fundamental metaphysical conception. For it is a self-experiencing and, therefore, self-representative system.
I conclude, then, so far, that by no device can we avoid conceiving the realm of Being as infinite in precisely the positive sense, now so fully illustrated. The Universe, as Subject-Object, contains a complete and perfect image, or view of itself. Hence it is, in structure, at once One, as a single system, and also an endless Kette. Its form is that of a Self. To observe this fact is simply to reflect upon the most elementary and fundamental implications of the concept of Being. The Logic of Being has, as a central theorem, the assertion, Whatever is, is apart of a self-imaged system, of the type herein discussed. This truth is common property for all, whether realists or idealists, whether sceptics or dogmatists. And hence our trivial illustration of the ideally perfect map of England within England, turns out to be, after all, a type and image of the universal constitution of things. I am obliged to regard this result as of the greatest weight for any metaphysical enterprise.[1] No philosophy that wholly ignores this ele-
- ↑ I was years ago much struck by the remarkable proof, in the first volume of Schroeder’s Algebra der Logik, of the purely formal proposition that no simply constituted Universe of Discourse could be defined, in terms of the Algebra of Logic, as the absolute whole of Being, without an immediately stateable self-contradiction, resulting from the mere definition of the symbols used in that Algebra. See Schroeder, Vol. I, p. 245. The metaphysical interest of this purely symbolic result is not mentioned by Schroeder himself. The proof given by him turns, however, upon showing that if you regard provisionally, as the “whole of the universe,” or as “all that is,” any simply defined universe of classes of objects, you are confronted by contradictions as soon as you reflect that the “totality of what is” also contains a realm of secondary objects that you may define by reflecting upon the classes contained in the first universe, and by classifying these classes themselves from new points of view. This realm of secondary objects, however, does not consistently belong to the primary universe that in a purely formal way you first defined. The true totality of Being can therefore only be defined by an endless process, or is an endless reflective system. This proof of Schroeder’s first brought home to me the fact that the necessity for defining reality in self-reflecting or endless terms is not dependent upon any one metaphysical interpretation of the world, whether realistic or idealistic, but is the consequence of a purely abstract account of the formal Logic of the concept of Reality in any of its forms.
