 4.
percipere, see wahrnehmen.
perfection, logical, I 309, 390 n. 3.
permanence, II 53, 163, 166-7, 4*3-
and duration, II 188 n. 6.
the Principle of, II 184-5.
permanent, the, II 378; see also change; substance.
the, and time-determination, II 195-8.
the idea of something, II 384.
the, sense-perception of, II 379.
perspicere, see einsehen.
phenomena, and noumena, II 439-40, 451, 458, 461.
definition of, II 440.
outer, time the mediate condition of, I 149.
phenomenon, see appearance and phenomenon,
phenomenalism, see subjectivism.
philosophy, definitions in, I 51.
discursive knowledge, I 218.
Philosophy, Critical, central contention of the, II 455.
Critical, problems of the, II 375-6.
Transcendental, II 145 n. 2, 153, 207 n. 2, 284 n. 4.
Transcendental, and Physiology, Rational, II 137, 137
n. 2, 153 n. 3.
physical science, judgements of, I 89.
physics, I 73; pure, I 81 ; modern, I 162.
Newtonian, II 218, 282.
Physics, Rational, II 284 n. 4.
Rational, and Psychology, Rational, II 153 n. 3.
Physiology, Rational, II 208, 284 n. 4; see also Philosophy, Trans-
cendental.
Plato, I 54, 60 n. i, 159 n. i, 160 n. 2, 203 n. 2, 216 n. 3, 246 n. i,
347 n.4, 405 n. i, 562, II 52 n. i, 101 n. 3, 130 n. 7,
441 n. 2.
GENERAL INDEX 489
play, of ideas, I 434, II 245, 263.
polytomy, I 306.
posit, meaning of, II 413.
posited, II 54 n. 2, 228, 252 n. 4.
position, see shape.
.absolute, II 228 n. 4.
temporal, II 255.
possibility, II 57, 345.
absolute, II 368.
actuality, and necessity, II 57.
actuality, and necessity, absolute, II 338 n. 3; real, II 338;
real and logical, II 336, 344; real or material, II 337.
actuality, and necessity, the Principles of, II 335-9.
and actuality, II 341, 350; see also necessity.
and intuition, II 354.
and outer intuition, II 354.
Leibnizian, II 366-8.
logical and real, I 66, II 344, 346, 351.
no wider than actuality, II 339-40, 343, 366-7.
pure category of, II 58.
real, II 95 n. i, 336 n. i, 353.
schematised category of, II 59.
transcendental schema of, II 59.
possible, the, and the actual, II 366-7.
Postulate, the First, II 345-6.
the meaning of the word, II 368-70
the Second, II 357-62.
the Third, II 362-4.
postulates, mathematical, II 369-70.
power, I 94 ; see also function,
powers, I 345, 345 n. 4.
predicables, the, I 307-8.
predicates, universal, I 257.
prediction, II 283.
present, the specious, I 366, II 398.
Price, I 584 n. i, II 150 n. 2, 151 n. 3, 175 n. 4, 205 n. 4, 279 n. i.
Prichard, I 17, 77 n. 2, 80 n. i, 177, 177 n. 2, 213 n. 5, 277 n. i, 290
n. 3, 337 n- 2, 405 n. i, 500 n. 7, 565 n. 2, 581 n. i,
582 n. i, II 34 n. 4, 136 n. 3, 214 n. 2, 217 n. 2, 225,
234 n. 2, 240 n. i, 241 n. 5, 242 n. 3, 249 n. 5, 266 n. 2,
268 n. i, 272 n. i, 296, 298 n. 2, 299 n. i, 300, 306,
316 n. 4, 325, 378 n. 3, 380.
principle, different kinds of, II 97-8.
empirical, a contradiction in terms, II 97.
Kant's ultimate, an analytic proposition, I 518.
principles, synthetic, discursive, I 218.
Principles, I 226, 234, 493~4-
Analytic of, I 236, II 24.
VOL. II Q*
490 GENERAL INDEX
Principles, Dynamical, the, II 99-100, 235.
Mathematical, the, II 99-100, 178-9.
Mathematical and Dynamical, the, I 101-3.
of the Understanding, see Understanding.
proof of the, II 82-3.
prior, objectively, I 80.
priority, logical, I 177.
temporal, I 77-80, 136-7, 177, II 122 n. 3.
problem, the Critical, II 233.
reality of Kant's, I 89-90.
procedure, analytic, I 283.
proof, indirect, II 104, 244, 244 n. 2; see also argument.
Proof, the Ontological, II 359.
proofs, multiplicity of, II 224.
multiplication of, II 225 n. i.
proportion, II 179.
proposition, kinds of, I 210; see also judgement,
propositions, arithmetical, II 129.
enumerative and universal, I 209.
pro tensive, and extensive, II 125 n. 3.
psychology, I 318.
pure, I 77.
qualities, primary, I 391 n. 4, II 135 n. 3, 412.
primary and secondary, I 59-61.
secondary, I 167 n. 3.
quality, and quantity, II 155.
pure category of, II 48.
schema of, II 48-52.
schema of the category of, II 61.
schematised category of, II 49.
synthesis of, II 147-9, 341.
quanta, I 157, II 125.
examples of, II 127.
quantitas, I 157.
and quantum, II 125-9.
quantitas phaenomenon, II 45.
quantitatesy II 127.
quantities, continuous, II 152.
determinate extensive, II 118.
in general, II 352.
quantity, see quality.
category of, I 543, II 432.
extensive, II 45, 112, 114, 116.
extensive and intensive, II 136, 148.
extensive, schematised category of, I 275, II 45, 115, 126.
extensive, synthesis of, II 100.
GENERAL INDEX 40.1
quantity, intensive, II 49 n. 3, 135, 140, 143-7; synthesis of, II 100.
pure category of, I 275-6, II 44, 115, 125.
schema of, II 44-8.
schema of the category of, II 60- 1.
synthesis of, I 576, II 341.
quantum^ see quantitas.
and aggregate, II 152.
determinate and indeterminate, II 45 n. 4, 128.
indeterminate, II 112 n. 2, 194.
