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Norman Kemp Smith.

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

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4 A 204 = B 249. 5 Wt j p p 87 _ 92



378 THE ANALYTIC OF PRINCIPLES

such as that of night and day or of the notes in a piece of
music, are themselves causal sequences. This criticism has
been replied to by Stadler x in the following terms :

" When Schopenhauer adduces the sequence of musical notes or of
day and night, as objective sequences which can be known without
the causal law, we need only meet him with the question, Where in
these cases is the substance that changes ? So soon as he is forced
to put his objection into the form required to bring it into relation to
the question of the possibility of knowledge, his error becomes obvious.
His instances must then be expressed thus : The instrument passes
from one state of sound into another ; the earth changes from the
measure of enlightenment which makes day, to that which makes
night. Of such changes no one will say that they are not referred
to a cause. And we may quote in this reference the appropriate
saying of Kant himself, ' Days are, as it were, the children of Time,
since the following day with that which it contains is the product of
the previous day.' "

Night and day, in so far as they are sequent events, must
be conceived in terms of causality, not in the sense that night
causes day, but as being determined by causes that account
not only for each separately, but also for the alternating
sequence of the one upon the other. Such causes are found
by the astronomer to lie in the changing positions of the earth
relatively to the sun.

Schopenhauer adds a further objection of a more subtle
nature, which has again been excellently stated and answered
by Stadler :

"Schopenhauer points out that what we call chance is just a
sequence of events which do not stand in causal connexion. ' I come
out of the house and a tile falls from the roof which strikes me; in
such a case there is no causal connexion between the falling of the
tile and my coming out of the house, yet the succession of these two
events is objectively determined in my apprehension of them.' How
have we to criticise this case from the transcendental point of view?
We know that successions become necessary, i.e. objective, for our
consciousness, when we regard them as changes of a substance which
are determined by a cause. But it is shown here that there are
successions in which the single members are changes of different
substances. If substance S changes its state A into B on account
of the cause X, and substance S' changes its state A' into B' on
account of the cause X', and if I call the first change V and the
second V, the question arises how the objectivity of the succession

1 Grundsdtze der reinen Erkenntniss-Tkeorte, p. 151. Quoted and translated
by Caird, i. p. 572. Caird sums up the matter in a sentence (p. 571) : " Kant is
snowing, not that objective succession is always causal, but that the determination
of a succession of perceptions as referring to a succession of states in an object,
involves the principle of causality."



SECOND ANALOGY 379

V V is related to the law of causality. Sequences such as VV are
very frequent, and our consciousness of the objectivity is certain.
Do we owe this consciousness to the same rule as holds good in
other cases ? Certainly. The distinction is not qualitative, but rests
only on the greater complication of the change in question. The
sequence V V can become objective only if I think it as a necessary
connexion. It must be so determined that V can only follow V in
'consciousness in general'; there must be a U, the introduction of
which is the cause that V follows V. To be convinced of this, I do
not need actually to know U. I know that on every occasion U
causes the succession V V. Of course, this presupposes that all data
of the states considered, A and A', remain identical. But whether
these data are very simple or endlessly complex, whether they are
likely to combine to the given result frequently or seldom, is in-
different for the objectifying of the event ; it is not the perception
of U, but the presupposition of it, which makes the change necessary
and so objective for us." 1

To turn now to the other difficulty which Kant himself
raises in A 202-3 = B 247-8, viz. that cause and effect would
frequently seem to be coexistent, and the " sole empirical
criterion " to be therefore absent. It may from this point of
view be maintained that the great majority of causes occur
simultaneously with their effects, and that such time sequence
as occurs is due solely to the fact that the cause cannot execute
itself in one single instant. Kant has little difficulty in dis-
posing of this objection. Causality concerns only the order,
not the lapse, of time ; and the sequence relation must remain
even though there is no interval between the two events. If
a leaden ball lies upon a cushion it makes a depression in it.
The ball and the depression are coexistent. None the less,
when viewed in their dynamical relation, the latter must be
regarded as sequent upon the former. If the leaden ball is
placed upon a smooth cushion a hollow is at once made, but
if a hollow exists in a cushion a ball need not appear. In
other words, the criteria for the determination of specific causal
relations are neither the presence nor the absence of sequence,
but are empirical considerations verifiable only upon special
investigation. 2 The observer is called upon to disentangle the
complicated web of given appearances under the guidance of
the quite general and formal principle that every event is due to
some antecedent cause. He must do so as best he can through
the application of his acquired insight, and, when necessary, by
means of the requisite experimental variation of conditions.

