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

We do not prescribe by this a definite empirical regressus advancing without end in a certain class of phenomena ; as, for instance, that from a living person one ought always to ascend in a series of ancestors, without ever expecting a first pair ; or, in the series of cosmical bodies, without admitting in the end an extremest sun. All that is demanded is a progressus from phenomena to phenomena, even if they should not furnish us with a real perception (if it is too weak in degree to become experience in our consciousness), because even thus they belong to a possible experience.

Every beginning is in time, and every limit of extension in space. Space and time, however, exist in the world of sense only. Hence phenomena only are limited in the world conditionally ; the zvorld itself, however, is limited neither conditionally nor unconditionally.

For the same reason, and because the world can never be given complete, and even the series of conditions of something given as conditioned cannot, as a cosmical series, be given as complete, the concept of the quantity of the world can be given through the regressus only, and not before it in any collective intuition, [p. 523] That regressus, however, consists only in the determining of the quantity, and does not give, therefore, any definite concept, nor the concept of any quantity which,

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with regard to a certain measure, could be called infinite. It does not therefore proceed to the infinite (as if given), but only into an indefinite distance, in order to give a quantity (of experience) which has first to be realised by that very regressus.

II

Solution of the Cosmological Idea of the Totality of the Division of a Whole given in Inttiition

If I divide a whole, given in intuition, I proceed from the conditioned to the conditions of its possibility. The division of the parts (subdivisio or decompositio) is a regressus in the series of those conditions. The absolute totality of this series could only be given, if the regressus could reach the simple parts. But if all parts in a continuously progressing decomposition are always divisible again, then the division, that is, the regressus from the conditioned to its conditions, goes on in infinitiifn ; because the conditions (the parts) are contained in the conditioned itself, and as that is given as complete in an [p. 524] intuition enclosed within limits, are all given with it. The regressus must therefore not be called a regressus in indefinitnm, such as was alone allowed by the former cosmological idea, where from the conditioned we had to proceed to conditions outside it, and therefore not given at the same time through it, but first to be added in the empirical regressus. It is not allowed, however, even in the case of a whole that is divisible in infinittcm, to say, that it consists of infinitely many parts. For although all parts are contained in the intuition of the whole, yet the whole division is not contained in it, because it consists

426 Transcendental Dialectic in the continuous decomposition, or in the regressus itself, which first makes that series real. As this regressus is infinite, all members (parts) at which it arrives are contained, no doubt, in the given whole as aggregates ; but not so the whole series of the division, which is successively infinite and never complete, and cannot, therefore, represent an infinite number, or any comprehension of it as a whole.

It is easy to apply this remark to space. Every space, perceived within its limits, is such a whole the parts of which, in spite of all decomposition, are always spaces again, and therefore divisible in infinitum, [p. 525]

From this follows, quite naturally, the second application to an external phenomenon, enclosed within its limits (body). The divisibility of this is founded on the divisibility of space, which constitutes the possibility of the body, as an extended whole. This is therefore divisible in infinitum, without consisting, however, of an infinite number of parts.

It might seem indeed, as a body must be represented as a substance in space, that, with regard to the law of the divisibility of space, it might differ from it, for we might possibly concede, that in the latter case decomposition could never do away with all composition, because in that case all space, which besides has nothing independent of its own, would cease to be (which is impossible), while, even if all composition of matter should be done away with in thought, it would not seem compatible with the concept of a substance that nothing should remain of it, because substance is meant to be the subject of all composition, and ought to remain in its

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