Ramus, Peter, I 190 n. 4.
rationalism, II 176.
Leibmzian, II 359 n. 3.
rationalists, I 323 ; see also doctrine.
reactioy II 295 n. 2.
real, the, II 207.
the, and sensation, II 136-8.
realism, I 337, II 176.
empirical, I 143 n. 3, II 375, 411.
empirical, and transcendental idealism, I 582-3, II 185, 247,
384-5, 426-7.
transcendental, II 377.
realistic tendencies, Kant's, I 70-1.
realitas phaenomenon, II 49 n. 3, 134, 135 n. 3, 137 n. 5, 138 n. 4 and
n. 6, 140, 191 n. 3, 285 n. 3.
reality, II 48.
and existence, II 357 n. i.
and negation, II 149.
empirical, and transcendental ideality, I 143-5.
objective, II 87, 345.
quantity of, II 287.
relation of appearances to, I 61-3.
reason, I 73, II 337.
Ideas of, I 198 n. i, II 73 n. 6.
Reason, Paralogisms of, II 419.
reason, sufficient, the principle of, II 255 n. 6.
recognition, I 489.
synthesis of, I 354, 356, 374-7, 379, 420, 488.
red, the idea, I 514 n. 2.
redness, I 125 n. 3, 268 n. i, II 35 n. 2.
reflexion, I 200 ; see also comparison.
regularity, and repetition, II 276-7.
regulative, II 179.
Reicke, I 289 n. i, 464 n. 3.
relation, determining, II 252.
schema of the category of, II 61.
schemata of, II 52-6.
492 GENERAL INDEX
relation, synthesis of, II 341.
systems of, I 172.
relations, I 85, II 163, 164; see also intuition, outer.
logical system of, I 173.
spatial and temporal, given, I 135.
temporal, see object.
Relativity, theory of, II 1 60 n. 5.
religion, I 72.
repetition, see regularity.
repetitions, I 349-50.
repraesentatio per notas communes, I 94, 194.
repraesentatio singularis, I 94.
representations, partial, I 119, 194.
reproducible, necessarily, I 415.
reproduction, I 489.
and association, I 485 n. 4, 489 n. i.
necessary, I 388, 391, 393~5-
synthesis of, I 354, 356, 363-6, 479-81.
synthesis of, pure transcendental, I 354, 371-4.
repulsion, and attraction, II 137, 138 n. 3, 149, 212, 295, 326 n. i, 328.
and attraction, moving forces of, II 137 n. 3, 149, 212, 295,
326 n. i.
resistance, II 135 n. 3, 212; see also impenetrability.
resistentia, II 295 n. 2.
reversibility, II 305 ; see also sense-perceptions,
revolution, Copermcan, I 75-6, 169, 176, 336-7, 344, 561-5.
Copernican, and the categories, I 567-9.
Riehl, I 299 n. 4, 533 n. i, II 27 n. 2.
rohy I 266 n. 4.
Ross, W. D., I 190 n. 2, 257 n. i and n. 4.
roundness, and squareness, I 134, 139.
Ruckwirkungy II 295 n. 2.
rule, see concept.
and law, I 446 n. i, 495.
condition of a, II 238, 243, 243 n. i.
definitions of, I 495.
rules, and laws, I 493-4.
Russell, Bertrand, I 55, 156 n. i.
St. Thomas, II 216 n. 6.
saltus, II 364.
Schattenbild, II 36 n. 4.
schema, see category ; concept.
in general, II 32-7.
mere, the idea of space and time a, I 114, II 354 n. x.
restriction of the category through the, II 31-2.
transcendental, II 18, 28-30, 39, 43, 435, 437.
GENERAL INDEX 4J3
schema, transcendental, special characteristics of the, II 37-9.
schemata, see concepts, empirical.
the number of the, II 63-5.
transcendental, I 542, II 19, 22, 40, 62, 181, 238; see also
time, modes of.
schematism, analogical or symbolic, II 73 n. 6.
importance of the chapter on, II 20-1.
of the understanding, I 170 n. i, II 73-5.
Schicksal, II 364 n. i.
Schhck, II 270 n. 3, 324 n. 3.
Schmidt, Raymund, I 253 n. 3, 378 n. 3, 495 n. i.
school, empirical, of philosophy, I 67.
rationalistic, of philosophy, I 67.
Schopenhauer, I 44 n. 3, II 294 n. 5, 323.
Schulz, I 158 n. 6, 182 n. i, 305 n. 4, 306 n. i, II 130 n. 6, 294 n. 5.
science, see idealism.
and experience, II 218-20.
modern, and the Principles of the Understanding, II 106—7.
physical, I 89.
Seele, I 95 n. 4.
Scgner, II 284 n. 2.
self, see categories.
empirical, nothing permanent in the, II 200.
existence of the, II 404-6.
phenomenal, see sense, inner.
self-consciousness, I 376, 512, 570-1, 575; see also apperception.
ancl apperception, I 512.
conditions of, categories as, I 426.
self-evidence, II 368.
self-evident, the, II 97 n. i.
self-knowledge, see apperception,
self-subsistent, II 184 n. i.
sensa, I 167.
sensatio, II 49 n. 3.
sensation, I 97, 539, II 49, 136-8, 138 n. 4, 141 n. 8, 337; see also sense-
perception.
degree of, construction of, II 146.
the real of, II 141 ; matter as, II 141 n. 8.
synthesis of, II 141.
what corresponds to a, II 50 n. 3.
sense, I 345, 531 n. 5; and imagination, II 385-6; and understanding,
I 98, II 441.
and meaning, I 304 n. 2.
illusion of, II 386 n. i.
influence on, degree of, II 143.
inner, I 99, 357, II 87, 397; see also apperception, empirical;
apprehension ; time ; understanding.
inner, and apperception, I 519, II 388, 392.
