Norman Kemp Smith.

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

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outer objects. In contrast to the subjective sensations of
taste and colour, it possesses objectivity. This mode of
distinguishing between space and the matter of sense implies
that extended objects are not mere ideas, but are sufficiently
independent to be capable of acting upon the sense organs, and
of thereby generating the sensations of the secondary qualities.

Kant, it must be observed, refers only to taste and colour.
He says nothing in regard to weight, impenetrability, and the
like. These are revealed through sensation, and therefore on
his view ought to be in exactly the same position as taste or
colour. But if so, the relative independence of the extended
object can hardly be maintained. Kant's distinction between
space and the sense qualities cannot, indeed, be made to
coincide with the Cartesian distinction between primary and
secondary qualities.

A second difference, from Kant's point of view, between
space and the sense qualities is that the former can be
represented a priori, in complete separation from everything
empirical, whereas the latter can only be known a posteriori.
This, as we have seen, is a very questionable assertion. The
further statement that all determinations of space can be
represented in the same a priori fashion is even more question-
able. At most the difference is only between a homogeneous
subjective form yielded by outer sense and the endlessly
varied and consequently unpredictable contents revealed by
the special senses. The contention that the former can be
known apart from the latter implies the existence of a pure
manifold additional to the manifold of sense.

Fifth Paragraph. In the next paragraph Kant emphasises
the distinction between the empirical and the transcendental
meanings of the term appearance. A rose, viewed empirically -,
as a thing with an intrinsic independent nature, may appear
of different colour to different observers.

" The transcendental conception of appearances in space, on the
other hand, is a Critical reminder that nothing intuited in space is
a thing in itself, that space is not a form inhering in things in them-
selves . . . and that what we call outer objects are nothing but
mere representations of our sensibility, the form of which is space."

In other words, the distinction drawn in the preceding
paragraph between colour as a subjective effect and space as

1 A 28-9. Cf. B I ; Prolegomena, 13, Remark II. at the end : "Cinnabar
excites the sensation of red in me." Cf. above, pp. 80-8 ; below, pp. 146 ff. , 274 ff.


an objective existence is no longer maintained. Kant, when
thus developing his position on subjectivist lines, allows no
kind of independent existence to anything in the known
world. Objects as known are mere Ideas (blosse Vorstellungen
unserer Sinnlichkeit\ the sole correlate of which is the un-
knowable thing in itself. But even in this paragraph both
tendencies find expression. " Colour, taste, etc., must not
rightly be regarded as properties of things, but only as
changes in the subject." This implies a threefold distinction
between subjective sensations, empirical objects in space, and
the thing in itself. The material world, investigated by
science, is recognised as possessing a relatively independent
mode of existence.

Substituted Fourth Paragraph of second edition. In prepar-
ing the second edition Kant himself evidently felt the awkward-
ness of this abrupt juxtaposition of the two very different
points of view ; and he accordingly adopts a non-commital
attitude, substituting a logical distinction for the ontological.
Space yields synthetic judgments a priori ; the sense qualities
do not. Only in the concluding sentence does there emerge
any definite phenomenalist implication. The sense qualities,
" as they are mere sensations and not intuitions, in themselves
reveal no object, least of all [an object] a priori"^ The
assertion that the secondary qualities have no ideality implies
a new and stricter use of the term ideal than we find anywhere
in the first edition a use which runs counter to Kant's own
constant employment of the term. On this interpretation it is
made to signify what though subjective is also a priori. Here,
as in many of the alterations of the second edition, Kant
is influenced by the desire to emphasise the points which
distinguish his idealism from that of Berkeley.

1 Kant continues the discussion of this general problem in A 45 ff. =B 62 ff.





Time : First Argument. This argument is in all respects the
same as the first argument on space. The thesis is that the
representation l of time is not of empirical origin. The proof
is based on the fact that this representation must be previously
given in order that the perception of coexistence or succession
be possible. It also runs on all fours with the first argument
in the Dissertation.

