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He will find sensations of bodily tensions, feelings of expectancy, etc., but no 'power." In other words, he will find what empirical analysis finds everywhere, a manifold of terms in relation. And when one proceeds to explain such a manifold, one will be led, as science in its field has been led, to the discovery of descriptive laws.

I conclude, in other words, that in adopting the descriptive method, science has exchanged a naïve and hasty notion of cause for a refined and rigorous notion. In the sense of the term that is most intelligible, the cause is the law, or its implication. Not necessarily the mechanical law; for analysis and description is, as we have seen, by no means limited to the type exhibited in physical science. But a logical cause, a mathematical cause, an ethical cause, will, I believe, turn out, in each case, to be a law or constant. And if this is so, science is to be credited with the descriptive method, and not debited.

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§ 9. The critique of science which has just been examined might be termed a 'methodological' critique, as distinguished from the 'metaphysical' critique to The Unreality which we must now turn. According to this critique, science has to do with 'appearance' or Kantian Argu- 'phenomenon' rather than 'reality,' because of the nature of its basal concepts, space and time. These concepts, it is argued, are inherently contradictory or lacking in self-sufficiency; and physical nature, as the realm of space and time, must be supposed to be in the end resolved into something else. They must be corrected, or 'overcome,' in some higher unity, as evil is held to be transmuted into good in the providence of God.

The classic prototype of this critique is to be found in Kant. According to that writer, space and time are

1 See below, pp. 261-264. Cf. Hume: Enquiry Concerning the Human Understanding, Selby-Bigge's edition, pp. 60-73.

For a discussion of the application to ethics see below, pp. 116-117. 'Bergson's critique of time is a blend of the methodological and metaphysical critiques; it is examined below, pp. 230, 234-235, 255-261. For Kant, cf. Critique of Pure Reason, Max Müller's translation, second edition, pp. 328 sq.

vitiated by "antinomies." This means that on the supposition of the reality of space and time, it is possible to prove, with equal certainty, several contradictory pairs of theses and counter-theses; such as that space has boundaries and has not, time has a beginning and has not, space and time have indivisible elements and have not, etc. The moral, according to Kant, is that we must reject the original supposition, and deny the reality of space and time. If we regard them merely as acts of synthesis, they become indeterminate; or rather they derive their determination from something else, such as the subject-matter to be synthesized, or the motive actuating the operation of synthesis. It is like saying that number is not independently real, but is only the operation of counting. The question as to how many numbers there are will then have no meaning. There will be as many numbers as the material counted requires, or as any one has occasion to enumerate. Similarly, space and time are held to conform to the subject-matter to which they are applied, or to the motive governing their employment. And it is in terms of these non-spacial and non-temporal factors, in terms of something 'higher' than nature or outside of it, that the world assumes its final shape.

In more recent times the supposed paradoxes of space and time have been traced back to a more fundamental paradox involved in 'term' and 'relation.' It is argued that if two terms are to be related, they must each be related to the relation, and since these interpolated relations must again be related, we are launched upon an infinite regress. Thus the English idealist, F. H. Bradley, is brought to the conclusion "that a relational of thought any one that moves by the machinery way of terms and relations must give appearance, and not truth." Or, as his disciple, A. E. Taylor, puts it, it is in some "supra-relational" mode of experience, in which even the concept of whole and part has been transcended,

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1 Appearance and Reality, first edition, p. 33; cf. Ch. III, passim.

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"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 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

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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.

2 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

1A. 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.

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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. 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

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