4?4 GENERAL INDEX
sense, inner and outer, ideality of, II 411-13.
inner and outer, reality of, II 410-11.
inner, and the phenomenal self, II 398-401, 415-16.
inner, and pure apperception, II 390.
inner, and time, I 148, II 413-15.
inner, determination of, II 38-9, 289, 390, 394.
inner, difficulties of, II 418-24.
inner, matter of, I 99, II 389, 393-4.
inner, no permanent ego in, II 379 n. i.
inner, paradox of, II 387-90.
inner, stuff of, I 99, II 389, 413.
inner, time the form of, I 100.
inner, to determine, meaning of, II 390.
outer, I 99 n. 2.
outer and inner, I 99-101, II 382 n. 3, 389, 410-13.
outer and inner, determination of, II 394.
passive, I 362.
senses, crudity of the, II 356.
matter of the, II 337.
sense-impressions, atomic, I 358.
sense-perception, I 334, 359, 477, 538; see also apprehension; inter-
action.
ancl scnsation, II 141, 143.
connexion with, II 367.
degree of, II 290.
sense-perceptions, actual and possible, II 307, 308 n. i, 309.
irreversibihty of, II 239, 240 n. 3, 269.
possible, II 260 n. 2, 267, 358.
reciprocal succession of, II 299-300, 304-8.
reversibility of, II 299-301, 305, 310.
synthesis of, II 168.
sensibility, I 94 ; see also space and time ; understanding.
conditions of, II 22.
form of, I 137.
formal conditions of, see categories.
forms of, I 102, 131, 134.
knowledge apart from, II 442.
limitation of our, II 445 ; by understanding, II 459.
pure, modes of, II 165 n. 8.
understanding not limited by, II 458-9.
series, causal, repetition of, II 277.
reversible, II 301 n. 4.
shape, II 127, 139.
shape and position, apparent, I 151 ; real, 1151.
sich etwas vorstellen, I 334 n. 2.
Sidgwick, II 119 n. 4.
Simmel, II 346 n. 3.
simultaneity, II 163, 166-7, 297, 413.
GENERAL INDEX
4^5
simultaneity, necessary, II 55, 322-3.
objective, II 195.
simultaneous, meaning of, II 297 n. 3, 327 n. i.
Sinn, I 304 n. 2, 531 n. 5.
size, II 45.
Smith, J.. A., I 190 n. 4.
smoke, the weight of, II 210.
solid, the, II 205.
solidity, II 2ii ; see also impenetrability.
space, I 262, II 310, 323 n. 2, 368 n. i ; see also idealism, Bcrkeleyan ;
interaction ; substances.
absolute, II 123 n. 4.
and synthesis, I 123.
condition, mediate, of inner experience, I 147.
empirical or relative, II 170 n. i.
empty, II 318, 365; and interaction, II 311, 317, 318 n. 3.
Euclidean, I 161, II 132 n. 6, 352.
knowledge of things in, II 381.
modes of, II 164.
necessity of, I 152-5.
permanent substances in, II 199, 384, 408-9 ; see also experience,
inner.
relative or material, II 123 n. 4.
represented as an infinite given quantity, I 123, II 122.
sensible, I 141.
to fill, II 205 n. 2, 2ii n. 8.
to occupy, II 205 n. 2, 211-12.
transcendental deduction of, I 321.
universality of, I 146-8, 151-2.
use of, transcendental and empirical, I 231.
space and time, I 107, 322, 324, 4™, 4^6, 474, 557, 567 n. i, II 78,
89, 113, 223, 353; see also apperception; apper-
ception, the unity of; apprehension; schema.
absolute, I 174, II 123 n. 4, 170 n. i.
ancj the categories, I 316-17, 431, 527.
and the synthetic unity of apperception, I 516.
as concepts, I 317 n. 2.
as conditions of God's existence, I 174.
as forms of intuition, I 540.
as pure intuitions, I 540.
as real things, I 174.
conclusions, I 130-1.
connexion with sensibility, I 164-5.
continuity of, II 119.
determinate, II 120.
empty, I 113, II 154-5.
ideality of, II 418, 453.
individuality of, I 173.
GENERAL INDEX
space and time, infinite, I 124.
infinity of, I 118-22.
involve unity, I 410, 540-1.
Kantian view of, I 134-6.
knowledge of, intuitional, I 172.
Leibnizian view of, I 133-4.
Metaphysical Exposition of, I 109-10.
Metaphysical and Transcendental Expositions of,
I 107-9.
necessity of, I 152-5.
Newtonian view of, I 132-3.
not concepts but intuitions, I 114-15.
not empirical, but a priori, ideas, I 110-14.
oneness of, I 115-17.
relation to things-m-thcmselves, I 180-1.
subjectivity of, I 165-7.
three possibilities, I 107, 132.
transcendental deduction of, I 109, 319 n. 2.
Transcendental Exposition of, I 127-30.
transcendental ideality of, I 131.
ultimate facts, I 152.
universality of, I 151-2.
without unity in themselves, I 503.
space-time, I 147, 162, 163, 175.
pure intuition of, I 161-2.
spatiahty, I 116, 120, 122, 125, 165 n. i, 193, 198 n. i.
spectacles, blue, I 143 n. 2, 166, 168, 180, 581.
sphaera, I 195 n. 6.
Sphare, I 283 n. i.
Spinoza, I 132 n. 7, 321 n 5, II 164 n. 3, 184 n. i.
spirit, or soul, concept of, I 351.
squareness, see roundness.
state, II 217 n. 6.
change of, II 285 n. i.
states, coexisting, direct perception of, II 330.
exchange of, II 217.
mental, I 63-7.
simultaneous, interaction of, II 323; reciprocal causality of, II
322, 327-8.
subjective, I 521.
Stebbmg, I 155, 156 n. 2, 157 n. i, 158 n. 4, 210 n. 2.
stimuli, physical, II 151.
subject, knowledge of, see object.
relation of object to the, II 413.
subjective, and objective, II 272.
subjectivism, and phenomenalism, I 583 n. i.
subsistence, II 203 ; see also inherence.
substance, II 70, 106; see also movable, the; substances; substratum.
GENERAL INDEX 497
substance, and accident, concept of, II 220.
and accidents, II 203.
and causal activity, II 283.
and substances, II 211, 214.
empirical criterion of, II 215-17.
