Page:Mind (New Series) Volume 8.djvu/360

 346 ROBERT LATTA : realisation (entelechy or tendance). The infinite develops into the finite, the qualitative into the quantitative. The infinitely little line is a direction, but in the direction there is contained implicitly every finite line having that direction : in other words, the line is a development of the direction. But, as we have seen, all such development is the develop- ment of a unity, or rather of a system, into its differences ; it is something permanent unfolding itself in its changes. Now this implies that reality is not a bare unity, from which the differences have been thought away, but a system of differences, a unity which implicitly contains its differences within itself. This is the principle of the law of Continuity, which governs Leibniz's mathematics l and which has a considerable function in his philosophy. According to the law of Continuity, a thing may (as Leibniz himself puts it) be regarded as "equivalent to a species of its opposite," 5 e.g., rest may be regarded as a species of motion (an infinitely little motion), equality as a species of inequality, unconscious- ness as a species of consciousness, the finite as a species of the infinite. By this, of course, is meant not that the thing is a species of which its opposite is genus, but that the re- lation between them is reciprocal, it being possible to regard each as a species of the other. But this implies that both are elements within some unity or system wbich is insepar- able from them. And it is this that leads Leibniz to insist so strongly on the explicit recognition of the principle of sufficient reason as a principle of method. The principle of sufficient reason is the principle that everything has a ground or reason which is at once identical with it and different from it, in other words that nothing is self-evident, purely self- identical. Thus the principle of sufficient reason is the principle that the ultimate reality is not a unity from which the differences have been thought away, but a system of elements in relation, a unity in difference. And of this principle the law of Continuity is manifestly a particular application, for it amounts to saying that, while all the varieties of things are real, no one of them is independent of the rest, the world is a system of " compossible " things. 1 Leibniz very frequently speaks of the law of Continuity as derived from the consideration of " the infinite " and as being the basis of the Calculus. For instance, in the Specimen Dynamicum (1687) he speaks of it as principium ordinis generate, nascens ex infinite et continui notione, accedente ad illud axioma, quod datis ordinatis etiam quxsita sunt ordinata (Gerhardt, Math. Schriften, vi., 250 ; cf. Cohen, Princip der Infinitesimal-Methode, 52 sqq.). 2 Math. Schriften, iv., 93. Leibniz says contradictoire, but the context shows that he means " contrary," opposite.