Immanuel Kant's Critique of Pure Reason — trans. F. Max Müller

Antithesis exists nowhere in the world anything simple, is not intended to mean more than that the existence [p. 437] of the absolutely simple cannot be proved from any experience or perception, whether external or internal, and that the absolutely simple is a mere idea, the objective reality of which can never be shown in any possible experience, so that in the explanation of phenomena it is without any application or object. For, if we assumed that an object of this transcendental idea might be found in experience, the empirical intuition of some one object would have to be such as to contain absolutely nothing manifold by the side of each other, and combined to a unity. But as, from our not being conscious of such a manifold, we cannot form any valid conclusion as to the entire impossibility of it in any objective intuition, and as without this no absolute simplicity can be established, it follows that such simplicity cannot be inferred from any perception whatsoever. As, therefore, an absolutely simple object can never be given in any possible experience, while the world of sense must be looked upon as the sum total of all possible experience, it follows that nothing simple exists in it.

•This second part of the antithesis goes far beyond the first, which only banished the simple from the intuition of the composite, while the second drives it out of the whole of nature. Hence we could not attempt to prove it out of the concept of any given object of external intuition (of the compound), but from its relation to a possible experience in general.

35^ Transcendental Dialectic

Thesis

[p. 438] OBSERVATIONS ON THE

On the Thesis

If I speak of a whole as necessarily consisting of separate parts, I understand by it a substantial whole only, as a real compound, that is, that contingent unity of the manifold, which, given as separate (at least in thought), is brought into a mutual connection, and thus constitutes one whole. We ought not to call space a compositum, but a totum, because in it its parts are possible only in the whole, and not the whole by its parts. It might therefore be called a composittcm ideale^ but not reale. But this is an unnecessary distinction. As space is no compound of substances, not even of real accidents, nothing remains of it, if I remove all composition in it, not even the point, for a point is possible only as the limit of a space, and therefore of a compound. Space and time do not [p. 440] therefore consist of simple parts. What belongs only to the condition of a substance, even though it possesses quantity (as, for instance, change), does not consist of the simple ; that is to say, a certain degree of change does not arise through the accumulation of many simple changes. We can infer the simple from the compound in self-subsisting objects only. Accidents of a state, however, are not self-subsisting. The proof of the necessity of the simple, as the component parts of all that is substantially composite, can therefore easily be injured, if it is extended

Transcendental Dialectic 357

Antithesis

SECOND ANTINOMY [p. 439]

II

On the Antithesis

Against the theory of the infinite divisibility of matter, the proof of which is mathematical only, objections have been raised by the Monadists, which become suspicious by their declining to admit the clearest mathematical proofs as founded on a true insight into the quality of space, so far as space is indeed the formal condition of the possibility of all matter, but treating them only as conclusions derived from abstract but arbitrary concepts, which ought not to be applied to real things. But how is it possible to conceive a different kind of intuition from that given in the original intuition of space, and how can its determinations a priori not apply to everything, since it becomes possible only by its filling that space ? If we were to listen to them, we should have to admit, beside the mathematical point, which is simple, but no part, but only the limit of a space, other physical points, simple likewise, but possessing this privilege that, as parts of space, they are able, by mere aggregation, to fill space. Without repeating here the many clear refutations of this absurdity, it being quite futile to attempt to reason away by purely discursive concepts the evidence of mathematics, I only remark, that if philosophy in this case seems to play tricks with mathematics, it does so because it [p. 441] forgets that in this discussion we are concerned with phe358 Transcendental Dialectic

Thesis too far, and applied to all compounds without distinction, as has often been the case.