^- made up of substances, II 184.
material, II 209-13.
perception of, II 204-7.
permanent phenomenal, II 380.
pure category of, II 52.
quantum of, II 184, 207-9, 219.
schematised category of, II 53.
traditional views of, II 184.
transcendental schema of, II 53.
substances, see necessity.
causality of, II 315.
coexistence of, II 298.
coexistent, II 325.
coexistent, reciprocal causality of, II 321, 327-8.
permanent, II 225, 262-3, 300-1, 307, 384; see also space.
permanent, change of, II 226.
permanent spatial, II 420.
substantia phaenomenon, II 53 n. 4, 185, 189, 191, 217, 379.
substantial, the, II 203 n. 5.
substantiality, empirical criterion of, II 325.
Substanzmle, dasy II 203 n. 5.
substratum, II 187 n. i, 189.
and substance, II 201-4.
subsumption, II 24 n. 5 ; see also categories.
and syllogism, II 66-8, 82.
succession, II 163, 166-7, 4X3» see also sense-perceptions; things.
the concept of, II 395.
necessary, I 327, II 54, 223, 281.
objective, II 195, 238-40, 247-8, 250, 252, 255, 258.
objective, and objective coexistence, II 264, 301, 311-12.
objective and necessary, II 263, 292.
objective and subjective, II 222, 236, 246, 253, 265-8.
objective, experience of, II 264.
reciprocal, II 307.
regular, II 54 n. 3.
subjective, and objective coexistence, II 300.
subjective, derived from objective, II 240-1.
Sulzer, I 182 n. i.
supposing, II 344.
syllogism, see subsumption.
synopsis, I 330 n. i, 347, 358 n. 4.
and syntheses, I 355.
and synthesis, I 346, 354.
498 GENERAL INDEX
r
synthesis, I 262, 347, 584; see also analysis; apprehension; categories;
combination; imagination; recognition; reproduction;
synopsis ; unity.
and the concept, I 271-4.
and concepts, I 387.
and consciousness, I 514.
and motion, II 395.
a priori, in all judgement, I 516.
concept of the, I 376.
conscious or unconscious, I 572-5.
figurative, I 141, 535, 537, II 351.
formal, II 338 n. 5.
function of, I 388.
functions of, I 432, 435, 438~43-
imaginative, see concept.
in general, I 258, 263, 284, II 338 11. 5.
intellectual, I 533, 535, 537, 552 n. i.
judgement is, I 219-21, 509.
mathematical, II 146.
mere, I 283-4, 291.
nature of, I 263-6.
necessity of, I 579-81.
pre-conscious and noumenal, I 577, II 280.
productive and reproductive, I 464.
pure, I 266, 276; and the category, I 259, 274-7; and the
empirical manifold, I 466 ; and experience, I 466.
successive, I 358, II 112-14, 257.
successiveness of, II 117-19, 128, 257.
threefold, I 353-6, 357-81.
timeless and noumenal, II 422.
transcendental, definition of, I 467.
transcendental, example of, I 576-7.
transcendental, is productive, I 536.
unconscious and timeless, II 393.
universal functions of, I 432, 441.
various kinds of, I 504, II 56 n. 2.
synthesis intellectuality I 535, II 393.
synthesis speciosa, I 535, II 393.
Teilbegnffe, I 119 n. 2, 194 n. 3.
Tedvorstellungen, I 119 n. 2, 194 n. 3.
telepathy, II 350.
temporality, I 119, 125, 198 n. i.
terminology, Kant's, I 47.
Tetens, I 100 n. 2, 138, 365 n. 2.
theory, transcendental, definition of, I 228.
thing, and idea, II 379.
GENERAL INDEX 4^9
thing, the meaning of, II 297.
the third, I 88, 91, II 28, 86-9, 90, 91, 93, 176, 461.
thing-m-itself, II 417, 439, 457; see also object, transcendental;
things-m-themselves.
unknowabihty of the, I 180-1, 583, II 453-5, 457.
things, -reciprocal succession of * determinations' or 'states' of, II 306.
reciprocal succession of the states of, II 308.
things -m-themselves, I 64, 70, 167 n. 3, II 461-2; see also space and
time ; time.
belief in, II 454.
influence of, I 139.
thinking, and knowing, I 65, 405 n. i, II 343.
and object, II 436.
creative, I 217 n. 5.
definition of, II 435.
discursive and analytic, I 216-19.
finite, I 526.
problematic, II 436-7.
synthetic, I 217 n. 5.
thought, see intuition.
and intuition, II 455-6, 460.
• and its object, II 342-5.
by itself, empty, I 455.
content of, I 193.
the demand of, I 549-52.
demands of, I 295-6, 553-4, II 174.
forms of, I 552-5; see also categories.
laws of, I 191, 192, 378.
pure, acts of, see categories ; concepts, pure.
self-consciousness of, II 402.
unity imposed by, I 285.
thoughts, empty, I 98.
time, II 28-9, 291-2, 421-2; see also apperception, original; image;
imagination ; Logic, Transcendental ; sense, inner.
abides and does not change, II 190.
absolute, II 165 n. 2, 177, 302; see also time itself.
absolute, cannot be perceived, II 255, 261, 292, 312 n. 4, 322.
advance of experience in, II 290.
and degree, II 291.
and inner sense, I 100, II 413-15.
and outer intuition, I 121-2, II 399.
and space, see space and time.
and things-m-themselves, I 181-3.
and the unity of apperception, I 500, II 161.
as a substratum, II 190.
awareness of, II 390.
awareness in, I 182.
cannot be outwardly intuited, I 148.