" The idea of time does not originate in, but is presupposed by the
senses. When a number of things act upon the senses, it is only by
means of the idea of time that they can be represented whether
as simultaneous or as successive. Nor does succession generate
the conception of time; but stimulates us to form it. Thus
the notion of time, even if acquired through experience, is very
badly defined as being a series of actual things existing one after
another. For I can understand what the word after signifies only
if I already know what time means. For those things are after one
another which exist at different times, as those are simultaneous which
exist at one and the same time." 2

Second Argument. Kant again applies to time the argu-
ment already employed by him in dealing with space. The
thesis is that time is given a priori. Proof is found in the
fact that it cannot be thought away, i.e. in the fact of its
subjective necessity. From this subjective necessity follows
its objective necessity, so far as all appearances are con-
cerned. In the second edition Kant added a phrase " as
the general condition of their possibility " which is seriously
misleading. The concluding sentence is thereby made to

1 Kant himself again uses the confusing term conception.

* M, i.



read as if Kant were arguing from the objective necessity
of time, i.e. from its necessity as a constituent in the appear-
ances apprehended, to its apriority. It is indeed possible
that Kant himself regarded this objective necessity of time
as contributing to the proof of its apriority. But no such
argument can be accepted. Time may be necessary to
appearances, once appearances are granted. This does not,
however, prove that it must therefore precede them a priori.
This alteration in the second edition is an excellent, though
unfortunate, example of Kant's invincible carelessness in the
exposition of his thought. It has contributed to a misreading
by Herbart and others of this and of the corresponding
argument on space.

" lyet us not talk of an absolute space as the presupposition of
all our constructed figures. Possibility is nothing but thought, and
it arises only when it is thought. Space is nothing but possibility,
for it contains nothing save images of the existent; and absolute
space is nothing save the abstracted general possibility of such
constructions, abstracted from it after completion of the construc-
tion. The necessity of the representation of space ought never to
have played any role in philosophy. To think away space is to
think away the possibility of that which has been previously posited
as actual. Obviously that is impossible, and the opposite is
necessary." *

Were Kant really arguing here and in the second argu-
ment on space solely from the objective necessity of time and
space, this criticism would be unanswerable. But even taking
the argument in its first edition form, as an argument from
the psychological necessity of time, it lies open to the same
objection as the argument on space. It rests upon a false
statement of fact. We cannot retain time in the absence
of all appearances of outer and inner sense. With the
removal of the given manifold, time itself must vanish.

Fourth Argument. 2 This argument differs only slightly, and
mainly through omissions, 3 from the fourth 4 of the arguments
in regard to space; but a few minor points call for notice.
(a) In the first sentence, instead of intuition, which alone is
under consideration in its contrast to conception, Kant
employs the phrase "pure form of intuition." (ft) In the
third sentence Kant uses the quite untenable phrase " given
through a single object {Gegenstand)? Time is not given

1 Herbart, Werke, ii. 30. Quoted by Vaihinger, iii. p. 198.

2 The third argument on time will be considered below in its connection
with the transcendental exposition.

3 The chief omission goes, as we shall see, to form the concluding argument
on time.

4 In the second edition, the third.


from without, nor is it due to an object. (V) The concluding
sentences properly belong to the transcendental exposition.
They are here introduced, not in the ambiguous manner of
the fourth 1 argument on space, but explicitly as a further
argument in proof of the intuitive character of time. The
synthetic proposition which Kant cites is taken neither from
the science of motion nor from arithmetic. It expresses the
nature of time itself, and for that reason is immediately con-
tained in the intuition of time.

Fifth Argument. This argument differs fundamentally
from the corresponding argument on space, whether of the
first or of the second edition, and must therefore be independ-
ently analysed. The thesis is again that time is an intuition.
Proof is derived from the fact that time is a representation
in which the parts arise only through limitation, and in which,
therefore, the whole must precede the parts. The original
(ursprungliche] time-representation, i.e. the fundamental repre-
sentation through limitation of which the parts arise as
secondary products, must be an intuition.

