[135]. Cf. Mr. H. G. Wells’s tale, The New Accumulator[Accumulator].
[136]. Compare once more the passage already quoted from Lotze, Metaphysic, i. 3. 33.
[137]. See Naturalism and Agnosticism, vol. i. lecture 2, and compare the elaborate proof given by Mach, Science of Mechanics, pp. 9-23, that all the so-called demonstrations of the general theory of the lever are mere reductions of the more complicated to the simplest cases of a relation which ultimately depends for its recognition on nothing more cogent than the evidence of the senses.
[138]. For some comments upon the “mechanical view” in the narrower and more special sense, see Chapter VI. of the present Book. It may be convenient, for the sake of precision, to call this more special form of the mechanical view the “mechanistic” theory of nature.
[139]. Psychology ought probably to be excluded from the sciences for which the mechanical view is fundamental. But Psychology does not deal with any part of the physical order. See the present writers review of Münsterberg’s “Grundzüge der Psychologie” in Mind for April 1902; and cf. infra, Bk. IV. chaps. 1, 2.
[140]. Compare with the argument of this chapter, Royce, “Nature, Consciousness, and Self-consciousness,” in Studies of Good and Evil; and “Mind and Nature,” by the present writer in International Journal of Ethics, October 1902. The inveterate prejudice that “laws of nature,” to be of scientific use, must be rigidly exact uniformities is so strong, that it may be worth while, even after the preceding discussion of general principles, to assist the reader by reminding him of the elementary fact that the most familiar quantities involved in our scientific formulæ (π, e, the vast majority of second and third roots, of logarithms of the natural numbers, of circular functions of angles, etc.) are incapable of exact evaluation. This of itself renders a scientific law, in the form in which it can be applied to the determination of actual occurrences, merely approximate, and thus shows that exact uniformity is unnecessary for the practical objects of the empirical sciences.
CHAPTER IV
SPACE AND TIME
[§ 1.] Are time and space ultimately real or only phenomenal? [§ 2.] The space and time of perception are limited, sensibly continuous, and consist of a quantitative element together with a qualitative character dependent on relation to the here and now of immediate individual feeling. [§ 3.] Conceptual space and time are created from the perceptual data by a combined process of synthesis, analysis, and abstraction. [§ 4.] They are unlimited, infinitely divisible, and there is valid positive ground for regarding them as mathematically continuous. Thus they form infinite continuous series of positions. They involve abstraction from all reference to the here and now of immediate feeling, and are thus homogeneous, i.e. the positions in them are indistinguishable. They are also commonly taken to be unities. [§ 5.] Perceptual space and time cannot be ultimately real, because they involve reference to the here and now of a finite experience; conceptual space and time cannot be ultimately real, because they contain no principle of internal distinction, and are thus not individual. [§ 6.] The attempt to take space and time as real leads to the difficulty about qualities and relations, and so to the indefinite regress. [§ 7.] Space and time contain no principle of unity; there may be many space and time orders in the Absolute which have no spatial or temporal connection with each other. [§ 8.] The antinomies of the infinite divisibility and extent of space and time arise from the indefinite regress involved in the scheme of qualities and relations, and are insoluble so long as the space and time construction is taken for Reality. [§ 9.] The space and time order is an imperfect phenomenal manifestation of the logical relation between the inner purposive lives of finite individuals. Time is an inevitable aspect of finite experience. How space and time are transcended in the Absolute experience we cannot say.
§ 1. The problems which arise for the metaphysician from the fact that the physical order, as it is presented to our senses, consists of elements having position in space and time, are among the oldest and most perplexing of all the riddles suggested by the course of our experience. Adequate discussion of them would demand not only far more space than we are at liberty to bestow on the topic, but such a familiarity with the mathematical theory of order and series as is scarcely possible to any one but an original mathematician. All that we can do in the present chapter is to deal very superficially with one or two of the leading problems, more with a view to indicating the nature of the questions which Metaphysics has to face, than of providing definite answers to them.