5oo GENERAL INDEX
time, concept of, II 398; see also temporality.
condition, mediate, of outer phenomena, I 149, II 383.
continuity of, II 256, 288, 291.
continuity and irreversibihty of, II 274.
determinate intuition of, II 393.
determinate position in, II 273.
determination of, II 38-9, 290.
direction of, II 256.
empirical idea of, II 187 n. r.
empirical knowledge of, II 274.
empirical unity of, II 197.
empty, II 165 n. 2, 218.
existence in, II 358.
form of, I 529; see also categories.
importance of, I 357-9.
in constant flux, II 200.
infinity of, I 123.
in general, II 173.
itself, II 165.
itself, cannot be perceived, II 165 n. 2, 170-1, 189-90, 227, 253,
273-4, 302.
mode of, I 395
modes of, II 163-7, 274, 414; and time-relations, II 166; and
transcendental schemata, II 163.
nature of, argument from, II 253.
necessary connexion in, II 274.
necessary succession of the parts of, II 253.
parts of, successive, II 188.
permanence of, II 199-200.
position in, II 252 n. 4, 258 n. 7; objective, II 251.
psychological development in, I 317-18.
relation in, II 161-2.
spatial image of, II 394~5, 399, 4°7-
totality of, II 62.
unity of, II 253 ; see also apperception.
universality of, I 148-51.
time-content, II 62.
time-determination, II 176, 379 n. i ; see also permanent, the.
a priori, rules of, II 163, 176-7.
empirical, II 176.
transcendental, II 29-30.
time-determinations, II 62, 164.
a priori, II 62.
empirical, II 163.
• substratum of, II 189.
time-order, II 62.
time-relations, II 162, 165, 186; see also time, modes of,
empirical knowledge of, II 292.
GENERAL INDEX 501
time-relations, objective, II 187, 245.
time-series, II 62.
empirical knowledge of the, II 254.
times, continuity in the sequence of, II 254.
Todd-Naylor, Miss Ursula, I 20.
Torricelli, I 75.
totality, I 44, 47.
totumy see composittim.
transcendent, I 230, 232, 232 n. 2.
and transcendental, II 430.
transcendental, I 129 n. 4; see also transcendent.
the word, I 229 n. 3, 230; see also theory.
transcendenlalia, I 230 n. i .
transcendentia, I 230 n. i.
triangle, I 272.
empirical concept of, I 141, II 352.
mathematical and empirical, I 140-1, II 34, 113.
triangularity, II 33.
trichotomy, I 306.
truth, II 92.
and correspondence, I 189, 193, 549.
empirical, II 234.
empirical, condition of, II 260.
empirical, formal conditions of, II 234-5.
logical and material, II 361, 361 n. 2.
transcendental, II 345, 348.
Umfang, I 195 n. 6, 283 n. i.
understanding, I 73, 94, 190, 334, II 337; see also apperception;
imagination; intuition; sense.
and appearances, I 472-3; and categories, I 471-2;
and imagination, 1 473-5 ; and inner sense, II 397;
and objects, II 255 ; and reason, I 366.
ancj sensibility, the union of, II 459-60.
as faculty of knowledge, I 470 ; as faculty of thought,
I 470 ; as law-giver, I 496-7, 545-6 ; as power of
knowing, I 352 ; as power of rules, I 492-3 ; as
power of thinking, I 352.
descriptions of, I 492, 515.
finite, II 460.
functions of, I 249.
imagination, and inner sense, II 390-3.
imagination as a lower form of, I 269 n. 3, 503,
536-7.
inner sense determined by, II 289, 390.
intuitive, 1217, 2i7n.5, 527.
502 GENERAL INDEX
understanding, limits sensibility, II 459.
necessary synthetic unity imposed by, I 507.
not limited by sensibility, II 458-9.
pure, and the unity of apperception, I 470-1.
pure concept of the, I 286-7, 351.
pure concepts of the, I 279, 474.
schematism of the, I 170 n. i, II 73-5.
synthesis of, II 391.
use of, logical, I 245 n. i, 510 n. i, II 337; use of,
transcendental and empirical, II 459.
Understanding, Principles of the, I 462, II 81, 90, 94, 98-100, 428-9;
see also science, modern.
proof of the Principles of the, II 82-3, 98, 103-6.
Pure, Principles of the, II 23.
undeutlichy I 266 n. 4.
Unding, I 132 n. 5, II 377 n. i.
Undinge, I 132, 174.
unity, analytic, I 256, 288-9, 293.
analytic and synthetic, I 287-8, 294, 437, 513 n. 4.
and synthesis, I 283-6.
apperception the source of all, I 459.
necessary synthetic, I 258, 372, 385, 394, 415, 429-30, 482,
II 229; see also appearances; consciousness; imagination,
transcendental synthesis of; manifold.
necessary synthetic, and apperception, I 396- 7.
necessary synthetic, imposed, I 372, 438, 507.
objective, I 460.
objective, the purest, I 410.
synthetic, I 289-93.
synthetic, a priori rules of, I 420.
synthetic, nature of, I 509.
universal, and general, I 77.
universality, see necessity,
'unthing*, II 377.
'unthmgs', I 132; see also Undinge.
unum, verum, bonum, I 230 n. i, 308-9.
urspninglich, I 118 n. 2, 512 n. i.
Urteil, and Urteilskraft, II 21 n. 3.
Urwesen, I 217 n. 3.
use, empirical, of categories, I 231 ; of understanding, judgement, and
reason, II 337.
empirical and transcendental, I 232, II 181; see also categories;
concepts; knowledge; space; understanding.
empirical and transcendental, of powers, I 346.
logical, of understanding, judgement, and reason, II 337.
transcendent and immanent, I 232.
transcendent and transcendental, II 430.
transcendental, of powers of the mind, I 231 n. 4.
GENERAL INDEX 503
f
Vaihinger, I 15, 38-40, 40 n. 3, 41 n. i, 53 n. 2 and n. 3, 70 n. 2,
93 n. 5, 116 n. 5, 122 n. 2, 123 n. 9, 126 n. 3, 140 n. 4,
153 n. 3, 182 n. i, 194 n. 5, 326 n. i, 328, 330 n. i,
345 n. 2, 346 n. 6, 347 n. 5, 354, 356, 364 n. 5, 376 n. 7,
380, 380 n. 4, 382, 410 n. 5, 413 n. i and n. 4, 421, 424
n. 3, 486 n. i, 489 n. 7, 498 n. i and n. 2, 512 n. 3, 516
n. 2, 528 n. 2, 573 n. 2, 574, II 26 n. i, 91 n. 3, 115
n.4, 290 n. i, 393, 39811.4.
validity, objective, I 225, 228, 240.
objective, and empirical intuition, II 431.
velocity, II 136 n. 3, 285 n. i.
