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Norman Kemp Smith.

A commentary to Kant's 'Critique of pure reason,' online

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doing he is committing himself to the thesis that the dis-
tinction is mediated, not by the understanding, but by Reason,
not by categories, but by Ideas. 1 As I have already indicated,
this tendency is crossed by another derived from his pre-
occupation with moral problems, namely, the desire to defend,
in a manner which his Critical teaching does not justify, the
noumenal existence of the self as a thinking being.

1 In the Fortschritte ( Wtrke (Hartenstein), viii. p. 548 ff. ) this final step is quite
definitely taken. Cf. below, pp. 390-1, 414-17, 426 ff., 558-61. We have, as we
shall find, to recognise a second fundamental conflict in Kant's thinking, additional
to that between subjectivism and phenomenalism. He alternates between what
may be entitled the sceptical and the Idealist views of the function of Reason
and of its relation to the understanding, or otherwise stated, between the regulative
and the absolutist view of the nature of thought. But this conflict first gains
explicit expression in the Dialectic,



THE TRANSCENDENTAL ANALYTIC
BOOK II

THE ANALYTIC OF PRINCIPLES

The distinction which Kant here introduces for the first
time between understanding (now viewed as the faculty only
of concepts) and the faculty of judgment (Urtheilskraff] is
artificial and extremely arbitrary. 1 As we have seen, 2 his
own real position involves a complete departure from the
traditional distinction between conceiving, judging, and reason-
ing, as separate processes. All thinking without exception
finds expression in judgment. Judgment is the fundamental
activity of the understanding. It is " an act which contains
all its other acts." Kant is bent, however, upon forcing the
contents of the Critique into the external framework supplied
by the traditional logic, viewed as an architectonic ; and we
have therefore no option save to take account of his exposi-
tion in the actual form which he has chosen to give to it.
Since general logic develops its teaching under three separate
headings, as the logic of conception, the logic of judgment,
and the logic of reasoning, the Critique has to be made to
conform to this tripartite division. The preceding book is
accordingly described as dealing with concepts, and this second
book as dealing with judgments or principles ; while under-
standing and the faculty of judgment, now viewed as inde-
pendent, are redefined to meet the exigencies of this new
arrangement, the former as being " the faculty of rules/' and
the latter as being " the faculty of subsuming under rules, i.e.
of distinguishing whether something does or does not stand
under a given rule (casus datae legis}"

The reader need not strive to discover any deep-lying
ground or justification for these definitions. 3 Architectonic,

1 For Kant's use of the terms 'canon' and 'dialectic' cf. above, pp. 72, 77-8,
173-4, and below, p. 425 ff. 2 Above, pp. 181-2.

3 As we shall have occasion to observe below (p. 336), when Kant defines
judgment as "the faculty of subsumption under rules," he is really defining it in

332



THE ANALYTIC OF PRINCIPLES 333

that ' open sesame ' for so many of the secrets of the
Critique, is the all-sufficient spell to resolve the mystery.
As a matter of fact, Kant is here taking advantage of the
popular meaning of the term judgment in the sense in which
we speak of a man of good judgment ; and in order that
judgment and understanding may be distinguished he then
imposes an artificial limitation upon the meaning in which
the latter term is to be employed.

As formal logic abstracts from all content, it cannot, Kant
maintains, supply rules for the exercise of " judgment." It is
otherwise with transcendental logic, which in the pure forms of
sensibility possesses a content enabling it to define in an a priori
manner the specific cases to which concepts must be applic-
able. The Analytic of Principles is thus able to supply " a
canon for the faculty of judgment, instructing it how to apply
to appearances the concepts of understanding which contain
the condition of a priori rules." 1 This will involve (i) the
defining of the sensuous conditions under which the a priori
rules may be applied the problem of the chapter on sche-
matism ; and (2) the formulating of the rules in their sensuous,
though a priori, concreteness the problem of the chapter on
" the system of all principles of pure understanding."

