1

"that. we come nearest to experiencing the real as it really is." Since the space-time world is essentially relational, and affords the most perfect instance of the concept of whole and part, it is thus discredited, without entering into the further difficulties added by space and time themselves. Since, however, the critique of relations does not apply exclusively to science, but applies equally to all knowledge employing the analytical method, one need not undertake the examination of it here. Suffice it to say that Bradley's view has been repeatedly refuted, not only by "outsiders," but by fellow-idealists who are in thorough accord with his general philosophical position.2

A characteristic contemporary revival of the Kantian proof of the unreality of space and time is to be found in A. E. Taylor's Elements of Metaphysics, from which I have already quoted. The supposition of the reality of space and time places us in the following dilemma. "We must either arbitrarily refuse to continue the indefinite regress beyond the point at which its difficulties become apparent, as is done by the assertion that space and time have finite bounds or indivisible parts, or we must hold that the absolute experience actually achieves the summation of an unending series." But "with the recognition that space and time are phenomenal, . . . the difficulty disappears.' For we may now say "that space and time, being constructions of our own, are really neither finite nor infinite series, but are the one or the other according to the purposes for which we use our construction." In other words, of space and time per se, we can say neither that they have, or have not, boundaries and indivisible parts. They may be regarded in the one way or in the other, according to the exigencies of thought. In themselves they are ambiguous. And we relieve ourselves of further responsibility in the matter

1 Elements of Metaphysics, pp. 147, 153; cf. Ch. IV.

Cf. below, pp. 157-158. The best refutation of Bradley is to be found in James's Pluralistic Universe, Appendix A, "The Thing and its Relations," passim. For an idealistic reply to Bradley, cf. J. Royce: The World and the Individual, Vol. I, Supplementary Essay.

by concluding that this ambiguity proves that in "the absolute experience" they must be "taken up, rearranged, and transcended" - although "precisely how this is effected, we, from our finite standpoint, cannot presume to say." 1

§ 10. Now what shall we say of this argument? In the first place, it is notable and significant that the problems Infinity and of infinity and continuity, which underlie the Continuity 'paradoxes' of space and time, are today receiving marked attention from logicians and mathematicians who have no metaphysical predilections. These writers, having no "absolute experience" to which to relegate their difficulties, are compelled to overcome them for themselves. They proceed upon the naïve assumption that since there are such things as infinity and continuity, whatever place they may turn out afterwards to hold in the universe at large, it must be possible to examine and describe them. The conclusions which they have reached may for our present purpose be expressed very simply.2

In the first place, it is held that the alternatives which constitute a dilemma for Kant, Taylor, et al., are not strictly coördinate. For the objection to one is empirical, while the objection to the other is dialectical. Thus, for example, the least unit of spacial extension that can be observed or defined is evidently divisible by two. There is no gainsaying the fact. On the other hand, if one asserts this and concludes that spacial extension is always divisible, his opponent cannot point out that such is not the fact, but only that it contradicts some preconceived notion, such as, a whole is made up of parts, etc. Empirically, then, it seems proper to conclude that since space is in point of fact infinitely divisible, we must, if necessary, amend the 'A. E. Taylor, op. cit., pp. 260, 263. I have discussed this writer's position more fully in Mind, N. S., Vol. XVI, 1908.

For full details, the reader may consult B. Russell's Principles of Mathematics, Ch. XLII, XLIII; or E. V. Huntington's "The Continuum as a Type of Order," in the Annals of Mathematics, Vols. VI, VII (1905).

notions which it contradicts. In other words, non-metaphysical mathematicians and logicians agree that space and time are infinite, and devote themselves on the one hand to the description of the fact, and on the other hand to the removal of the dialectical difficulties that it involves.

Thus it is contended that the notion of a whole as 'made up of parts' involves a confusion between the notion of a whole as containing its parts, and a whole as arrived at by the successive enumeration and synthesis of its parts. The latter notion is subjective and accidental. We may, for example, define a line as an infinite class of points. It is true that a line cannot be 'made up' by adding point to point, but why should it be, since we can define it as a whole? An infinite series cannot be exhausted by the successive enumeration of its terms; but why should it be, when we can define the law of the series? In other words, there is no paradox in knowing an infinite whole, once we rid ourselves of the notion that to know means to take a successive inventory of the content.

