Page:The World and the Individual, First Series (1899).djvu/602

Rh come first, b second, etc., is determined by the definition, all at once. The definition of the Kette does not, however, like your acts in counting, first determine ɑ and afterwards b. In the truly valid series it is the ɑ and b that are simultaneously first and next. You must not confuse then the eternally valid and simultaneously predetermined aspects of this order with the temporal succession of your verifications of the order.

So far, then, you have taken the series as a valid Order, whose ideal totality lies in the singleness of a plan that it is supposed to express. And now comes the second stage of the process of defining our Kette as real. Here is indeed the decisive step. All the members of the series are at once validly predetermined. That we have seen. Whatever can be precisely defined, however, can be supposed immediately given. So now simply suppose that the members are all seen, experienced, presented, not as they follow one after another, in your successive apperception of a few of them, but precisely as the definition predetermines them, namely, all at once. Hereupon you define the series as a fact, not merely valid, but presented. And so to define it is to define it as actually infinite.

And now I challenge you: “Where is the contradiction in this conception of the presented infinite totality?” Try to point out the precise place of the contradictory element in the system as defined.

You may reply: “The contradiction lies here: That the series has no last term is admitted; yet if all its terms are present, the series must be completely presented. But a completed and ordered series must have a last term. How otherwise should it be completed?”

I rejoin: There is finality and finality, completion and completion. The sort of finality possessed by the series is expressly of one sort, and not of another. By hypothesis the series is not in such wise completely presented that its last term is seen. For it has indeed no last term. But it is, by hypothesis, so presented that all the terms, precisely as the single purpose of the definition demands them, are present. The definition was not self-contradictory in demanding them