Such is Kant's own very misleading account of the
purposes of these two chapters. There are other and sounder
reasons why they should be introduced. In the Analytic
of Concepts, as we have seen, 2 the transcendental deduction
only succeeds in proving that a priori forms of unity are
required for the possibility of experience. No proof is given
that the various categories are just the particular forms
required, and that they are one and all indispensable. This
omission can be made good only by a series of proofs, directed
to showing, in reference to each separate category, its validity
within experience and its indispensableness for the possibility
of experience. These proofs are given in the second of the
two chapters. The chapter on schematism is preparatory in
character ; it draws attention to the importance of the temporal
aspect of human experience, and defines the categories in the
form in which they present themselves in an experience thus
conditioned by a priori intuition.

terms of the process of reasoning, and thus violating the principle which he is
professedly following in dividing the Transcendental Logic into the Analytic of
Concepts, the Analytic of Judgment, and the Dialectic of Reasoning.
1 A 132 = 6 171. 2 Pp. 252-3, 258-9, 287-8.






CHAPTER I

THE SCHEMATISM OF PURE CONCEPTS OF UNDERSTANDING l

The more artificial aspect of Kant's argument again ap-
pears in the reason which he assigns for the existence of a
problem of schematism, namely, that pure concepts, and the
sensuous intuitions which have to be subsumed under them,
are completely opposite in nature. No such explanation
can be accepted. For if category and sensuous intuition are
really heterogeneous, no subsumption is possible ; and if they
are not really heterogeneous, no such problem as Kant here
refers to will exist. The heterogeneity which Kant here
asserts is merely that difference of nature which follows from
the diversity of their functions. The category is formal and
determines structure ; intuition yields the content which is
thereby organised. Accordingly, the "third thing," which
Kant postulates as required to bring category and intuition
together, is not properly so describable ; it is simply the two
co-operating in the manner required for the possibility of
experience. Kant's method of stating the problem of
schematism is, however, so completely misleading, that
before we can profitably proceed, the various strands in his
highly artificial argument must be further disentangled.
This is an ungrateful task, but has at least the compensating
interest of admirably illustrating the kind of influence which
Kant's logical architectonic is constantly exercising upon his
statement of Critical principles.

The architectonic has in this connection two very
unfortunate consequences. It leads Kant to describe sche-
matism as a process of subsumption, and to speak of the
transcendental schema as " a third thing." Neither assertion is
legitimate. Schematism, properly understood, is not a process
of subsumption, but, as Kant has already recognised in A 124,

1 The passages that have gone to constitute this chapter are probably quite
1'ate in date of writing. This would seem to be proved by the view taken of
productive imagination, and also by the fact that in the Reflexionen there is no
mention of schematism.

334



SCHEMATISM 335

of synthetic interpretation. Creative synthesis, whereby con-
tents are apprehended in terms of functional relations, not
subsumption of particulars under universals that are homo-
geneous with them, is what Kant must ultimately mean by
the schematism of the pure forms of understanding. A
category, that is to say, may not be viewed as a predicate
of a possible judgment, and as being applied to a subject
independently apprehended ; its function is to articulate
the judgment as a whole. The category of substance and
attribute, for instance, is the form of the categorical judgment,
and may not be equated with any one of its single parts.

Thus the criticisms which we have already passed upon
Kant's mode of formulating the distinction between formal and
transcendental logic, 1 are no less applicable to the sections now
before us. The terminology which Kant is here employing
is borrowed from the traditional logic, and is out of harmony
with his Critical principles.

Kant's description of the schema as a third thing, additional
to category and intuition, and intermediate between them, is
also a result of his misleading mode of formulating his
problem. What Kant professes to do is to interpret the
relation of the categories to the intuitional material as
analogous to that holding between a class concept and the
particulars which can be subsumed under it. This is implied
in his use of the plate and circle illustration. 2 But as the
relation holding between categories and the material of sense
is that of form and matter, structure and content, the analogy
is thoroughly misleading. As all content, strictly so called,
falls on the side of the intuitional material, there is no con-
tent, i.e. no quality or attribute, which is common to both.
And thus it happens that the inappropriateness of the analogy
which Kant is seeking to enforce is ultimately the sole ground
which he is able to offer in support of his description of the
schema as " a third thing."