In the two following paragraphs (A 204-5 = 6 249-51)

1 Loc. cit.

2 The connected question how we can determine the ball and the cushion as
objectively coexistent is the problem of the third Analogy,



38o THE ANALYTIC OF PRINCIPLES

Kant raises points which he later discussed more fully in the
Metaphysical First Principles of Natural Science^ As adequate
explanation of the argument would be a very lengthy matter,
and not of any very real importance for the understanding
of the general Critical position, we may omit all treatment
of it. In the sections of the Metaphysical First Principles
just cited, the reader will find the necessary comment and
explanation. Such bearing as these two paragraphs have
upon Kant's view of the nature of the causal relation has
been noted above. 2

In the section on Anticipations of Perception* Kant has
stated that the principle of the continuity of change involves
empirical factors, and therefore falls outside the limits of
transcendental philosophy. To this more correct attitude
Kant, unfortunately, did not hold. In A 207-11 = B 252-6 he
professes to establish the principle in a priori transcendental
fashion as a necessary consequence of the nature of time. This
proof is indeed thrice repeated with unessential variations,
thereby clearly showing that these paragraphs also are of
composite origin. The argument in all three cases consists in
inferring from the continuity of time the continuity of all
changes in time. As the parts of time are themselves times,
of which no one is the smallest, so in all generation in time,
the cause must in its action pass through all the degrees of
quantity from zero to that of the final effect.

"Every change has a cause which evinces its causality in the
whole time in which the change takes place. This cause, therefore,
does not engender the change suddenly (at once or in one moment),
but in a time, so that, as the time increases from its initial moment
a to its completion in , the quantity of the reality (b - a) is in like
manner generated through all lesser degrees which are contained
between the first and the last." 4

This argument is inconclusive. As Kant himself recognises
in regard to space, 5 we may not without special proof assume
that what is true of time must be true of the contents of time.
If time, change, and causation can be equated, what is true
of one will be true of all three. But the assumption upon
which the argument thus rests has not itself been substantiated.

In the third proof 6 the argument is stated in extreme
subjectivist terms which involve the further assumption that

1 III. Erkldrung I and 2, Lehrsatz i (especially Anmerkung thereto). Cf.
also II. Erkldrung I and 5, and the last pages of the Allgemeine Anmerkung.

2 Pp. 351, 373-4- Cf. pp. 318-21.

3 A 170-1 = B 212-13, above, p. 353, n. 2. 4 A 208 = B 253-4.

5 Metaphysical First Principles , //. Lehrsatz 4, Anmerkung 2.

6 A 209- 10= B 255-6.



THIRD ANALOGY 381

what is true of apprehension is ipso facto true of everything
apprehended. The possibility of establishing the law of
dynamical continuity follows, Kant declares, as a consequence
of its being a law of our subjective apprehension.

"We anticipate only our own apprehension, the formal condition
of which, inasmuch as it inheres in the mind prior to all given
appearances, must certainly be capable of being known a priori'' *

Kant's attitude towards the physical principle of con-
tinuity underwent considerable change. In his New Doctrine
of Motion and Rest (i/SS) 2 he maintains that it cannot be
proved, and that physicists may rightly refuse to recognise
it even as an hypothesis. It is in the Essay on Negative
Quantity (i/63) 3 that Kant first adopts the attitude of the
Critique, and rejects the "speculative" objections raised
against the mathematical conception of the infinitely small.
In the Metaphysical First Principles of Natural Science^ the
principle of continuity is defended and developed, but only
in its application to material existence, not in its relation
to the causal process.

