Norman Kemp Smith.

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

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should have been constrained to develop a position more
precise and less ambiguous than that expressed in the defini-
tions of reality and degree given in the chapter on Schematism.
With these preliminary explanations we may pass to Kant's
second proof of his principle.

A link of connection between the two proofs may be found
in the reason which Kant in the first proof gives for his asser-
tion that sensation cannot possess extensive magnitude the
reason, namely, that as its apprehension takes place in a single
moment, it involves no element of synthesis. In his second
proof Kant modifies this contention, and maintains that we
can abstract from the extensive magnitude of the appearance,
and yet can recognise a synthesis as being involved.

"The real which corresponds to sensations in general, as opposed
to negation = o, represents only something the very conception of
which contains an existence [em Sein\ and signifies nothing but the
synthesis in an empirical consciousness in general." 2

1 Loc. cit. Italics not in Kant. 2 Cf. A 175 = 6217. Cf. above, pp. 350-1.


Kant adds that in a single moment we can represent to
ourselves as involved in the bare sensation

"... a synthesis of the uniform progression from zero to the given
empirical consciousness."

These statements are far from clear ; but it is hardly neces-
sary to criticise them in detail. Since Kant is endeavouring
to prove that a schema, that of reality or limitation, is in-
volved in the apprehension of sensation, he is bound in
consistency to maintain, in accordance with the teaching of
his deduction of the categories, that the application of the
schema demands some species of synthesis.

The third proof, added in the second edition, 1 is somewhat
more explicit, and represents a further and last stage in Kant's
vain endeavour to harmonise the teaching of this section with
his general principles. In the empirical consciousness of
sensation there is

"... a synthesis of the different quantities involved in the generation
of a sensation from its beginning in pure intuition = o to its particular
required magnitude."

Or again, apprehension of magnitude is apprehension

"... in which the empirical consciousness can in a certain time
increase from zero up to its given measure."

Here, again, what Kant asserts as occurring in our awareness of
sensation calls for much more rigorous demonstration. Like
the argument of the second proof, it is not independently
established ; it is a mere corollary to the general principles
of his deduction of the categories.

Thus Kant's thesis, that the apprehension of sense quali-
ties as intensive magnitudes presupposes a synthesis according
to an a priori schema, is both obscure in statement, and
unconvincing in argument ; and some of the assertions made,
especially in reference to the occurrence of synthesis, would
seem to be hardly less arbitrary than the connection which
Kant professes to trace between logical " quality," as affirma-
tion or negation, and the dynamical intensity of sensuous
qualities. For, as already indicated, 2 logical "quality" and
intensive magnitude have nothing in common save the

Kant next proceeds to a discussion of the general problem
of continuity. The connection is somewhat forced. But if
we overlook the artificial ordering of the argument and are

1 B 217-18. 2 Cf. above, pp. 192, 341.


ntent to regard what is given as in the nature of paren-
thetical comment, we find in the middle paragraph of this
section an excellent statement of his view of the nature of
continuity and a very clear statement of his dynamical theory
of matter.

Kant develops the conception of continuity (a) in reference
to space and time, and (ft) in its application to the intensity
of sensations and of their causes.

(a) Kant's own words require no comment :

" Space and time are quanta continua because no part of them can
be given, save as enclosed between limits (points or moments), and
therefore as being itself a space or a time. Space therefore consists
only of spaces, time only of times. Points and moments are only
limits, i.e. mere positions that limit space and time. But positions
always presuppose the intuitions which they limit or are intended to
limit ; and out of mere positions, viewed as constituents capable of
being given prior to space and time, neither space nor time can be
constructed. Such magnitudes may also be called flowing^ since
the synthesis of productive imagination involved in their production
is a progression in time, and the continuity of time is ordinarily
denoted by the expression flowing" 1