"Now it is clear [!] that there must be a third thing, which is
homogeneous on the one hand with the category and on the other
with the appearance, and which thus makes the application of the
one to the other possible." 3

On the contrary, the true Critical teaching is that category
and intuition, that is to say, form and content, mutually con-

1 Cf. above, p. 176 ff.

2 Cf. A 137 = B 176. "The empirical concept of a plate is homogeneous
with the pure geometrical concept of a circle, since the roundness which is thought
in the former can be intuited in the latter."

3 A 138 = 6 177.



336 THE ANALYTIC OF PRINCIPLES

dition one another, and that the so-called schema is simply a
name for the latter as apprehended in terms of the former.

But there is a further complication. Kant, as we have
already observed, 1 defines judgment as being

"... the faculty of subsuming under rules, i.e. of distinguishing
whether something does or does not stand under a given rule (casus
datae legis}"

Now this view of judgment really connects with the syllogism,
not with the proposition. 2 As Kant states in his Logic, there
are

"... three essential elements in all inference: (i) a universal rule
which is entitled the major premiss; (2) the proposition which sub-
sumes a cognition under the condition of the universal rule, and
which is entitled the minor premiss ; and lastly, (3) the conclusion,
the proposition which asserts or denies of the subsumed cognition
the predicate of the rule." 3

Regarded in this way, as the application of a ru/e, subsump-
tion is more broadly viewed and becomes a more appropriate
analogy for the relation of category to content. And obvi-
ously it is this comparison that Kant has chiefly in mind in
these introductory sections. For only when the subsumption
is that of a particular instance under a universal rule, can the
necessity of a mediating condition be allowed.

Such, then, are the straits to which Kant is reduced in the
endeavour to hold loyally to his architectonic. He has to
identify the two very different kinds of subsumption which
find expression in the proposition and in the syllogism respect-
ively ; and when his analogy between logical subsumption,
thus loosely interpreted, and synthetic interpretation, proves
inapplicable, he uses the failure of the analogy as an argument
to prove the necessity of " a third thing." On his own Critical
teaching, as elsewhere expounded, no such third thing need
be postulated. Even the definitions which he proceeds to
give of the various schemata do not really support this
description of them.

But though Kant's method of introducing and expound-
ing the argument of this chapter is thus misleading, the
contents themselves are of intrinsic value, and have a three-
fold bearing : (a) on the doctrine of productive imagination ;
(fr) on the relation holding between image and concept ; and

1 Above, p. 334.

2 Cf. E. Curtius, Das Schematismuskapitel in der Kritik der reinen Vernunft
(Kantstudien, Bd. xix. p. 348 ff.). 3 Op. cit. 58.



SCHEMATA AND IMAGES 337

(c) on the nature of the categories in their distinction from
the pure forms of understanding.

(a) Kant gives definite and precise expression to the two
chief characteristics of the productive imagination, namely, that
it deals with an a priori manifold of pure intuition x and that
it exercises a " hidden art in the depths of the human soul." 2
Kant's description of the schema as " a third thing," at once
intellectual and sensuous, seems to be in large part due to the
transference to it of predicates already applied to the faculty
which is supposed to be its source. The distinction between
the transcendental schema and the particularised image is
also given as analogous to that between the pure and the
empirical faculties of imagination. In A 141-2 = B 180-1, Kant
speaks of the empirical faculty of productive imagination,
and so is led, to the great confusion of his exposition, though
also to the enrichment of his teaching, to allow of empirical
as well as of transcendental schemata, and thus contrary to
his own real position to recognise schemata of such empirical
objects as dog or horse a view which empirical psychology
has since adopted in its doctrine of the schematic image.
This passage was doubtless written at the time when he was
inclining to the view that the empirical processes run parallel
with the transcendental. 3 Kant's final view is that empirical
imagination is always reproductive. This brings us, however,
to our second main point.

(b] Kant makes a statement which serves as a valuable
corrective of his looser assertions in other parts of the Critique.^

Five points set after one another, thus, , form an

image of the number five. The schema of the number five is,
however, of very different nature, and must not be identified
with any such image. It is

"... rather the representation of a method whereby a multiplicity [in
this case five] may be represented in an image in accordance with a
certain concept, than this image itself. . . ." 5

This becomes more evident in the case of large numbers, such
as a thousand. The thought or schema of the number remains
just as clear and definite as in the case of smaller numbers,
but cannot be so adequately embodied and surveyed in a con-
crete image.