C. Third Analogy. All substances, in so far as they are
coexistent, stand in thoroughgoing communion? i.e. in reciprocity
with one another. Or, as in the second edition : All substances,
so far as they can be perceived to coexist in space, are in
thoroughgoing reciprocity^.

This section contains four separate proofs. The first
three paragraphs in the text of the first edition contain the
first proof. The fourth paragraph supplies a second proof,
and the fifth paragraph a third. In the second edition Kant
adds a fourth proof (the first paragraph of the text of the
second edition).

We may lead up to these proofs by first formulating (a)
the fundamental assumption upon which they proceed, and
(b) the thesis which they profess to establish, (a) The argu-
ment involves the same initial assumption as the preceding
Analogies, viz. that representations exist exclusively in suc-
cession, or stated in phenomenalist terms, that the objectively
coexistent can be apprehended only in and through representa-
tions that are sequent to one another in time. 6 Upon this

1 A 210= B 256. z w. ii. p. 22.

3 W. ii. p. 168. 4 Loc. dt.

6 For lack of a more suitable English equivalent I have translated Gcmeinschaft
as "communion." As Kant points out in A 213 = 6 260, the German term is
itself ambiguous, signifying commercium (i.e. dynamical interaction) as well as
communio.

8 Cf. above, pp. 348, 358-9, 367-8, 371-2.



382 THE ANALYTIC OF PRINCIPLES

assumption the problem of the third Analogy is to explain
how from representations all of which are in succession we
can determine the objectively coexistent, (b) In the Disserta-
tion 1 Kant had maintained that though the possibility of
dynamical communion of substances is not necessarily involved
in their mere existence, such interaction may be assumed as
a consequence of their common origin in, and dependence
upon, a Divine Being. In the Critique no such metaphysical
speculations are any longer in order, and Kant recognises
that as regards things in themselves it is not possible to
decide whether dynamical interaction is, or is not, necessarily
involved in coexistence. The problem of this third Analogy
concerns only appearances, which as such must be subject to
the conditions of unitary experience ; and one such condition
is that they be apprehended as belonging to a single objective
order of nature, and therefore as standing in reciprocal
relations of interaction. The apprehension of substances as
reciprocally determining one another is y Kant contends, an
indispensable condition of their being known even as coexistent.
Such is Kant's thesis. The proof may first be stated in what
may be called its typical or generic form. Kant's four
successive proofs can then be related to it as to a common
standard.

Two things, A and B, can be apprehended as coexistent
only in so far as we can experience them in either order, i.e.
when the order of our perceptions of them is reversible. If
they existed in succession, this could never be possible. The
earlier member of a time series is past when the succeeding
member is present, and what belongs to the past can never
be an object of perception. The fact that the order in which
things can be perceived is reversible would thus seem to prove
that they do not exist successively to one another in time. 2
That, however, is not the case. By itself such experience
does not really suffice to yield consciousness of coexistence.
It can yield only consciousness of an alternating succession. 3
A further factor, namely, interpretation of the reversibility of
our perceptions as due to their being conditioned by objects
which stand in the relation of reciprocal determination, must
first be postulated. If these objects mutually determine one
another to be what they are, no one of them can be antecedent
to or subsequent upon the others ; and by their mutual
reference each will date the others as simultaneous with
itself. In other words, the perception of the coexistence of

1 17 ff. Cf. Nachtragc zu Kants Kritik^ Ixxxvi, with B. Erdmann's com-
ment, p. 35.

2 A2ii-i2 = B 258. Cf. A 2ii = B 257. 3 A2ii = B257.



THIRD ANALOGY 383

objects involves the conception of them as mutually determin-
ing one another. The principle of communion or reciprocity
conditions the experience of coexistence, and is therefore
valid for objects apprehended in that manner.

Kant also maintains, more by implication than by explicit
statement, that as A and B need not stand in any direct
relation, the apprehension of them as coexistent involves the
conception of an all-embracing order of nature within which
they fall and which determines them to be what they are. If
any one of them, even the most minute and insignificant,
were conceived as altered, corresponding simultaneous varia-
tions would have to be postulated for all the others. The
unity of the phenomenal world is the counterpart of the unity
of apperception. Unity of experience involves principles
which prescribe a corresponding unity in the natural realm.
Dynamical communion is the sufficient and necessary fulfilment
of this demand. It carries to completion the unity demanded
by the preceding Analogies of substance and causality. Kant
sums up his position in a note to A 218 = B 265.

