Page:Mind (New Series) Volume 8.djvu/358

 344 ROBERT LATTA: maticians of Spinoza's own day were showing that rectilineal figures are not " totally different in essence " from circles and that finite quantity is the product of an infinite series, having a definite law or characteristic. The various geo- metrical figures are, it is true, not products of one another nor products of discrete quantities of any kind ; but they are products or expressions of the qualities or characteristics of extension. Infinite extension is not something totally different in essence from all finite figures, something to be obtained only by getting rid of all finite extension. To call it " infinite " is to insist on its qualities or relations as deter- mining its quantities, to regard it as a system from which certain finite figures, in all their finitude, necessarily follow, or rather a system of which these finite figures are the expression. And in general " infinite " quantity, in so far as it is really anything, is a negative name for quality, and to say that the finite presupposes the infinite is to say that quantity presupposes quality. This is the truth involved in Spinoza's account of the Attributes of Substance as infinite in their kind; 1 but it is a truth which is inconsistent with Spinoza's other contention that Substance is absolutely infinite. To think of anything as infinitely great or as infinitely little is to recognise negatively that the conception under which we are thinking it is inadequate, that the thing (as conceived by us) and its other are elements or differences within a higher unity. A circle, the radius of which is infinite, is a circle which is not a circle, and when we speak of it we mean to indicate that the conception of a circle as an independent finite figure is inadequate and that the difference between a circle and a straight line is a difference determined by some higher unity, which (so far) we do not explain. In the same way, when we speak of infinite space we mean that the space of mathematics is, by itself, an inadequate conception and that the system of space must itself be an element in some more comprehensive system. And in general, to say that a thing is infinite in its kind is to say that its kind is relative to some other kind and that neither is to be fully understood except through that of which they are both differences. 2 In other words, a thing which is infinite in its kind is a thing which is to some extent indeterminate. A thing absolutely infinite will consequently be a thing absolutely indeterminate. That is to say, a thing 1 Eth., i., Def. 6 ; of. Ep. ii. and Korte Verhandeling, appendix, prop. iii. 2 This, of course, means (what Spinoza would deny) that finite Modes, as well as Attributes, are each infinite in its kind. Thus, according to Leibniz, every finite thing " contains infinity," v. infra.