complete the series will fail. In this sense, therefore, the series indeed has no “totality,” because it needs none. In this sense, finally, it would indeed be contradictory to speak of it as a totality. And all this is admitted, and need not be further illustrated.
(2) The sense in which the series is a totality is, however, if the series is real, not at all the sense in which it merely has no last member. The series is not to be exhausted in the sense in which it is indeed inexhaustible. But you may and must take it otherwise. The sense in which it is a totality expressly depends upon that concept of totum simul which I have everywhere in this discussion emphasized. To grasp this aspect of the case, you must view it in two stages. Take the series then first as a purely conceptual entity, as a mere idea, or “bare possibility.” The one purpose of the perfect internal self-representation of any system of elements in the fashion, and according to the type of self-representation, here in question, defines, for any Kette formed upon the basis of that purpose, all of the ideal objects that are to belong to the Kette. And this purpose defines them all at once, as we saw in dealing with f1 (n), and the rest of those series that are involved in any Kette. Now this endless wealth of detail is defined at one stroke, so that it is henceforth eternally predetermined, as a valid truth, precisely what does and what does not belong to that Kette. And the various series and this Kette are here one and the same thing. To find whether this or that element belongs to the Kette, may or may not involve, for you, a long time. It will involve for you succession, processes of counting, and much more of the sort indefinitely. This, however, is due to your fortune as a human observer. But the definition of the series has predetermined at one stroke all the results that you thus, taking them in succession, can never exhaust, and has predetermined these results as a fixed Order, wherein every element has its precise place, next after a previous element, next before a subsequent one. As for the before and after, in this Order, they, too, are ideally predetermined, not as themselves successions, but as valid and simultaneous relations. That ɑ