"The unity of the world-whole, in which all appearances have to
be connected, is evidently a mere consequence of the tacitly assumed
principle of the communion of all substances which are coexistent.
For if they were isolated, they would not as parts constitute a
whole. And if their coexistence alone did not necessitate their
connection (the reciprocal action of the manifold) we could not
argue from the former, which is a merely ideal relation, to the
latter, which is a real relation. We have, however, in the proper
context, shown that communion is really the ground of the possibility
of an empirical knowledge of coexistence, and that therefore the
actual inference is merely from this empirical knowledge to com-
munion as its condition."

To turn now to Kant's successive proofs. The first 1 calls
for no special comment. It coincides with the above. The
second 2 proof is an incompletely stated argument, which
differs from the first only in its more concrete statement of
the main thesis and in its limitation of the argument to
spatial existences. Dynamical community is the indispensable
condition of our apprehension of any merely spatial side-by-
sideness. Kant now adds that it is the dynamical continuity
of the spatial world which enables us to apprehend the
coexistence of its constituents. The important bearing of
this argument we shall consider in its connection with the
proof which Kant added in the second edition.

1 A 21 1-13 = B 258-60 : first three paragraphs (first edition).
2 A 213-14 = 6 260-1 : fourth paragraph (first edition).



384 THE ANALYTIC OF PRINCIPLES

The third 1 proof is probably the earliest in date of writing.
It draws a misleading distinction between subjective and
objective coexistence, and seems to argue that only the latter
form of coexistence need presuppose the employment of the
category of reciprocity. That runs directly counter to the
central thesis of the other proofs, that only in terms of
dynamical relation is coexistence at all apprehensible. That
the above distinction indicates an early date of writing would
seem to be confirmed by the obscure phrase " community of
apperception" which is reminiscent of the prominence given
to apperception in Kant's earlier views, and by the concluding
sentence in which Kant employs terms inherence, conse-
quence, and composition that are also characteristic of the
earlier stages of his Critical enquiries. 2

It is significant that in the new argument 3 of the second
edition the space factor, emphasised in the second proof of the
first edition, is again made prominent. 4 The principle is, in-
deed, reformulated in such manner as to suggest its limitation
to spatial existences. " All substances, so far as they can be
perceived to coexist in space> are in thoroughgoing reciprocity."
Now it is decidedly doubtful whether Kant means to limit the
category of reciprocity to spatial existences. As we have
already noted, 5 he would seem to hold that though the category
of causality can acquire meaning only in its application to
events in space, it may in its subsequent employment be
extended to the states of inner sense. The latter are effects
dynamically caused, and among their causal conditions are
mechanical processes in space. The extension of the category
of reciprocity to include sensations and desires undoubtedly
gives rise to much greater difficulties than those involved in
the universal application of the causal principle. On the other
hand, its limitation to material bodies must render the co-
ordination of mental states and mechanical processes highly
doubtful, and would carry with it all the difficulties of an
epiphenomenal view of psychical existences. The truth prob-
ably is that in this matter Kant had not thought out his posi-
tion in any quite definite manner ; and that owing to the
influence, on the one hand of the dualistic teaching of the
traditional Cartesian physics, and on the other of his increasing
appreciation of the part which space must play in the defini-

1 A 214-15 = 6 261-2 : fifth paragraph (first edition).

2 Cf. above, pp. 189-90, 208 ff. 3 B 257-8 : first paragraph (second edition).

4 Cf. B 291-3, partially quoted above, pp. 310-11. In the Metaphysical First
Principles (III. Lehrsatz, 4) the principle that action and reaction are always equal
is similarly limited to the outer relations of material bodies in space, and Kant
adds that all change in bodies is motion. Cf. W. xi. p. 234 ; and above, p. 147.

