concept comes to us as positive, and wholly in advance of counting. It involves, first, the general definition of a Kette, of the type here in question, whose properties, taken in their abstraction, are as exactly definable as those of a triangle. Not every such Kette is a Self, or a Gedankenwelt; for of course the general concept of a system possessing some sort of one-to-one correspondence, can be applied in any region, however abstract; and a Kette may therefore be defined where the objects in question are taken to be either dead matter or else mere fiction. Consequently the mathematical world is simply full of Ketten of the present and of other types. But the notable facts are, first, that the present type of Kette becomes the very model of an ordered system, and, secondly, that it becomes this by virtue of the fact that in structure it is precisely parallel to the structure of an ideal Self. Herein the intellect does indeed, of itself, comprehend its own work, even though this work be but an ideal creation.
But all order in the world of space, of time, of quantity, or of morals, however rich its wealth of life, of meaning, or of beauty may be, is order because it presents to us systems of facts that may be viewed as having a first, a second, a third constituent, or some higher form of order; while the rank, dignity, worth, magnitude, proportion, structure, description, explanation, law, or other reasonableness of any of these objects in our world depends, for us, upon our power to recognize in them what, for a given purpose, comes first, what second, and so on, amongst their elements or their higher constituents. The absolutely universal application of the concept of order wherever the intellect recognizes in any sense its own, in heaven or upon earth, shows us the interest of considering even these barest abstractions regarding simple order. The number-series is indeed the absolutely abstract, but also the absolutely universal and inclusive type of all order, — the one thing that every rational being, however much he may differ in constitution from us men, must, in some shape, possess, just in so far as he knows any complete order or system at all, divine or diabolical, moral or physical, æsthetic or social,
