Let us again apply the remark to an external phenomenon enclosed in limits, that is, a body.The divisibility of a body rests upon the divisibility of space, which is the condition of the possibility of the body as an extended whole.A body is consequently divisible to infinity, though it does not, for that reason, consist of an infinite number of parts.
It certainly seems that, as a body must be cogitated as substance in space, the law of divisibility would not be applicable to it as substance.For we may and ought to grant, in the case of space, that division or decomposition, to any extent, never can utterly annihilate composition (that is to say, the smallest part of space must still consist of spaces); otherwise space would entirely cease to exist-which is impossible.But, the assertion on the other band that when all composition in matter is annihilated in thought, nothing remains, does not seem to harmonize with the conception of substance, which must be properly the subject of all composition and must remain, even after the conjunction of its attributes in space-which constituted a body- is annihilated in thought.But this is not the case with substance in the phenomenal world, which is not a thing in itself cogitated by the pure category.Phenomenal substance is not an absolute subject; it is merely a permanent sensuous image, and nothing more than an intuition, in which the unconditioned is not to be found.
But, although this rule of progress to infinity is legitimate and applicable to the subdivision of a phenomenon, as a mere occupation or filling of space, it is not applicable to a whole consisting of a number of distinct parts and constituting a quantum discretum- that is to say, an organized body.It cannot be admitted that every part in an organized whole is itself organized, and that, in analysing it to infinity, we must always meet with organized parts; although we may allow that the parts of the matter which we decompose in infinitum, may be organized.For the infinity of the division of a phenomenon in space rests altogether on the fact that the divisibility of a phenomenon is given only in and through this infinity, that is, an undetermined number of parts is given, while the parts themselves are given and determined only in and through the subdivision; in a word, the infinity of the division necessarily presupposes that the whole is not already divided in se.Hence our division determines a number of parts in the whole- a number which extends just as far as the actual regress in the division; while, on the other hand, the very notion of a body organized to infinity represents the whole as already and in itself divided.We expect, therefore, to find in it a determinate, but at the same time, infinite, number of parts- which is self-contradictory.For we should thus have a whole containing a series of members which could not be completed in any regress- which is infinite, and at the same time complete in an organized composite.Infinite divisibility is applicable only to a quantum continuum, and is based entirely on the infinite divisibility of space, But in a quantum discretum the multitude of parts or units is always determined, and hence always equal to some number.To what extent a body may be organized, experience alone can inform us; and although, so far as our experience of this or that body has extended, we may not have discovered any inorganic part, such parts must exist in possible experience.But how far the transcendental division of a phenomenon must extend, we cannot know from experience- it is a question which experience cannot answer; it is answered only by the principle of reason which forbids us to consider the empirical regress, in the analysis of extended body, as ever absolutely complete.
Concluding Remark on the Solution of the Transcendental Mathematical Ideas- and Introductory to the Solution of the Dynamical Ideas.
We presented the antinomy of pure reason in a tabular form, and we endeavoured to show the ground of this self-contradiction on the part of reason, and the only means of bringing it to a conclusion-znamely, by declaring both contradictory statements to be false.We represented in these antinomies the conditions of phenomena as belonging to the conditioned according to relations of space and time-which is the usual supposition of the common understanding.In this respect, all dialectical representations of totality, in the series of conditions to a given conditioned, were perfectly homogeneous.The condition was always a member of the series along with the conditioned, and thus the homogeneity of the whole series was assured.
In this case the regress could never be cogitated as complete; or, if this was the case, a member really conditioned was falsely regarded as a primal member, consequently as unconditioned.In such an antinomy, therefore, we did not consider the object, that is, the conditioned, but the series of conditions belonging to the object, and the magnitude of that series.And thus arose the difficulty- a difficulty not to be settled by any decision regarding the claims of the two parties, but simply by cutting the knot- by declaring the series proposed by reason to be either too long or too short for the understanding, which could in neither case make its conceptions adequate with the ideas.