To this argument Kant makes two explanatory additions.
(a) As particular times arise through limitation of one single
time, time must in its original intuition be given as infinite,
i.e. as unlimited. The infinitude of time is not, therefore,
as might seem to be implied by the prominence given to
it, and by analogy with the final arguments of both the
first and the second edition, a part of the proof that it
is an intuition, but only a consequence of the feature by
which its intuitive character is independently established.
The unwary reader, having in mind the corresponding argu-
ment on space, is almost inevitably misled. All reference to
infinitude could, so far as this argument is concerned, have
been omitted. The mode in which the argument opens
seems indeed to indicate that Kant was not himself altogether
clear as to the cross-relations between the arguments on space
and time respectively. The real parallel to this argument is
to be found in the second part of the fourth 1 argument on
space. That part was omitted by Kant in his fourth argu-
ment on time, and is here developed into a separate argument.
This is, of course, a further cause of confusion to the reader,
who is not prepared for such arbitrary rearrangement. In-
deed it is not surprising to find that when Kant became the
reader of his own work, in preparing it for the second edition,
he was himself misled by the intricate perversity of his exposi-
tion. In re-reading the argument he seems to have forgotten
that it represents the second part of the fourth 1 argument

1 In the second edition, the third/


on space. Interpreting it in the light of the fifth l argument
on space which he had been recasting for the second edition,
it seemed to him possible, by a slight alteration, to bring
this argument on time into line with that new proof. 2 This
unfortunately results in the perverting of the entire para-
graph. The argument demands an opposition between intui-
tion in which the whole precedes the parts, and conception in
which the parts precede the whole. In order to bring the
opposition into line with the new argument on space, accord-
ing to which a conception contains an infinite number of
parts, not in it, but only under it, Kant substitutes for the
previous parenthesis the statement that " concepts contain
only partial representations," meaning, apparently, that their
constituent elements are merely abstracted attributes, not
real concrete parts, or in other words, not strictly parts at
all, but only partial representations. But this does not at
all agree with the context. The point at issue is thereby

(b) The main argument rests upon and presupposes a
very definite view as to the manner in which alone, according
to Kant, concepts are formed. Only if this view be granted
as true of all concepts without exception is the argument
cogent. This doctrine 3 of the concept is accordingly stated
by Kant in the words of the parenthesis. The partial repre-
sentations, i.e. the different properties which go to constitute
the object or content conceived, precede the representation
of the whole. "The aggregation of co-ordinate attributes
(Merkmale) constitutes the totality of the concept." 4 Upon
the use which Kant thus makes of the traditional doctrine
of the concept, and upon its lack of consistency with his
recognition of relational categories, we have already dwelt. 5

Third Argument and the Transcendental Exposition. The
third argument ought to have been omitted in the second
edition, and its substance incorporated in the new transcend-
ental exposition, as was done with the corresponding argu-
ment concerning space. The excuse which Kant offers for
not making the change, namely, his desire for brevity, is not
valid. By insertion in the new section the whole matter
could have been stated just as briefly as before.

The purpose of the transcendental exposition has been
already defined. It is to show how time, when viewed in the
manner required by the results of the metaphysical deduction,

1 In the second edition, the fourth.

2 Cf. Vaihinger, ii. pp. 380-1.

3 Cf. second part of fourth (third) argument on space.

4 Kant's Logik, Einleiiung, 8, Eng. trans, p. 49.

5 Cf. above, pp. 99-100.


as an a priori intuition, renders synthetic a priori judgments

This exposition, as it appears in the third argument of the
first edition, grounds the apodictic character of two axioms
in regard to time l on the proved apriority of the representa-
tion of time, and then by implication finds in these axioms
a fresh proof of the apriority of time.

