ditioned to the conditions not given contemporaneously and along with it, but discoverable only through the empirical regress. We are not, however, entitled to affirm of a whole of this kind, which is divisible in infinitum, that it consists of an infinite number of parts. For, although all the parts are contained in the intuition of the whole, the whole division is not contained therein. The division is contained only in the progressing decomposition-in the regress itself, which is the condition of the possibility and actuality of the series. Now, as this regress is infinite, all the members (parts) to which it attains must be contained in the given whole as an aggregate. But the complete series of division is not contained therein. For this series, being infinite in succession and always incomplete, cannot represent an infinite number of members, and still less a composition of these members into a whole.

To apply this remark to space. Every limited part of space presented to intuition is a whole, the parts of which are always spaces-to whatever extent subdivided. Every limited space is hence divisible to infinity.

Let us again apply the remark to an external phænomenon 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 hand, that when all composition in matter is annihilated in thought, nothing remains, does not seem to harmonise 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 phænomenal world, which is not a thing in itself cogitated by the pure category. Phænomenal sul stance is not an absolute

subject; it is merely a permanent sensuous image, and nothing nore 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 phænomenon, 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 organised body. It cannot be admitted that every part in an organised whole is itself organised, and that, in analysing it to infinity, we must always meet with organised parts; although we may allow that the parts of the matter which we decompose in infinitum, may be organised. For the infinity of the division of a phænomenon in space rests altogether on the fact that the divisibility of a phanomenon 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 organised 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 organised 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 phænomenon 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-namely, by declaring both contradictory statements to be false. We represented in these antinomies the conditions of phænomena 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.

But we have overlooked, up to this point, an essential difference existing between the conceptions of the understanding which reason endeavours to raise to the rank of ideas-two of these indicating a mathematical, and two a dynamical synthesis of phænomena. Hitherto, it was not necessary to signalize this distinction; for, just as in our general representation of all transcendental ideas, we considered them under phænomenal conditions, so, in the two mathematical ideas, our discussion

is concerned solely with an object in the world of phænomena. But as we are now about to proceed to the consideration of the dynamical conceptions of the understanding, and their adequateness with ideas, we must not lose sight of this distinction. We shall find that it opens up to us an entirely new view of the conflict in which reason is involved. For, while in the first two antinomies, both parties were dismissed, on the ground of having advanced statements based upon false hypotheses; in the present case the hope appears of discovering a hypothesis which may be consistent with the demands of reason, and, the judge completing the statement of the grounds of claim, which both parties had left in an unsatisfactory state, the question may be settled on its own merits, not by dismissing the claimants, but by a comparison of the arguments on both sides.-If we consider merely their extension, and whether they are adequate with ideas, the series of conditions may be regarded as all homogeneous. But the conception of the understanding which lies at the basis of these ideas, contains either a synthesis of the homogeneous, (presupposed in every quantity-in its composition as well as in its division) or of the heterogeneous, which is the case in the dynamical synthesis of cause and effect, as well as of the necessary and the contingent.

Thus it happens, that in the mathematical series of phænomena no other than a sensuous condition is admissible-a condition which is itself a member of the series; while the dynamical series of sensuous conditions admits a heterogeneous condition, which is not a member of the series, but, as purely intelligible, lies out of and beyond it. And thus reason is satisfied, and an unconditioned placed at the head of the series of phænomena, without introducing confusion into or discontinuing it, contrary to the principles of the understanding.

Now, from the fact that the dynamical ideas admit a condition of phænomena which does not form a part of the series of phænomena, arises a result which we should not have expected from an antinomy. In former cases, the result was that both contradictory dialectical statements were declared to be false. In the present case, we find the conditioned in the dynamical series connected with an empirically unconditioned, but non-sensuous condition; and thus satisfaction is done to the understanding on the one hand and to the reason on the

other. While, moreover, the dialectical arguments for unconditioned totality in mere phænomena fall to the ground, both propositions of reason may be shown to be true in their proper signification. This could not happen in the case of the cosmological ideas which demanded a mathematically unconditioned unity; for no condition could be placed at the head of the series of phænomena, except one which was itself a phænomenon, and consequently a member of the series.

III.

Solution of the Cosmological Idea of the Totality of the Deduction of Cosmical Events from their Causes.

There are only two modes of causality cogitable-the causality of nature, or of freedom. The first is the conjunction of a particular state with another preceding it in the world of sense, the former following the latter by virtue of a law. Now, as the causality of phænomena is subject to conditions of time, and the preceding state, if it had always existed, could not have produced an effect which would make its first appearance at a particular time, the causality of a cause must itself be an effect-must itself have begun to be, and therefore, according to the principle of the understanding, itself requires a cause.

We must understand, on the contrary, by the term freedom, in the cosmological sense, a faculty of the spontaneous origination of a state; the causality of which, therefore, is not subordinated to another cause determining it in time. Freedom is in this sense a pure transcendental idea, which, in the first place, contains no empirical element; the object of which, in the second place, cannot be given or determined in any experience, because it is a universal law of the very possibility of experience, that everything which happens must have a cause, that consequently the causality of a cause, being itself something that has happened, must also have a cause. In this view

*For the understanding cannot admit among phænomena a condition which is itself empirically unconditioned. But if it is possible to cogitate an intelligible condition-one which is not a member of the series of phanomena-for a conditioned phænomenon, without breaking the series of empirical conditions, such a condition may be admissible as empirically unconditioned, and the empirical regress continue regular, unceasing, and intact.