5 Above pp. 311-12; below, pp. 473-7.



THIRD ANALOGY 385

tion and proof of the principles of understanding, he limited
the category of reciprocity to spatial existences, without con-
sidering how far such procedure is capable of being reconciled
with his determinist view of the empirical self. His procedure
is also open to a second objection, namely, that while thus
reformulating the principle, he fails to remodel his proof in a
sufficiently thoroughgoing fashion. The chief stress is still
laid upon the temporal element ; and in order to obtain a
proof of the principle that will harmonise with the prominence
given to the space-factor, we are thrown back upon such supple-
mentary suggestions as we can extract from the second argu-
ment of the first edition. It is there stated that "without
dynamical communion even spatial community (communio
spatii) could never be known empirically." l That is an asser-
tion which, if true, will yield a proof of the principle of reci-
procity analogous to that which has been given of the principle
of causality ; for it will show that just as the conception of
causality is involved in, and makes possible, the awareness of
time, so the conception of reciprocity is involved in, and makes
possible, the awareness of space.

The proof will be as follows. The parts of space have
to be conceived as spatially interrelated. Space is not a col-
lection of independent spaces ; particular spaces exist only in
and through the spaces which enclose them. In other words,
the parts of space mutually condition one another. Each part
exists only in and through its relations, direct or indirect, to
all the others ; the awareness of their coexistence involves the
awareness of this reciprocal determination. But space cannot,
any more than time, be known in and by itself; 2 and what is
true of space must therefore hold of the contents, in terms of
the interrelations of which space can alone be experienced.
How, then, can the reciprocal determination of substances in
space be apprehended by a consciousness which is subject in
all its experiences to the conditions of time ? As Kant has
pointed out in A 2ii=B 258, 3 objective coexistence is dis-
tinguished from objective sequence by reversibility of the per-
ceptions through which it is apprehended. When A and B
coexist, our perceptions can begin with A and pass to B, or
start from B and proceed to A. There is also, as Kant
observes in the second proof, a further condition, namely, that
the transition is in each case made through a continuous series
of changing perceptions.

1 A 213 = B 260.

2 The inconsistency of Kant's view of pure manifolds of time and space with
the argument of the Analytic of Principles is too obvious to call for detailed
comment.

Cf. B 257.

2 C



386 THE ANALYTIC OF PRINCIPLES

" Only the continuous influences in all parts of space can lead
our senses from one object to another. The light, which plays
between our eye and the celestial bodies, produces a mediate com-
munion between us and them, and thereby establishes the coexistence
of the latter. We cannot empirically change our position (perceive
such a change), unless matter in all parts of space makes the percep-
tion of our position possible to us. Only by means of its reciprocal
influence can matter establish the simultaneous existence of its parts,
and thereby, though only mediately, their coexistence with even the
most remote objects. Without communion, every perception of an
appearance in space is broken off from every other, and the chain of
empirical representations, i.e. experience, would have to begin entirely
anew with every new object, without the least connection with pre-
ceding representations, and without standing to them in any relation
of time." 1

But even such reversibility of continuous series does not by
itself establish coexistence. For in the imagination 2 we can
represent such series, without thereby acquiring the right to
assert that they exist not as series but as simultaneous wholes.
And as Kant might also have pointed out, even in sense-per-
ception we can experience reversible continuous series that do
not in any way justify the inference to coexistence. We may,
for instance, produce on a musical instrument a series of con-
tinuously changing sounds, and then in immediate succession
produce the same series in reverse order. An additional factor
is therefore required, namely, the interpretation of the reversi-
bility of our perceptions as being grounded in objects which,
because spatially extended, and spatially continuous with one
another, can yield continuous series of perceptions, and which,
because of their thoroughgoing .reciprocity, make possible the
reversing of these series. To summarise the argument in a
sentence : as the objectively coexistent, if it is to be known
at all, can only be known through sequent representations, the
condition of its apprehension is the possibility of interpreting
reversible continuous series as due to the reciprocal interaction



Online LibraryNorman Kemp SmithA commentary to Kant's 'Critique of pure reason,' → online text (page 47 of 72)