The new transcendental exposition extends the above by
two further statements : (a) that only through the intuition of
time can any conception of change, and therewith of motion
(as change of place), be formed ; and (b} that it is because the
intuition of time is an a priori intuition that the synthetic
a priori propositions of the " general doctrine of motion " are
possible. To take each in turn, (a} Save by reference to
time the conception of motion is self-contradictory. It in-
volves the ascription to one and the same thing of contra-
dictory predicates, e.g. that an object both is and is not in
a certain place. From this fact, that time makes possible
what is not possible in pure conception, Kant, in his earlier
rationalistic period, had derived a proof of the subjectivity
of time. 2 (b} In 1786 in the Metaphysical First Principles of
Natural Science Kant had developed the fundamental principles
of the general science of motion. He takes the opportunity
of the second edition (1787) of the Critique to assign this place
to them in his general system. The implication is that the
doctrine of motion stands to time in the relation in which
geometry stands to space. Kant is probably here replying,
as Vaihinger has suggested, 3 to an objection made by Garve
to the first edition, that no science, corresponding .to
geometry, is based on the intuition of time. For two reasons,
however, the analogy between mechanics and geometry
breaks down. In the first place, the conception of motion
is empirical ; and in the second place, it presupposes space
as well as time. 4

Kant elsewhere explicitly disavows this view that the
science of motion is based on time. He had already done
so in the preceding year (1786) in the Metaphysical First

1 These axioms are: (i) time has only one dimension; (2) different times
are not simultaneous but successive. In the fourth argument the synthetic
character of these axioms is taken as further evidence of the intuitive nature of
time. This passage also is really part of the transcendental exposition. That
exposition has to account for the synthetic character of the axioms as well as for
their apodictic character ; and as a matter of fact the intuitive and consequent
synthetic character of the a priori knowledge which arises from time is much
more emphasised in the transcendental exposition than its apodictic nature.

2 Cf. RcJUxiontn, ii. 374 ff. 3 Vaihinger, ii. p. 387.

4 Cf. A 41 = B 58: "Motion which combines both [space and time] pre-
supposes something empirical."


Principles. He there points out * that as time has only one
dimension, mathematics is not applicable to the phenomena
of inner sense. At most we can determine in regard to them
(in addition, of course, to the two axioms already cited)
only the law that all these changes are continuous. Also
in Kant's Ueber Philosophic iiberhaupt (written some time
between 1780 and 1790, and very probably in or about the
year 1789) we find the following utterance :

" The general doctrine of time, unlike the pure doctrine of
space (geometry), does not yield sufficient material for a whole
science." 2

Why, then, should Kant in 1787 have so inconsistently
departed from his own teaching ? This is a question to which
I can find no answer. Apparently without reason, and con-
trary to his more abiding judgment, he here repeats the
suggestion which he had casually thrown out in the Disserta-
tion 3 of 1 770 :

" Pure mathematics treats of space in geometry and of time in
pure mechanics."

But in the Dissertation the point is only touched upon
in passing. The context permits of the interpretation that
while geometry deals with space, mechanics deals with time
in addition to space.


In the Dissertation, and again in the chapter on Schemat-
ism in the Critique itself, still another view is suggested,
namely, that the science of arithmetic is also concerned with
the intuition of time. The passage just quoted from the
Dissertation proceeds as follows :

" Pure mathematics treats of space in geometry and of time in
pure mechanics. To these has to be added a certain concept
which is in itself intellectual, but which demands for its concrete
actualisation (actuatio) the auxiliary notions of time and space (in
the successive addition and in the juxtaposition of a plurality).
This is the concept of number which is dealt with in Arithmetic" 4

This view of arithmetic is to be found in both editions of
the Critique. Arithmetic depends upon the synthetic activity

1 W. iv. p. 471.

Ueber Philosophic iiberhaupt (Hartenstein, vi. p. 395).
3 12. 4 Loc. cit.


of the understanding ; the conceptual element is absolutely

" Our counting (as is easily seen in the case of large numbers) is
a synthesis according to concepts, because it is executed according
to a common ground of unity, as, for instance, the decade (JDekadik)" 1
" The pure image ... of all objects of the senses in general is time.
But the pure schema of quantity, in so far as it is a concept of the
understanding, is number, a representation which combines the
successive addition of one to one (homogeneous). Thus number is
nothing but the unity of the synthesis of the manifold of a homo-
geneous intuition in general, whereby I generate time itself in the
apprehension of the intuition." 2

This is also the teaching of the Methodology? Now it
may be observed that in none of these passages is arithmetic
declared to be the science of time, or even to be based on the
intuition of time. In 1783, however, in the Prolegomena,
Kant expresses himself in much more ambiguous terms, for
his words imply that there is a parallelism between geometry
and arithmetic.