" This representation of a general procedure of imagination in pro-
viding its image for a concept, I name the schema to this concept." 6

1 A 138 = 6 177. Cf. above, pp. 96-7. 2 A 141 = 6180.

3 Cf. above, pp. 268-9. 4 Cf. above, pp. 133-4.

5 A 140 = B 179. 6 Loc, cit.

Z



338 THE ANALYTIC OF PRINCIPLES

But even in the simplest cases an image can never be com-
pletely adequate to the concept. The image of a triangle, for
instance, is always some particular triangle, and therefore
represents only a part of the total connotation. As the
schema represents a universal rule of production in accordance
with a concept, it resembles the concept in its incapacity to
subsist in an objective form. Images become possible only
through and in accordance with schemata, but can never
themselves be identified with them. Schemata, therefore, and
not images such is the implied conclusion form the true
subject-matter of the mathematical sciences. Images are
always particular ; schemata are always universal. Images
represent existences ; schemata represent methods of con-
struction.

There are three criticisms which must be passed upon this
position. In the first place, the selection of the triangle as
an illustration tends to obscure the main point of Kant's
argument. As there are three very different species of
triangle, the concept triangle is a class concept in a degree and
manner which is not to be found in the concepts, say, of the
circle or of the number five. So that while Kant may seem
to be chiefly insisting upon the inadequacy 1 of the image to
represent more than a part of the connotation of the corre-
sponding concept, his real intention is to emphasise that the
schema expresses the conceptual rule whereby, even in images
that cover the whole connotation, the true meaning of the
image can alone be determined.

Secondly, the above definition of the schema as being
" the representation of a general procedure of imagination in
providing an image for a concept " is obviously bound up with
Kant's view of it as " a third thing," additional to the concept,
and as intermediate between it and the image. 2 But as we
have already found occasion to note, in discussing Kant's
doctrine of the "construction" of mathematical concepts, 3
this threefold distinction is out of harmony with his Critical
principles. It results from his retention of the traditional
view of the concept as in all cases a mere concept, i.e. an
abstracted or class concept. In defining the schema Kant is
defining the true nature of the concept as against the false
interpretation of it in the traditional class-theory ; he mis-
represents the logic of his own standpoint when he interpolates

1 Cf. E. Curtius, op. cit. p. 356.

2 Kant's other definition of the schema as " a rule for the determination of
our intuition in accordance with a certain universal concept" (A 141 = 6 180) is
open to similar objections. When, however, Kant states that "schemata, and
not images, underlie our pure sensuous concepts," he seems to be inclining to the
truer view that the schema is the concept. 3 Above, pp. 131-3.



SCHEMATA AND CATEGORIES 339

a third kind of representation intermediate between the con-
cept and the image. The concept ' triangle/ as a concept, is
(to employ Kant's own not very satisfactory terms) the
representation of the method of constructing a certain type of
object ; and the only other mode of representing this kind of
object is the image. There may, indeed, as Kant has him-
self suggested, be a species of image that may be entitled
schematic ; but if that be identified with a blurred or in-
determinate or merely symbolic form of representation, it
can have nothing in common with the transcendental or
conceptual schema, save the name.

Thirdly, the entire discussion of the nature of the
schemata of " sensuous concepts " and of their relation to
the sense image, is out of order in this chapter ; and however
valuable in itself, bewilders the reader who very properly
assumes for it a relevancy which it does not possess. The
pure concepts of the understanding, whose schemata Kant
is endeavouring to define, are altogether different in nature
from sensuous representations, and can never be reduced in
any form or degree to an image. They are wholly transcend-
ental, representing pure syntheses unified through categories
in accordance with the form of inner sense. This, however,
brings us to our last main point.