(b) When Kant proceeds to apply the principle of con-
tinuity to intensive magnitude, his conclusion rests upon a
somewhat different basis. He argues that appearances must
be continuous owing to the fact that they are apprehended in
space and time. 2 So far as they are extended in space and
enduring in time that may perhaps be true ; but Kant's asser-
tion has a wider sweep. It implies that sensations and the
physical conditions of sensation, as for instance the sensation
of red or the force of gravity, are capable of existing in
every possible degree between zero and any given intensity.
This affords the key to his method of formulating his second
and third proofs of the principle of Anticipations of Perception,
which, in the form in which he interprets it, contains this
further implication of continuity. These proofs are inspired
by the desire to make all apprehension, even that of simple
sensation, a temporal process, and by that indirect means to
establish for sensuous intensity and its objective conditions
a continuity similar to that of space and time. The proof is,

1 A 169-70=6 211-12. For comment upon Kant's view of the point as a
limit, cf. below, p. 489 ff.

2 Though Kant maintains in A 171 = B 212-13 that owing to our dependence
upon empirical data and our necessary ignorance of the nature of the causal rela-
tion we cannot similarly demonstrate the principle of the continuity of change, he
has himself, in characteristically inconsistent fashion, given three such demonstra-
tions. Cf. below, pp. 380-1.

2 A


however, as we have seen, inconclusive. This application of
continuity must be regarded as more in the nature of a mere
hypothesis than Kant is willing to recognise. As regards
sensations, it would seem to have been positively disproved
by the results of experimental psychology.

From his supposed proof of the continuity of all intensive
magnitudes Kant draws two further conclusions : first, that
experience can never be made to yield proof of the void in
either space or time. For if all reality can exist in innumer-
able degrees, and if each sense has a determinate degree of
receptivity, the complete absence of reality can never be itself
experienced. Inference to such absence is also impossible
for a second reason, namely, that one and the same exten-
sive magnitude may be completely occupied by an infinite
number of different intensive degrees, indefinitely approxi-
mating to, and yet also indefinitely differing from, zero.
Kant is here referring to the dynamical theory of matter
which he had long held, 1 and which he expounds in opposition
to the current mechanistic view. 2 The mechanistic theory
rests, he contends, upon an assumption purely metaphysical
and therefore wholly dogmatic, that the real in space has
no internal differences, but is uniform like the empty space
in which it exists. 3 In accordance with this assumption
physicists infer that all qualitative differences in our sensa-
tions must be due to merely quantitative differences in their
material causes, and ultimately to differences in the number
and distribution of the constituent parts of material bodies.

1 Cf. Kant's Monadologia physica (1756), and New Doctrine of Motion and Rest
(1758). Kant's final statement of this dynamical theory is given in his Meta-
physical First Principles of Natural Science (1786).

2 In this matter Kant regards himself as defending the Newtonian theory of an
attractive gravitational force. The mechanistic view admits only one form of action,
viz. transference of motion through impact and pressure. " From . . . Democritus
to Descartes, indeed up to our own day, the mechanistic method of explanation
. . . has, under the title of atomism or corpuscular philosophy, maintained its
authority with but slight modification ; and has continued to exercise its influ-
ence upon the principles of natural science. Its essential teaching consists in the
assumption of the absolute impenetrability of primitive matter, in the absolute
homogeneity of its constitution (difference of shape being the sole remaining
difference), and in the absolutely indestructible coherence of matter in its funda-
mental corpuscles " (Metaphysical First Principles, W. vol. iv. p. 533 ; ii. All-
gemeine Anmerkung, 4).

3 This is additional to its other correlative assumption of the absolute void.
" The absolute void and the absolutely full are in the doctrine of nature very much
what blind chance and blind fate are in metaphysical cosmology, namely, a barrier
to the enquiring reason, which either causes its place to be taken by arbitrary
fictions, or lays it to rest on the pillow of obscure qualities" (Metaphysical First
Principles, W. vol. iv. p. 532 (I read forschende for herrschende)\ "There are
only two methods of procedure . . . : the mechanistic, through combinatior
of the absolutely full with the absolute void, or an opposite dynamical methc
that of explaining all material differences through mere differences in the
bination of the original forces of repulsion and attraction" (loc. cit.}.


