respondent systems of the type here in question are mere Appearance, they are, at all events, Appearance worthy of study. A list of a few conceptions that are more or less obviously of the present type may make us pause before we lightly reject, as absurd, the offered definition.
First, then, the series of whole Numbers, as conceived objects, forms such a self-representative system. The same is true of all the secondary number-systems of higher arithmetic (the negative numbers, the rational numbers, the irrational numbers, the totality of the real numbers, the complex numbers) . And all continuous and discrete mathematical systems of any infinite type are similarly self-representative. But the mathematical objects are by no means the most philosophically interesting of the instances of our concept. For, next, we have the Self, the concept so elaborately studied by Mr. Bradley, and condemned by him as Appearance. And, indeed, if the Self is anything final at all, it is certainly in its complete expression (although of course not in our own psychological life from instant to instant) a self-representative system; and its metaphysical fate stands or falls with the possibility of such systems. Dedekind’s really very profound use of meine Gedankenwelt as his typical instance of the infinite, also suggests the interesting relation between the concept of the Self and that of the mere mathematical form called the number-series, a relation to which we shall soon return. Thirdly, the totality of Being, if conceived as in any way defined or characterized, or even as in any way even definable or characterizable, constitutes, in the present sense, a self-representative system. Obvious it is that our own Fourth Conception of Being defines the Absolute as a self-representative system. And, furthermore, despite his horror of the infinite, and despite his rejection of the Self as a final category, Mr. Bradley himself perforce has to describe his own Absolute as a self-representative system of our type, as we soon shall see. And if he attempted to view it otherwise, it would not be the Absolute or anything real at all. In brief, every system of which anybody can rationally assert anything is either a self-repre-