Veranderungy and Wechsel, II 217 n. 7.
Verbindungy II 159 n. 5, 173 n. 2.
Verknupfungy II 159 n. 5, 160, 173 n. 2, 335 n. 6.
Vermdgen, I 94 n. 4, 345 n. 4.
verstehen, or intelhgete, I 334 n. 6.
Verwandtschafty I 366 n. 6.
verworren, I 266 n. 4.
void, the, II 365 ; see also atoms.
Vorstellungy I 94 n. 5, 108 n. i.
Vorstellungsfdhigkeity I 95 n. 4.
wahrnehmen, or percipeie, I 334 n. 3.
Ward, I 578 n. 3.
Watson, II 217 n. 7.
Wechsely Il2i6n. 4, 2i7n.5; see also Verandetung.
Wechselwirkung, I 297 n. 4, II 55 n. 3, 294 n. 2.
weight, II 135 n. 3, 207.
Weitlaufigkeity I 44 n. 7.
Whitehead, I 49.
Wille, II 50 n. 3, 290 n. i.
Wirklichkeity II 58 n. 2.
Wolff, Casper, I 578.
words, concrete and abstract, I 193.
world, phenomenal, as one experience, II 366 n. 3.
the sensible and the intelligible, II 459.
worlds, possible, II 353.
possible, the best of all, II 366.
world-whole, unity of the, II 331.
Zufally II 364 n. i.
ziifalligy I 519 n. 5.
zusammenfasseriy I 263 n, 4.
Zusammenfassung, or comprehensio, I 359 n. 7.
Zustand, II 217 n. 6, 251 n. i.
INDEX OF ANNOTATED PASSAGES
The left-hand references in each column (e.g. A 4 — B8) indicate the page where
the passage annotated occurs in the first and second editions of the Kntik.
The right-hand references (eg I 81) indicate the volume and page where the
annotation is to be found in the present commentary.
A XVII
I 44
B
34
102
A
34 *-
B
5i
I 149
BXVI
I 75
A
20
-= B
34
94
A
36-
B
53
I 181
B XVIII
I 65
95
A
37 -
B
53
I 181
72
96
A
37 -
B
54
I 63
BXIX
65
97
I 181
72
A
20
= B
35
104
A
38-
B
54
Ii8i
BXXIIn
75
A
21
- B
35
102
A
38-
B
55
Ii8i
B XXVII
70
104
A
39"=
B
56
Ii32
B XXXVIII
54
A
22
- B
36
52
I 174
B XXXIX n ]
[ 99
A
23
= B
37
IOO
A
40 =.
B
56
I 133
I]
[378
107
I 174
I]
^383
A
23
13
38
no
A
40 -.
B
57
I 132
I]
[407
in
I 133
BXLn 11
378
125
I 174
11
[382
153
Ii76
I]
[3*5
A
24
127
A
4i -
B
58
I 148
I]
[408
B
38
108
A
43 -
B
60
I 133
I]
[409
A
24
T>
39
U5
I 171
11
410
A
25
123
A
43 ~
B
61
I 171
B XLI n 11
[382
B
39
123
A
45 -
B
62
I 60
I]
384
A
25
- B
39
"5
A
45 ="
B
63
I 60
11
[386
116
A
46
B
63
I 60
I]
410
B
40
108
A
48-
B
66
I 167
I]
[ 412
B
4i
127
A
49 -
B
66
I 167
B XLIV ]
[ 48
A
26
- B
42
102
II 412
49
A
27
- B
43
104
B
67
II4I2
A i
77
A
28
60
II4I3
B i
77
A
29
60
11414
B 2
76
B
44
60
B
68
I 217
B 3
76
A
30
- B
46
125
II 399
77
153
II 412
B 4ff
77
A
31
- B
47
IO9
11414
80
A
32
B
47
109
H4i5
A 4 - B 8
81
H5
B
69
II4I2
A 5 - B 9
81
123
II 416
A 6 - B 10
81
A
32
- B
48
118
B
70
I 174
83
119
II4I2
A 8
88
120
B
70 n
II4I7
B 12
88
123
B
7i
I 174
B i4ff
81
B
48
119
I 178
B 22
82
127
II 412
A 19 = B 33
73
B
49
127
B
72
In8
A 19 = B 34
95
A
32
= B
49
132
1178
A 20
102
A
34
- B
50
ISO
II4i2
5o6
INDEX OF PASSAGES
B 73
II4I2
A 79
= 6105
1286
A 99
A 5o =
B 74
I 73
290
A 51 -=
B 75
I 96
A 80
- Bio6
297
A 52 -
B 76
1187
A 81
= B 107
307
A 54 =
B 78
I 188
A 82
- B 108
3°7
A 100
A 55 -
B 79
I 222
B 110
305
A 101
A 55 -
B 80
I 222
B in
1305
A 56 -
B 80
I 223
II340
A 102
1226
A 84
- B 116
I 3H
A 103
A 56 -
B 81
1226
A 84
- B 117
I 3H
I 23I
I 3*5
A 104
A 57 -
B 81
I 224
A 85
- B 117
I 3J5
I 225
I 316
A 105
A 60 --
B 84
I 189
A 85
-- B 118
I 200
A 61 =
B 85
I 190
1317
A 61 -
B 86
I 190
A 86
- Bii8
I 200
A 106
A 62 =
B 86
I 190
I 3l6
A 62 =
B 87
I 233
A 86
--= B 119
I 200
A 63 ---
B 87
I 235
1317
A 107
A 63
B 88
I 235
A 87
- B 119
316
A 64 -
B 89
1234
317
1237
319
A 65 ~
B 90
I238
A 87
-- B 120
319
A 66 -
B 90
I238
A 88
— B 120
320
A 108
A 68 -
B 93
I2l6
A 89
B 122
322
I 217
324
1247
A 90
-- B 122
325
