Elements of metaphysics

by A. E. Taylor

[103]. On the category of Ground and Consequent and the principle of Sufficient Reason, consult Bosanquet, Logic, bk. i. chap. 6, and bk. ii. chap. 7.

[104]. It is no answer to this suggestion to urge that the present, being real, cannot be conditioned by the future, which is unreal. Such a rejoinder commits the metaphysical petitio principii of taking for granted that only the present is real. It is obvious that one might say with equal cogency that the past, being over and gone, is now unreal and therefore cannot influence the real present.

[105]. For a fuller explanation of what is meant by continuity, consult Dedekind, Stetigkeit und irrationale Zahlen, specially §§ 3-5, or Lamb’s Infinitesimal Calculus, chap. 1. Readers who have been accustomed to the treatment of continuity by the older philosophical writers should specially remark (1) that continuity is properly a characteristic of series, and (2) that though continuity implies indefinite divisibility, the reverse is not, as was sometimes assumed by earlier writers, true. The series of rational numbers is a familiar illustration of endless divisibility without continuity.

[106]. There would arise further difficulties as to whether the magnitude of this lapse is a function of A, or whether it is the same in all cases of causal sequence. But until some one can be found to defend such a general theory of causal sequence it is premature to discuss difficulties of detail.

[107]. For the English reader the best sources of information as to the “descriptive” theory of science are probably volume i. of Professor Ward’s Naturalism and Agnosticism; and Mach, the Science of Mechanics (Eng. trans.). Students who read Gennan may advantageously add Avenarius, Philosophie als Denken der Welt gemäss dem Princip des kleinsten Kraftmasses. Professor J. A. Stewart is surely mistaken (Mind, July 1902) in treating the doctrine as a discovery of “idealist” metaphysicians. Whatever may be thought of some of the uses to which “idealists” put the theory, they cannot claim the credit of its invention.

[108]. Cf. Mach, op. cit., p. 483 ff.; Pearson, Grammar of Science, chap. 4.

[109]. E.g., eclipses can be calculated equally well for the future or the past.

[110]. Infra, Bk. III. chap. 4. It will be enough to refer in passing to the curious blunder which is committed when the principle of Causality is confounded with the doctrines of the Conservation of Mass and Energy. That the principle of Causality has nothing to do with these special physical theories is manifest from the considerations: (1) That it is at least not self-evident that all causal relation is physical. Philosophers have indeed denied that one mental state directly causes another, but no one has based his denial on the assertion that there can be no causality without mass and energy. (2) The principle of Causality, as we have seen, is a postulate. If we are ever to intervene successfully in the course of events, it must be possible with at least approximate accuracy to regard events as determined by their antecedents. The doctrines of conservation of mass and energy are, on the contrary, empirical generalisations from the observed behaviour of material systems. Neither science nor practical life in the least requires them as an indispensable condition of success. In practical life they are never appealed to, and the ablest exponents of science are most ready to admit that we have no proof of their validity except so far as it can be established by actual observation. In short, they are largely a posteriori, while the principle of Causality is, as already explained, a priori. See infra, Bk. III. chap. 6, § 6.

[111]. Neither can have a first term, because each has two opposite senses, positive and negative in the one case, before and after in the other.

[112]. I suppose I need not remind my reader that when a number is spoken of as the actual sum of an infinite series (as when 2 is called the sum of the series 1 + 1/2 + 1/4 + 1/8 + ... to infinity), the word sum is used in a derivative and improper sense for the limiting value assumed by the sum of n terms as n increases indefinitely[indefinitely]. See Lamb, Infinitesimal Calculus, p. 11.