presented by the mistakes of the dogmatists of both parties has been completely set aside.
The thesis might also have been unfairly demonstrated, by the introduction of an erroneous conception of the infinity of a given quantity. A quantity is infinite, if a greater than itself cannot possibly exist. The quantity is measured by the number of given units- which are taken as a standard—contained in it. Now no number can be the greatest, because one or more units can always be added. It follows that an infinite given quantity, consequently an infinite world (both as regards time and extension) is impossible. It is, therefore, limited in both respects. In this manner I might have conducted my proof; but the conception given in it does not agree with the true conception of an infinite whole. In this there is no representation of its quantity, it is not said how large it is; consequently its conception is not the conception of a maximum. We cogitate in it merely its relation to an arbitrarily assumed unit, in relation to which it is greater than any number. Now, just as the unit which is taken is greater or smaller, the infinite will be greater or smaller; but the infinity, which consists merely in the relation to this given unit, must remain always the same, although the absolute quantity of the whole is not thereby cognized.
The true (transcendental) conception of infinity is: that the successive synthesis of unity in the measurement of a given quantum can never be completed.[1] Hence it follows, without possibility of mistake, that an eternity of actual successive states up to a given (the present) moment cannot have elapsed, and that the world must therefore have a beginning.
In regard to the second part of the thesis, the difficulty as to an infinite and yet elapsed series disappears; for the manifold of a world infinite in extension is contemporaneously given. But, in order to cogitate the total of this manifold, as we cannot have the aid of limits constituting by themselves this total in intuition, we are obliged to give some account of our conception, which in this case cannot proceed from the whole to the determined quantity of the parts, but must demonstrate the possibility of a whole by means of a successive synthesis of the parts. But as this synthesis must constitute a series that cannot be completed, it is impossible for us to cogitate prior to it, and consequently not by means of it, a totality. For the conception of totality itself is in the present case the representation of a completed synthesis of the parts; and this completion, and consequently its conception, is impossible.
ON THE ANTITHESIS.
The proof in favour of the infinity of the cosmical succession and the cosmical content is based upon the consideration that, in the opposite case, a void time and a void space must constitute the limits of the world. Now I am not unaware, that there are some ways of escaping this conclusion. It may, for example, be alleged, that a limit to the world, as regards both space and time, is quite possible, without at the same time holding the existence of an absolute time before the beginning of the world, or an absolute space extending beyond the actual world—which is impossible. I am quite well satisfied with the latter part of this opinion of the philosophers of the Leibnitzian school. Space is merely the form of external intuition, but not a real object which can itself be externally intuited; it is not a correlate of phenomena, it is the form of phenomena itself. Space, therefore, cannot be regarded as absolutely and in itself something determinative of the existence of things, because it is not itself an object, but only the form of possible objects. Consequently, things, as phenomena, determine space; that is to say, they render it possible that, of all the possible predicates of space (size and relation), certain may belong to reality. But we cannot affirm the converse, that space, as something self-subsistent, can determine real things in regard to size or shape, for it is in itself not a real thing. Space (filled or void)<ref>It is evident that what is meant here is, that empty space, in so far as it is
- ↑ The quantum in this sense contains a congeries of given units, which is greater than any number—and this is the mathematical conception of the infinite.