A 109
1248
A 90
- B 123
324
A no
1252
325
A 69 -
B 93
1253
327
A 69 -
B 94
I 202
A 91
B 123
325
A in
I 247
328
I248
A 91
B 124
328
A 70 —
B 95
I 204
A 92
-- B 124
337
I2II
A 92
B 125
337
A 71 =
B 96
I 205
A 93
B 125
339
A 112
A 71 =•
B 97
I 205
341
A 72^-
B 97
I 205
A 93
B 126
339
A 74-
B 100
I 205
341
A 76
B 102
I 200
343
A 113
1267
A 94
B 126
344
A 77 -
B 102
1262
A 94
345
A 77-
Bio3
1263
A 95
345
A 78 -=-
B 103
1263
350
A 78 -
B 104
1267
A 96
197
I 274
350
A 1 14
1276
35i
A 79 -
B 104
I256
A 97
350
1277
352
I 281
1354
A 115
A 79 -
B 105
I 202
A 98
I 53
I256
1348
Aii6
I28l
II397
I 357
1358
I 359
II 397
1368
1369
I37i
1363
I 375
1376
1378
1383
I 386
I 388
I 393
1391
I 393
1396
1398
1399
1403
I 406
1408
I 412
1417
1439
1441
1305
1426
1427
1305
1426
1430
1432
1441
1433
1441
I 442
1444
1308
1444
1446
1450
I452
1495
I 308
1447
1449
1450
1308
1448
1308
I 448
INDEX OF PASSAGES
507
A 116
1460
Bi37
I5i7
8167
1578
1458
Bi38
I 113
A 131 •=
B 170
I 237
A 117
1460
I 518
A 132 -=
B 171
II 24
A 11711
I 460
6139
I 518
Ai33n=^
B 173 n
I 190
An8
I464
I 5*9
A 135 *~
Bi74
II 21
I467
B 140
I 5i9
A 136 --
Bi75
II 22
I 468
8141
1522
II 23
I 535
Bl42
I 520
II 73
A 119
I470
II 93
A 137 -
8176
II 26
A J2O
1476
Bi43
1524
A 138 -
Bi77
II 28
1478
6144
1527
II 29
A 121
I 481
Bi45
1528
A 139 =•
6178
II 31
A 122
1481
II448
A 140 =-
6179
II 32
1483
B 146
1530
II 73
A 123
1483
Bi47
1530
A 141 —
Bi8o
II 35
I484
Bi48
I 178
II 73
I 486
I 531
A 141 -
B 181
II 36
A 124
I 486
B 150
1532
II 73
1487
1534
A 142 --
Bi8i
II 37
1488
B 151
1535
II 38
A 125
I489
B 152
1536
A 142 -
Bi82
II 44
1490
1537
II 46
A 126
1492
II387
A 143 =-
B 182
II 44
1495
Bi53
H388
II 46
I 496
II39o
II 49
A 127
I 140
Bi54
II 393
II 140
1492
Bi55
A 143 --
Bi83
II 49
I 496
Bi56
II 395
II 52
A 128
I 140
H399
II 140
1497
A 144 -
Bi83
II 55
A 129
1497
B 15611
II400
A 144 -
B 184
II 55
A 130
1497
Bi57
II40I
II 56
Bi29
1503
B i57n
II404
H 59
Bi3o
I 503
B 15811
II 404
II342
I 504
Bi59
I 240
A 145 -
B 184
H 56
505
1538
II 57
6131
507
B 160
1538
H 59
510
1539
II 60
6131 n
220
1540
II 62
Bl32
51°
B i6on
I 98
II 63
511
I 103
II342
512
I 541
A 145 =
6185
II 62
Bi33
511
11414
II 68
513
Bi6i
I54i
II 74
B J33«
194
1542
A 146 -
Bi85
II 62
2OI
Bi6m
I54i
II 68
Bi34
1515
II4i4
A 146 -
Bi86
II 45
B 13411
I 2OI
B 162
1543
II 62
I SIS
1544
II 69
B 135
I SIS
Bi63
I 545
A 147 =
Bi86
II 23
I 518
Bi64
1545
II 62
Bi36
1516
Bi65
I 139
II 63
B 137
I 113
1545
II 71
5o8
INDEX OF PASSAGES
A 148 - B 188 II 83
A 166 = 6206 II 132
A 181 = B 223 II 176
A 149 = B 188 II 82
A 166 — B 207 II 132
II 181
II 83
B 207 II 134
Ai8i = 8224 II 181
A 149 - B 189 II 82
II 141
II 182
A 150 = B 189 I 189
A 166 = B 208 II 134
8224 11190
II 83
A 167 •= B 208 II 134
II 202
A 150 = B 190 I 189
A 167 = B 209 II 134
A 182 = 8225 IIi86
A 151 = B 190 1214
II 83
Ai68 = B2io II 135
Hi36
II 202
A 182 - B 226 II 166
II 84
II 140
II 202
A 151 = B 191 I 214
A 169 = 8210 II 150
A 183 - B 226 II 165
II 84
A 169 = B2ii II 14°
II 186
A 153 ^ 8192 II 83
IIiS2
II 187
A 154 ^ B 193 II 84
A 155 - B 194 II 86
A 170 - B2ii II 152
A 170 — B 212 II 152
II 202
A 183 - B 227 II 166
II 87
II 155
A 184 -- B 227 I 86
A 156 - B 195 II 89
II 90
A 171 = B2I2 II H9
II 153
II 211
A 185 =- B 228 II 208
A 156 - B 196 II 90
II 155
II 209
A 157 B 196 II 91
11284
11 210
II 92
A 171 - 6213 II 145
A 186 =- B 229 II 197
A 158 - B 197 II 94
II 153
II 203
II 95
11284
A 186 -- B 230 II 203
A 159 - B 198 II 97
A 172 - B2i3 11284
A 187 -•= B23Q 11203
A 160 - B 199 II 92
A 172 -- 6214 II 13?
