A Commentary to Kant's 'Critique of Pure Reason'

by Norman Kemp Smith

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 argument involves the same initial assumption as the preceding Analogies, viz. that representations exist exclusively in succession, or stated in phenomenalist terms, that the objectively coexistent can be apprehended only in and through representations that are sequent to one another in time.[1230] Upon this 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 Dissertation[1231] 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, 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.[1232] 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.[1233] 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 objects involves the conception of them as mutually determining 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 variations 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 communion as its condition.”

To turn now to Kant’s successive proofs. The first[1234] calls for no special comment. It coincides with the above. The second[1235] 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.

The third[1236] 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, consequence, and composition—that are also characteristic of the earlier stages of his Critical enquiries.[1237]

It is significant that in the new argument[1238] of the second edition the space factor, emphasised in the second proof of the first edition, is again made prominent.[1239] The principle is, indeed, 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,[1240] 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 probably is that in this matter Kant had not thought out his position 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 definition and proof of the principles of understanding, he limited the category of reciprocity to spatial existences, without considering 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 supplementary suggestions as we can extract from the second argument of the first edition. It is there stated that “without dynamical communion even spatial community (communio spatii) could never be known empirically.”[1241] That is an assertion which, if true, will yield a proof of the principle of reciprocity 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 collection 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;[1242] 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 211 = B 258,[1243] objective coexistence is distinguished from objective sequence by reversibility of the perceptions 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.

“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 communion 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 perception 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 preceding representations, and without standing to them in any relation of time.”[1244]