If two bodies of the same volume differ in weight or in inertia,
the variation must be traced to differences in the amount of
matter, or, otherwise stated, to differences in the amount of un-
occupied space, in the two bodies. To this view Kant opposes
his own hypothesis for it is in this more modest form that it
is presented in these paragraphs namely, that matter occupies
space by intensity and not by mere bulk, and that it may
therefore be diminished indefinitely in degree without for that
reason ceasing completely to fill the same extensive area.
Thus an expanded force such as heat, filling space without
leaving the smallest part of it empty, may be indefinitely
diminished in degree, and yet may still with these lesser
degrees continue to occupy that space as completely as before.
This may not, Kant admits, be the true explanation of physical
differences, but it at least has the merit of freeing the under;
standing from metaphysical preconceptions, and of demon-
strating the possibility of an alternative to the current view.
If matter has intensity as well as extensity, and so can vary
in quality as well as in quantity, physical science may perhaps
be fruitfully developed on dynamical lines.


The principle of the Analogies is : Experience is possible
only through the representation of a necessary connection of

Kant introduces the three analogies with the statement of
an underlying principle, which corresponds to the central thesis
of the transcendental deduction. In the second edition this
general principle is reformulated, and a new proof is added.
These alterations do not seem, however, to be of any special
significance. The two proofs repeat the main argument of the
transcendental deduction, but with special emphasis upon the
temporal aspect of experience. The categories of relation,
as schematised, yield the Analogies , which acquire objective
validity in so far as they render experience possible. The
first proof (given in the second paragraph of the first edition)
maintains that they are indispensable for apperception, and
the second proof (that of the second edition) that they are
indispensable for knowledge of objects. The references to
time in the second proof are too condensed to be intelligible
save in the light of the more explicit arguments given in
support of the three Analogies.

1 In the first edition Kant formulates this principle in the light of his extremely
misleading distinction between mathematical and dynamical principles (cf. above,
pp. 345-7) : "All appearances, as regards their existence, are subject a priori to
rules determining their relation to one another in one time."


The first paragraph in the first edition must be a later
interpolation, as its assertion that simultaneity is a mode of
time conflicts with the proof given of the first Analogy, but
agrees with what must be regarded as a later interpolated
passage introductory to that proof. 1 This paragraph is also
peculiar in another respect. Hitherto Kant has traced the
existence of the three analogies to the three categories of
relation, each of which conditions a separate schema. But in
this paragraph he bases their threefold form on the fact that
time has three modes, duration, sequence, 2 and coexistence,
and that there is therefore a threefold problem : first, what is
involved in consciousness of duration ; secondly, what is
involved in consciousness of succession ; and thirdly, what
is involved in consciousness of coexistence. This is not,
however, a satisfactory mode of stating the matter, for it
might seem to imply that the three aspects of time can be
separately apprehended, and that each has its own independ-
ent conditions. What Kant really proves is that all three
involve one another. We can only be conscious of duration
in contrast to succession, and of succession in contrast to the
permanent, while both involve consciousness of coexistence.
The three analogies thus treat of three aspects of the same
problem, the first connecting with the category of substance,
the second with that of causality, and the third with that
of reciprocity.

The only point that calls for further comment 3 concerns
Kant's adoption of the term Analogy as a title for the three
principles of " relation." The term is employed in contra-
distinction to constitutive principle or axiom ; and Kant
points out that this usage of the term must be carefully
distinguished from the other or mathematical. " In philosophy
analogy is not the likeness of two quantitative but of two
qualitative relations." In mathematical analogy a fourth term
can be discovered from three given terms ; but in an ' analogy
of experience' we possess a rule that suffices only for the
determination of the relation to a term not given, never for
knowledge of this term itself. Thus if we are informed that
15 is to x as 5 is to 10, the value of x can be determined as
30. But if it be stated that a given event stands to an
antecedent event as effect to cause, only the relation holding
between the events can be specified, not the actual cause
itself. The principle of causality thus serves only as

1 Cf. below, p. 358.

2 In A 182 = B 225 the stronger term change (Wechsel) is employed.

8 A 178-80=6 221-3 ( n tne distinction between mathematical and dynamic
principles) has been commented upon above, pp. 345-7.


regulative principle, directing us to search for the cause of an
event among its antecedents.

