Page:Mind (New Series) Volume 8.djvu/359

 THE PHILOSOPHY OF SPINOZA AND LEIBNIZ. 345 absolutely infinite must be a thing of which we have no conception whatever, for if we had an inadequate conception of it, it would be infinite in its kind, and if we had a perfectly adequate conception of it, it would no longer be infinite in the sense of indeterminate, it would be absolutely deter- mined. In short, the mathematical infinite is always the indeterminate, while the infinite as applied to the real uni- verse is the self-determined. Now the characteristic feature of the philosophy of Leibniz is that, however imperfectly, it endeavours to give a positive solution of the problem of reality. And this is closely con- nected with Leibniz's point of view in Mathematics. Instead of regarding the infinite as the negation of the finite, to be reached by thinking away the finite, he conceives the infinite as the reality of the finite, to be reached by thinking out the nite. Every finite thing, according to Leibniz, " contains infinity " : it is in some way constituted by the infinite, made up of infinitesimals. His account of the way in which the infinite actually constitutes or determines the finite is far from being perfectly satisfactory ; but he has a sure grasp of the principle that the determining infinite means quality, characteristic, relation of some kind, and that it is impos- sible to get behind relations, behind the world as a system, or, in other words, to reach substance depositis affectionibus. Thus in the letter to Grandi already quoted (p. 342) Leibniz writes : Infinitude vera non cadit nisi in infinitum virtutis omni parte carens. . . et quantitates illce calculi nostri extraordinaria sunt fictiones, non ideo tamen spernenda sunt. . . cum in calculo perinde sit ac si essent vera quantitates, habeantque fundamentum in re et veritatem quandam idealem ut radices imaginarice. 1 All quantity is accordingly quantity of something non-quanti- tative, quantity of some quality or characteristic. A finite straight line is a quantity of uniform direction, a finite curve is a quantity of direction which varies according to some law, a finite extension is a quantity of something extended. " Extension presupposes some quality, some attribute, some nature in the extended thing, which quality extends or diffuses itself along with the thing, continues itself." 2 This quality is conceived by Leibniz as potentiality, not in the sense of empty capacity (puissance nue), but in the sense of something which contains implicitly within itself its own 1 Gerhardt, Leibniz's Math. Schriften, iv., 218 ; cf. iiL, 500 : Reale infinitum fortasse est ipsum absolutum, quod non ex partibus con- r, sed partes habentia eminenti ratione et velut gradu perfectionis "Leibniz. Erdmann's ed., 692 b; Gerhardt's ed., vi., 584.