"Geometry is based upon the pure intuition of space. Arith-
metic produces its concepts of number through successive addition
of units in time, and pure mechanics especially can produce its
concepts of motion only by means of the representation of time." 4

The passage is by no means explicit ; the " especially "
(yornehmlicti] seems to indicate a feeling on Kant's part that
the description which he is giving of arithmetic is not really
satisfactory. Unfortunately this casual statement, though
never repeated by Kant in any of his other writings, was
developed by Schulze in his Erlduterungen.

"Since geometry has space and arithmetic has counting as its
object (and counting can only take place by means of time), it is
evident in what manner geometry and arithmetic, that is to say
pure mathematics, is possible." 5

1 A 78 - B 104.

2 A 142-3 = 6 182. It should be observed that in Kant's view schemata
"exist nowhere but in thought" (A 141 = 6 180). It may also be noted that
time is taken as conditioning the schemata of all the categories.

3 A7i7ff.=B745ff. * Ia

5 Erlduterungen uber des Herrn Professor Kant Critik der reinen Vtrnunft
(Konigsberg, 1784), p. 24. Johann Schulze (or Schultz) was professor of mathe-
matics in Konigsberg. He was also Hofprediger^ and is frequently referred to as
Pastor Schulze. Kant has eulogised him ( IV. x. p. 128) as " the best philosophical
head that I am acquainted with in our part of the world." In preparing the
Erlduterungen, which is a paraphrase or simplified statement of the argument of
the Critique, with appended comment, Schulze had the advantage of Kant's
advice in all difficulties. Kant also read his manuscript, and suggested a few
modifications (op. cit. pp. 329, 343).



Largely, as it would seem, 1 through Schulze, whose
Erlduterungen did much to spread Kant's teaching, this view
came to be the current understanding of Kant's position.
The nature of arithmetic, as thus popularly interpreted, is
expounded by Schopenhauer in the following terms :

"In time every moment is conditioned by the preceding. The
ground of existence, as law of the sequence, is thus simple, because
time has only one dimension, and no manifoldness of relations can
be possible in it. Every moment is conditioned by the preceding ;
only through the latter can we attain to the former ; only because
the latter was, and has elapsed, does the former now exist. All
counting rests upon this nexus of the parts of time ; its words merely
serve to mark the single steps of the succession. This is true of
the whole of arithmetic, which throughout teaches nothing but the
methodical abbreviations of counting. Every number presupposes
the preceding numbers as grounds of its existence ; I can only reach
them through all the preceding, and only by means of this insight
into the ground of its existence do I know that, where ten are, there
are also eight, six, four." 2

Schulze was at once challenged to show that this was
really Kant's teaching, and the passage which he cited was
Kant's definition of the schema of number, above quoted. 3
It is therefore advisable that we should briefly discuss the
many difficulties which this passage involves. What does
Kant mean by asserting that in the apprehension of number
we generate time ? Does he merely mean that time is required
for the process of counting ? Counting is a process through
which numerical relations are discovered ; and it undoubtedly
occupies time. But so do all processes of apprehension, in
the study of geometry no less than of arithmetic. That this
is not Kant's meaning, and that it is not even what Schulze,
notwithstanding his seemingly explicit mode of statement,
intends to assert, is clearly shown by a letter written by Kant
to Schulze in November 1788. Schulze, it appears, had
spoken of this very matter.

" Time, as you justly remark, has no influence upon the properties
of numbers (as pure determinations of quantity), such as it may have

Online LibraryNorman Kemp SmithA commentary to Kant's 'Critique of pure reason,' → online text (page 19 of 72)