The infinite of philosophy, corrupted though it is with much undigested and misunderstood mathematics, contains a motive of its own. It is that which lacks external relation, not merely in so far as it is of a spatial, temporal or numerical character, but in any manner at all.
The idea of the infinite is as old as the Ionian philosophy, when Anaximander (610 ex.) declared that the one in the many, the basis of being in Nature, was to ireipov, the infinite. The reality of infinitude has been the source of much controversy, and the tendency of many modern philosophers is to deny it, for there is unquestionably a difficulty in the entrance of the unrelated into the cognitive relation. The discursive nature of knowledge makes us bring every object into a context. This difficulty of finding a context for the in finite is the basis of those antinomies of Kant (q.v.) which concern it. °An infinite number,* says Bosanquet, be a number which is no particular number, for every particular num ber is finite. It follows from this that infinite number is unreal .° On the other hand F. H. Bradley states the contrary, in the clearest terms, •We may be asked whether Nature is finite, or infinite. . . . if Nature is infinite, we have the absurdity of a something which exists; and still does not exist. For actual existence is, obviously, all finite. But, on the other band, if Nature is finite, then Nature must have an end, and this again is impossible. For a limit of extension must be relative to an ex Ivi tension . ljeyond. And to fall back on empty space I not help us at all. For this (itself a mere a surdity) repeats the dilemma in an ag gravated form. But we cannot escape the con clusion that Nature is infinite. And this will be true not of our physical system alone, but of every other extended world that can possibly exist. . . . Every physical world is, essentially and necessarily, infinite.* It seems as if had a dearer and more logical view of infinity, To alreiPov than many moderns such as Bosanquet. He says, Xebreras *iv dvvapte eivat to arttpov. He means of course, that, with regard to finite human in telligence, the infinite remains unrealized, al though logically it could be realized, and of course, when we speak of infinite time, or in finite creative change in nature, we speak of something which potentially exists. but is only
gradually becoming actual. In other words, we can transcend whatever relations we choose, so long as we do not transcend Relation.
Professor Royce of Harvard has undertaken the task of vindicating the concept of the actual Infinite against the charge of self-contradiction. He is controverting Mr. F. H. Bradley of Ox ford, who while he admits lwe cannot escape the conclusion that Nature is infinite,* expresses also his belief that such an assertion is a con tradiction in terms. Professor Royce attempts to accomplish this vindication by proving the following theses: 1. The true Infinite, both in multitude and in organization, although in one sense endless, and so incapable in that sense of being com pletely grasped, is in another, and precise sense, something perfectly determitate. Nor is it a mere monotonous repetition of the same, over and over. Each of its determinations has indi viduality, uniqueness and novelty about its own nature.
2. This determinateness is a character which, indeed, includes and involves the endlessness of an infinite series; but the mere endlessness of the series is not its primary character, but simply a negatively stated result of the self representative character of the whole system.
3. The endlessness of the series means that by no merely successive process of counting, in God or in man, is its wholeness ever ex hausted.
4. In consequence, the whole endless series, in so far as it is a reality, must be present, as a determinate order, but also all at once, to the absolute experience. It is the process of suc cessive counting, as such, that remains, to the end, incomplete, so as to imply that its own pos sibilities are not yet realized. Hence, the re current processes of thought reveal eternal truth about the infinite constitution of real Be ing— their everlastingly pursued Other; but themselves,— as mereprocesses in time — they are not that Other. The true Other is, there fore, that self-representative system of which they are at once portions, imitations and ex pressions.