Or consider the ancient paradox of motion. It is held that Achilles cannot overtake the tortoise, because he can cut down the tortoise's lead only by an infinite, that is, endless, series of diminishing gaps. But this simply means that the operation of overtaking is a continuous process. If it were necessary for us to understand this process by enumerating every least phase of it, we should never conclude, and would be brought in despair to say that Achilles never can overtake the tortoise. But we need do nothing

1 It may even be necessary to conclude, contrary to the usual notion, that a part may in a certain sense be equal to the whole. Cf. e.g. Royce: The World and the Individual, Vol. I, Supplementary Essay. I am not sure that this is the case; but it might be the case. In other words, the notion of whole and part is subject to correction in the light of any instances of it that may be observed; and an 'infinite' and 'continuous' whole is such an instance.

For an interesting popular discussion of this and similar paradoxes in the light of modern mathematics, cf. James: Some Problems of Philosophy, Chap. X, XI. What follows above is in part a criticism of this author's

of the kind, since we can define the particular series in question, and provide by formula for all of its terms. And if it be objected that Achilles, at least, in traversing the intervening space, must successively pass through all of its least units, we may reply that he has a like infinitely divisible time in which to do it.

This very meagre treatment of the matter will serve, I trust, to suggest the method by which the seeming paradoxes of space and time may be dispelled. Such a method serves not only to throw light on the nature of space and time, and so to save the already over-burdened 'absolute' from the necessity of assuming entire responsibility for them; but it also justifies space and time, and establishes their reality in their own terms. In short, if science be defective or limited, it is not because space and time, its fundamental concepts, are unreal.

11. The most important critique of science is yet to be considered: that critique, namely, which rests on the assertion of the priority of consciousness. Since The Priority of this assertion constitutes the central thesis of idealism, and, as such, will occupy us during the next three chapters, a brief mention of it must suffice here.

Consciousness

In his book on Hume, Huxley writes as follows: "If the materialist affirms that the universe and all its phenomena are resolvable into matter and motion, Berkeley replies, True; but what you call matter and motion are known to us only as forms of consciousness; their being is to be conceived or known; and the existence of a state of consciousness, apart from a thinking mind, is a contradiction in terms. I conceive that this reasoning is irrefragable. And therefore, if I were obliged to choose between absolute materialism and absolute idealism, I should feel compelled to accept the latter alternative." Huxley's acceptance

of this argument is very significant. For in the great controversies of the last century, he has been one of the most 1T. H. Huxley: Hume, p. 279.

distinguished protagonists of science. Despite his scientific affiliations and habits of mind, he was prevented from being an idealist only because he was an agnostic. The "reasoning" which constitutes the chief support of idealism he regarded as "irrefragable"-in common with the majority of the philosophers of his own and the present generation.

Science, it is argued, abstracts things from their relation to knowledge. Concretely, everything is 'object' for a subject; something perceived, thought, or willed. This is supposed to become apparent at the moment when one becomes reflective or self-conscious-at the moment when one recognizes the central place of that 'I' which is naïvely overlooked, or, in the case of science, deliberately omitted. The real nature of things is grasped only when things are taken in this context. Viewed in this light, the world of science loses its self-sufficiency. It is, to be sure, internally systematic and consistent. But we are now to recognize that it is literally the world of science; formed to suit the purpose of scientific thought, and expressing, in the last analysis, the capacities and motives of knowledge. So it is to knowledge itself—to sense, thought, or purpose, that one must look for the root and stem of reality.

The critical examination of idealism must be reserved until we shall have become more fully acquainted with its grounds. But it is important to point out the essential agreement between idealism and the motive or standpoint of religion. We have already seen that while science, on the one hand, seeks to eliminate the personal equation, and to banish from mind the hopes and fears that are at stake, religion, on the other hand, makes the application and draws the moral. Religion, in other words, is essentially a judgment of the bearing of reality on life. Now idealism asserts that reality is grounded in life, and ultimately controlled in its interests. Idealism not only construes things

1 See above, pp. 28-29.