iterative meaning clear quite apart from any theory as to whether time and succession are appearance or reality.
Now the system N is, by definition, simply that system of thoughts which, if present at once, would express a complete self-consciousness as to the act of thinking that To-day is Tuesday. Were I just now not only to think this thought, but to think all that is directly implied in the mere fact that I think this thought, I should have present to me, at once, the whole system N as an ordered system of thoughts. Precisely so, the whole determined Gedankenwelt, if present at once, would be a Self, completely reflective regarding the fact that all of these thoughts were its own thoughts. But this complete reflection would, in all its portions, involve an ordered system of thoughts, whose purely abstract form, taken merely as an order, is everywhere precisely that of the number-system.
Self-representation, then, in the sense now so fully exemplified, is not merely, as it were, the property or accident of the number-system; but is, logically speaking, its genetic principle. When order is not a mere “external conjunction,” when we know not merely that facts seem in order, but what the order is, and how it is one order through all of its manifold expressions, we do so by virtue of comprehending the internal meaning of a plan whereby a system of conceived objects comes to be represented through a portion of itself. Dedekind has shown that this view is adequate to the logical development of the various properties of the number-system. What we here observe is that the consequent constitution of the number-system is explicitly defined as, of course in the barest and most abstract outline, the form of a completed Self. Here, then, the Intellect, “of its own movement,” “itself by itself,” defines what, in our temporal experience, whether sensuous or thoughtful, it of course nowhere finds given, namely, a self-representative system of objects, parallel in structure to what the structure of a Gedankenwelt would be if it were the Welt of a completely self-conscious Thought, none of whose acts failed to be its own intellectual objects. This
