Page:Mind (New Series) Volume 12.djvu/211

 BECENT WORK ON THE PHILOSOPHY OF LEIBNIZ. 197 principle is false, and the positions of the said particle might be taken as independent variable instead of the moments of time. Leibniz's doctrine of space and time is said and I think rightly to be astonishingly like Kant's : space and time are not real, nor relations of self-subsistent reals, nor abstract conceptions in the sense of being derived from sense-data ; they are creations of the mind, belonging to the system of pure principles of knowledge, by which the possibility of objects as phenomena is secured (p. 263). 1 Space and time are orders of phenomena, not of sub- stances ; their ideality was first inferred from the difficulties of the continuum. When monads are said to have position, this is only to be understood figuratively : the spatial order of phe- nomena is not the image of a non-spatial order of substances ; we might regard the monad as the expression of spatial order, but not spatial order as reflecting the order of monads. Time and space, as against Descartes, are co-ordinated by Leibniz. There is nothing constant in things but the law of the series, and the time order, as with Kant, is deduced from causality, not vice versa. The next chapter (chap, vii.), on the conception of force, utilises the doctrines as to the differential which one would have supposed the rejection of the infinitesimal would have rendered unavailable. The first postulate, it says, by which the real is defined, is determinateness of content in the moment; but this content has being only as a term in the series, not in isolation. Thus the momentary content must be conceptually fixed by a law involving past and future. This is effected by force, which, we are assured, is for Leibniz synonymous with reality (p. 288). Force is a special form of differential : it is what is real in motion, i.e., the present state as pre-involving the future. The new mathematical method, we are told and Leibniz does seem to have held this view enables us to retain the Eleatic postulates as to the rational conditions of being, without excluding plurality and change (p. 292). This claim can be made, we must reply, not by the Calculus, but by the principles of Weierstrass and Cantor : indeed Weierstrass may be regarded as the modern Zeno, since he, first of moderns, accepted the principle of Zeno's argu- ment, rejected by Dr. Cassirer, that every value of a variable is a constant. (This is the abstract form of the assertion that the arrow in its flight is always at rest.) The principle of conservation is next discussed. Previous and subsequent events are always connected by an equation, " cause - effect ". The possibility of satisfying the equation itself decides what events are causally related : the cause is an event, just as the effect is. The principle of conservation is not got from ex- perience, but is a postulate. Dr. Cassirer appears not to perceive 1 In my opinion, Leibniz had also another theory inconsistent with this one, and if monads mirror the universe, there must be real relations corresponding to the spatial relations of phenomena ; but this is a point to which I shall return later.