(c] Kant's manner of employing the term category is a
typical example of his characteristic carelessness in the use of
his technical terms. Sometimes- it signifies the pure forms of
understanding. But more frequently it stands for what he
now, for the first time, entitles schemata, namely, the pure
conceptual forms as modified through relation to time. To
take as examples the two chief categories of relation. The
first category of relation, viewed as a form of the pure
understanding, is the merely logical conception of that which
is always a subject and never a predicate. The correspond-
ing schema is the conception of that which has permanent
existence in time ; it is not the logical notion of subject,
but the transcendental conception of substance. The pure
logical conception of ground and consequence is similarly dis-
tinguished from the transcendental schema of cause and effect.

This contrast is of supreme importance in the Critical
philosophy, and ought therefore to have been marked by a
careful distinction of terms. Had Kant restricted the term
category to denote the pure forms, and invariably employed
the term schemata to signify their more concrete counterparts,
many ambiguities and confusions would have been prevented.
The table of categories, in its distinction from the table of
logical forms, would then have been named the table of



340 THE ANALYTIC OF PRINCIPLES

schemata, and the definitions given in this chapter would
have been appended to it, as the proper supplement to the
metaphysical deduction, completing it by a careful definition
of each separate schema. For what Kant usually means
when he speaks of the categories are the schemata ; and the
chapter before us therefore contains their delayed definitions. 1
As Kant has constantly been insisting, and as he again so
emphatically teaches in this chapter, the pure forms of
understanding, taken in and by themselves, apart from the
forms of intuition, have no relation to any object, and
are mere logical functions without content or determinate
meaning.

From this point of view the misleading influence of Kant's
architectonic may again be noted. It forces him to preface
his argument by introductory remarks which run entirely
counter to the very point which he is chiefly concerned to
illustrate and enforce, namely, the inseparability of conception
and intuition in all experience and knowledge. He does,
indeed, draw attention to the fact that the conditions which
serve to realise the pure concepts of understanding also at
the same time restrict them, but it is with their empirical
employment that he is here chiefly concerned.

Caird's 2 mode of expounding Kant's doctrine of schematism
may serve as an example of the misleading influence of Kant's
artificial method of introducing his argument. As Caird
accepts Kant's initial statements at their face value, he is
led to read the entire chapter in accordance with them, and
so to interpret it as being a virtual recantation of the assump-
tions which underlie the statement of its problem. The
truer view would rather seem to be that the introduction is
demanded by the exigencies of Kant's architectonic, and
therefore yields no true account either of the essential purpose
of the chapter or of its actual contents. Cohen not unjustly
remarks that

"... recent writers are guilty of a very strange misreading of Kant
when they maintain, as if in opposition to him, a thought to which
his doctrine of schematism gives profound expression, namely, that
intuition and conception do not function independently, and that
thought, and still more knowledge, is and must always be intuitive." 8

Cohen fails, however, to draw attention to the cause of the
misunderstanding for which Kant must certainly share the
blame. Riehl, 4 while adopting a somewhat similar view to

1 Cf. Riehl, Philos. Krit. 2nd ed. i. pp. 488, 533. Cf. above, pp. 195-6, 198 ;
below, pp. 404-5-

2 Critical Philosophy, i. bk. i. chap. v. , especially pp. 437 and 440.

3 Theorie der Erfahrung, second edition, p. 384. 4 Op. cit. p. 532.



SCHEMATA AND CATEGORIES 341

that here given, traces Kant's misleading mode of stating the
problem to his holding a false view of the universality of the
concept. Such criticism of Kant, like that passed by Caird,
is in many respects justified, but the occasion upon which the
admonition is made to follow would none the less seem to be
ill-chosen.

It may be asked why Kant in this chapter so completely
ignores space. No really satisfactory answer seems to present
itself. It is true that time is the one universal form of all
intuition, of outer as well as of inner experience. It is also
true that, as Kant elsewhere shows, consciousness of time
presupposes consciousness of space for its own possibility,
and so to that extent may be regarded as including the
latter form of consciousness within itself. Nevertheless
Kant's concentration on the temporal aspect of experience
is exceedingly arbitrary, and results in certain unfortunate
consequences. Owing to the manner in which Kant en-
visages his problem l he is bound, indeed, to lay the greater



Online LibraryNorman Kemp SmithA commentary to Kant's 'Critique of pure reason,' → online text (page 42 of 72)