they are products of processes in which both space and things are indispensable factors. And as thus partially produced and limited by things, spatial properties have derived from things their characteristic of divisibility. But theorists have erroneously transferred this divisibility to space itself, to which it cannot possibly belong. Thus modern philosophy from its start is infected with a fatal error. For once more I affirm that the divisibility—either infinite or finite-of space is a contradiction in terms.

Section 3. The Discreteness of Space

Some attention must also be given to the puzzle so much exploited by recent disciples of Hegel—the alleged contradiction between the continuity and the discreteness of space. For example, I have just alluded to Adamson's having caught a glimpse of the real proof of space's continuity. But he did not fully realize the significance of this insight. And so he soon asserts a second and contradictory feature in space, its discreteness, "the inexhaustibility, the endless capacity for being divided of a really continuous whole. But it is all a chimera. The two contradictory features do not belong to the same object. The continuity belongs to one infinite and immutable space. The discreteness or divisibility belongs to the countless host of finite, ever-changing spatial relations of things to each other.

"But no one quite equals Bradley in this art of inventing contradictions. First, he proves that space is not a relation. The mere fact that we are driven

always to speak of its parts is sufficient evidence. What could be the parts of a relation?" But as I have shown we are driven to speak of it as not having parts.

Second, he proves that it is nothing but a relation. But how can that which is absolutely one be a relation? These are but samples of the follies that issue from thinking of space as divided into parts. And they are all set aside by the simple question: If space has parts, what then separates the parts?

Section 4. The Reality of Space

(1) Let us consider in course the four celebrated arguments by which Kant is supposed to have annihilated the reality of space. The first is: "Space is not an empirical experience which has been derived from external experience. .1 No experience of

1

the external relations of sensible things could yield the idea of space, because without the consciousness of space there would be no external experience whatever." Now all that is a foolish truism; it says nothing except that without the idea of space I could not have the idea of externality. Again the doctrine that space is an illusion, a mere idea inside of me makes it impossible that things should be outside of me or of each other.

(2) "Space is a necessary a-priori idea which is presupposed in all external perception. By no effort can we think space away, etc." The first proof seemed absurd enough, but this far surpasses it in absurdity. We must believe space to be real, we can1Critique, Pure Reason, Tran. Esthetic, § I.

not think it away; therefore, it must be an illusion!

(3) "Space is not a general conception of the relation of things but a pure perception. . . . It is true that we speak as if there were many spaces, but we really mean only parts of one and the same space." That argument I have exploded by demonstrating in Section 2 that space has no parts, is absolutely continuous.

(4) Kant's final argument is very vague, almost unintelligible. But both its vagueness and its falsity are explained in Section 1. There I have proved that the much mooted distinction between perceptual and conceptual space is really a distinction between space and the spatial relations of things; and that the ignoring of this obvious distinction is the taproot of almost all the errors and paradoxes infesting the spatial problem.

Kant's four proofs of the ideality of space are amazingly feeble and empty. Dissatisfaction with them soon led his successors to take another path; but a retrograde one toward the theories of Berkeley and Malebranche. Kant's doctrine of space as a mental form leaves everything at loose ends; the application of the form does not determine whether a given object shall appear as a cube or some other figure; the choice between the various forms is altogether arbitrary. But plainly we have no such liberty as that; the relations of things in our subjective forms of space are quite independent of our will; try our best we cannot conceive an inch as longer

than a mile or a wagon-wheel as triangular. Hence arose absolute idealism; the determining factor in our spatial experience was not the individual mind, but the divine or absolute mind. But that seems only a sort of burlesque realism. What common sense calls a universe of things, this new view calls God or the Absolute.

There is then nothing self-contradictory in space properly conceived. The alleged contradictions have sprung from ignoring two obvious facts: first, that space has no parts; second, that spatial relationsdistance, direction, figure, etc.—are effects or products of a causal process wherein both real space and real things are factors. Cancel either kind of reality, and you make knowledge and thought impossible.

CHAPTER VI

TIME

Section 1. Temporal Relations

My solution of the space problem, then, rests upon the distinction between space and the spatial relations of things. All thinkers have recognized, more or less vaguely, that distinction. Newton, especially, insisted upon it most strenuously. The common view, he said, wrongly supposes that sensuous time and space are the true ones; they define them according to their relations to common things. But besides these there must be an absolute space and time not determined by their relations to anything external. Instead of absolute and sensuous space— terms having a dogmatic and misleading ring—I have put the simple facts, space and the spatial relations of things. Then by showing that these two terms are to each other as cause to its effects, the antinomies and other perplexities infesting the space problem have been made to vanish.

I have now to show that the problem of time, with its still darker enigmas, can likewise be solved by clear insistence upon the distinction between time and the temporal relations of things.

In order to outline my meaning let me first refer to that famous, oft-quoted passage from one of the world's greatest thinkers, St. Augustine: "What then is time? If no one asks me, I know; if I try to