Riehl has suggested a very different explanation of the
term, namely, as signifying that the categories of relation are
employed only on the analogy of the corresponding, pure
logical forms.

" In so far as I know matter in terms of its empirical properties
as the substance of outer experiences, I do not gain knowledge of
the nature of matter but only of its relation to my thinking. In all
judgments upon outer things I employ matter as the subject. That
knowledge is therefore nothing but an analogy to the conceptual
relation of a subject to its predicates. Matter is related to its
properties and effects in the realm of appearance as the subject of a
categorical judgment is related to its predicates. In so far as an
antecedent is entitled the cause of an event, we do not gain
knowledge of its nature but only of the analogy of the relation of
cause and effect with that of antecedent and consequent in a
hypothetical proposition ; the connection of the changes is analogous
to the conceptual relation of ground and consequence ; the principle
of the sufficient ground of changes is an analogy of experience" J

This explanation may at first sight seem to be supported
by Kant's own statement in the concluding paragraph of the
section before us.

" Through these principles we are justified in combining
appearances only according to an analogy with the logical and
general unity of concepts. . . ." 2

This assertion is, however, incidental to Kant's explanation
that the analogies are not principles of " transcendental "
(i.e. transcendent), but only of empirical application an
explanation itself in turn occasioned by his desire to connect
his present argument with the chapter on Schematism. This
interpretation of the term analogy is probably, therefore, of
the nature of an afterthought. Having adopted the term on
the grounds above stated in A 179-80=6 222, he finds in it
an opportunity to reinforce his previous assertion of the
restricting character of the time condition through which
categories are transformed into schemata. The entire
paragraph is probably, as Adickes remarks, a later inter-
polation. But there are further reasons why we cannot accept
this passage as representing the real origin of the term
analogy. It would involve adoption of the subjectivist stand-
point from which Riehl, despite his otherwise realistic reading

1 Philos. Krit. 2nd ed. i. p. 545. Caird adopts a similar view, i. pp. 540,

2 A i8i=B 224.


of Kant, interprets Kant's phenomenalist doctrines. For 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. 1 It would also seem to
imply, what is by no means Kant's invariable position, the
absolute validity of the logical forms. And lastly, it would
involve the priority of the logical to the real use of the
categories, a violation of Critical principles of which Kant is
himself occasionally guilty, but never, as it would seem, in
this exaggerated form.

A. First Analogy. All appearances contain the permanent
(substance) as the object itself, and the changeable as its mere
determination, i.e. as a mode in which the object exists. Or as
in the second edition : In all change of appearances substance
is permanent ; its quantum in Nature neither increases nor

The second paragraph 2 is of composite character. Its
first part (consisting of the first three sentences) and its second
part give separate proofs, involving assertions directly contra-
dictory of one another. The one asserts change and simul-
taneity to be modes of time ; the other denies this. They
cannot, therefore, be of the same date. The first would seem
to be the later ; it connects with the first paragraph of the
preceding section.