II 217
II 99
A 173 - 8215 II 135
A 188 - B 231 II 197
II 102
A 175 - 8217 II 135
II 198
A 161 =- 8200 II 98
IIi46
II 218
A 162 — B 201 II 99
A 176 - B 217 II 146
A 188 -- B 232 II 197
II 100
A 176 - B2i8 II 135
II 198
A 162 — B 202 II 99
II 148
A 189 II 221
II 120
A 176 II 1 60
A 189 - B 232 II 198
A 162 II in
A 177 II 1 60
6232 II 221
B20in II zoo
8218 II 159
11225
II xsg
IIi68
6233 II 225
B 202 II in
8219 IIi68
II226
II 114
Hi73
B 234 II 225
II 120
II 175
II228
6203 II 121
II 229
A 189 - B 234 11 230
11126
A 177 — B 219 II 161
11231
A 162 = 8203 11 112
IIi63
A 190 - B235 H230
II 122
IIi66
II232
A 163 - Bao3 II 113
A 177 --- B 220 II 161
II 233
II 120
11167
A 191 = B 236 II 230
A 163 -= B 204 II 124
A 178 - 6220 IIi78
11231
II 125
A 178 « 8221 II 147
11233
II 127
IIi78
11234
II 129
IIiSo
II 235
A 164 - B 204 II 130
A 179 — B22I II 102
Il236
A 164 =-- B 205 II 129
IIl46
II24I
IIi30
III78
11242
A 165 = 8206 II 132
Ai8o - 8223 II 181
II 243
A 166 II 134
Ai8i = 8223 II 82
A 192 = 8237 11230
INDEX OF PASSAGES 509
A 192 = 8237 11240
A 208 = B 253 II 285
A 220 = B 268 II 351
11241
II 290
A 221 = 8269 II 348
11242
A 208 - B 254 II 285
A 222 = B 269 II 346
11243
A 209 -- B 254 II 288
II348
A 193 =•- 8238 11230
A 210 - 8255 11289
H349
II 240
A 210 = 8256 11276
A 223 = B 270 II 347
11241
11292
II348
11242
A 211 II294
II350
II 243
B 256 II 294
A 223 = B 271 II 348
II245
Il298
II 351
A 194 ^ 8239 11230
A 211 =- 8256 11276
A 224 — B 271 I 141
Il24o
II292
A 225 ^-' B 272 II 357
11241
8257 II298
II358
11242
II 300
II 359
Il243
11 302
A 225 - 8273 II358
II 245
II303
A 226 -- B 273 II 357
11246
II 306
II358
II253
A 2ii =- 8258 II 297
8274 II376
A 194 =- 8240 11246
II 310
B 275 II 376
A 195 — B 240 II 246
8258 11298
B 276 I 147
Il247
11309
II376
11248
A 212 =• 8258 II 310
II 381
A 196 -- 8241 11248
A 212 =- 8259 II 310
B 2760 II 382
Il249
A 213 -= 8260 II 151
B 277 II 196
A 197 -^ B 242 II 249
II 311
II376
A 198 -- B 243 II 250
II 316
II379
A 198 -- 8244 11252
A 214 -- 8260 II 311
B 277 n II 382
A 199 -- B 244 II 252
II 316
B 278 II 196
II 253
A 214 8261 II 311
II376
II 273
II 316
II379
A 199 --=- 6245 11253
II3i9
II 381
II273
H323
II385
A 200 -- B 245 II 253
II328
8279 II385
II254
A 215 -- 8261 II 316
A 226 — B 279 II 362
II255
Il3i9
A 228 -- B 280 II 363
A 200 - B 246 II 253
II323
A 229 - B 282 II 364
II255
A 215 ---= 8262 II 166
A 230 = B 282 II 366
A 201 •= B 246 II 253
II 177
A 231 -= B 284 II 367
II255
II 316
A 232 = B 284 II 368
II 257
II3i9
A 232 - B 285 II 368
A 202 - B 247 II 283
A 216 ---- 8263 II 177
A 234 - B 286 II 337
A 202 - B 248 II 283
A 217 = 6264 II 175
H359
A 203 - B 249 II 268
II 176
A 234 = B 287 II 369
A 204 -= 8249 11215
II282
A 218 -8265 II335
A2i8n= 826511 II 323
8288 II353
8289 II353
A 205 = 8250 II 215
A 205 — B 251 II 216
II33i
A 218 - 8266 11335
B 291 II 200
A 235 = 8294 "427
A 206 -= 8251 II 217
A 206 - B 252 II 283
A 219 -8267 11335
A 220 = B 267 II 88
A 236 -^ 8295 II427
A 237 = B 296 II 428
11284
II 89
A 238 -- B 297 II 429
A 207 - B 252 II 283
11284
II34I
A 220 = B 268 II 344
A 238 - B 298 II 429
A 239 = B 298 II 429
A 207 - B 253 II 284
II 345
II 43 1
INDEX OF
A 239 -
6299
Il43i
6306
II 451 A 257 =
B 313
II459
A 240 -
6299
I 113
H452
A 258 -
B 313
II 455
I 159
6307
II452
A 258 -
B 314
II 455
H432
IU53
11460
A 240 -
B3oo
II 433
B3o8
II453
A 292 -=
B348
I 174
A 241
II433
II454
B 412
I1384
A 241 n
I 3°3
B 309
II453
I
} 423 n
II 402
6300
I 303
II454
A 42611-^
B 45411
II 112
A 242 n
I 303
A 253
" B 309
II455
II 128
A 242
A 245
A 246 -
6303
II433
II 434
II 435
A 254
A 254
- 6309
- B 310
II 455
II 455
II 4*6
A 570 --
648011
B598
II 139
I 80
II 36
A 247 --
A 248 -
A 248
A 249
A 250
6304
6305
II 435
II427
II440
II 442
UAA1
A 255
A 255
- B3io
AA TO^
II455
II 457
II 455
II 457
II458
A 581 --
A 713 --
A 714 -
A 717 -
A 720 —
6609
B74i
B745
I 140
I 160
II 101
II 127
II 127
A 2 C T
443
A 256
- B 311
11455
A 729 ^
B7S7
I 197
** *•> j •
II 444
A 256
6312
II 455
A 734 -
6762
II 101
II 445
II 459
A 735 -
B 763
II 101
A 252
I 70
A 257
- 6312
II 455
A 736
B7<H
II 103
A 253
II447
II459
II 104
6305
II450
A 257
B3'3
II 455
A 737 ~-
6765
II 104
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