In the first edition the principle is defined as expressing
the schema of the dual category of substance and attribute.
In the second edition it is reformulated in much less
satisfactory form, as being the scientific principle of the
conservation (i.e. indestructibility) of matter. This second
formulation emphasises the weaker side of the argument of
the first edition, and is largely due to the perverting influence
of Kant's method of distinguishing between the Analytic of
Concepts and the Analytic of Judgments. It reveals Kant's
growing tendency to contrast the two divisions of the Analytic,
as dealing, the one with ordinary experience, and the other
with its scientific reorganisation. 3

The first proof in the first edition gives explicit expression
to a presupposition underlying this entire section, namely,
that all apprehension is necessarily successive, or in other
words that it is impossible to apprehend a manifold save in
succession. 4 From this assumption it follows that if such
succession is not only to occur but is to be apprehended as
occurring, and if we are to be able to distinguish between

Cf. below, pp. 373-4. 2 That is to say, in the first edition.

3 Cf. above, pp. 332-3, 343-4.
4 Cf. above, p. 348; below, pp. 367-8, 371-2, 381-2.


the successive order of all our apprehensions and the order
of coexisting independent existences, a permanent must be
thought into the succession, that is to say, the successive
experiences must be interpreted into an objective order in
terms of the category of abiding substance and changing
attributes. Kant neither here nor elsewhere makes any at-
tempt to explain how this position is to be reconciled with
his doctrine that space can be intuited as well as time ; and
there is equal difficulty in reconciling it with the doctrine
developed in his second proof (in the second division of this
same paragraph) that time itself does not change but only
the appearances in it.

As above shown, 1 there are two tendencies in Kant's treat-
ment of time, each of which carries with it its own set of con-
nected consequences. There is the view that consciousness of
time as a whole preconditions consciousness of any part of it.
This tends to recognition of simultaneity as a mode of time
and of the simultaneous as apprehended in a single non-
successive act of apprehension. On the other hand, there is
the counter-view that consciousness of time is only possible
through the successive combination of its parts. This leads
to the assertion that simultaneity is not a mode of time, and
that time itself cannot be apprehended save as the result ol
synthesis in accordance with unifying categories. Through
the categories there arises consciousness of objectivity, and so
for the first time consciousness of a distinction between the
subjective which exists invariably and exclusively in succes-
sion, and the objective which may exist either as successive
or as permanent, and in whose existence both elements are,
indeed, inseparably involved.

To turn now to Kant's second 2 proof of the principle ; 3
it is as follows. All our perceptions are in time, and in time
are represented as either coexistent or successive. Time
itself cannot change, 4 for only as in it can change be repre-

1 Cf. above, pp. 94, 135-8, 309 ff., 347-8.

2 That is to say, in the first edition.

3 The new proof added in the second edition calls for no special comment.
In all essentials it agrees with this second proof of the first edition. It differs
only in such ways as are called for by the mode of formulating the principle
in the second edition.

4 This statement, as Caird has pointed out (i. p. 541), is extremely questionable.
" It may be objected that to say that ' time itself does not change' is like saying
that passing away does not itself pass away. So far the endurance of time and
the permanence of the changing might even seem to mean only that the moments
of time never cease to pass away, and the changing -never ceases to change. A
perpetual flux would therefore sufficiently ' represent ' all the permanence that is
in time." This is not, however, in itself a vital objection to Kant's argument.
For he is here stating more than his argument really requires. Events are dated
in a single time, not in an unchanging time. Kant's statement betrays the


sented. Time, however, cannot by itself be apprehended.
As such, it is the mere empty form of our perceptions.
There must be found in the objects of perception some abiding
substrate or substance which will represent the permanence of
time in consciousness, and through relation to which coexist-
ence and succession of events may be perceived. And since
only in relation to this substrate can time relations be appre-
hended, it must be altogether unchangeable, and may there-
fore 1 be called substance. And being unchangeable it can
neither increase nor diminish in quantity. Kant, without
further argument, at once identifies this substance with

This proof may be restated in briefer fashion. 2 The
consciousness of events in time involves the dating of them
in time. But that is only possible in so far as we have a
representation of the time in which they are to be dated.
Time, however, not being by itself experienced, must be
represented in consciousness by an abiding substrate in which

Online LibraryNorman Kemp SmithA commentary to Kant's 'Critique of pure reason,' → online text (page 44 of 72)