Page:Mind (New Series) Volume 8.djvu/350

 336 KOBEKT LATTA: philosophy : the whole truth is an unfolding of what is implied in them. But the definitions of geometry are determined by space-experience ; they are definitions of objects from which all characteristics except those of space have been thought away. And it is impossible to go a step beyond the definitions of geometry, to deduce anything from them, without a reference to the space which is their medium. Thus, as Tschirnhausen pointed out to Spinoza, 1 from the definition of a circle taken by itself it is impossible to deduce any of the properties of the circle except the uniformity of curvature by which it is distinguished essentially from all other curves. All the other properties of the circle can be deduced only through its being brought into relation with other things, such as radii, intersecting lines, etc. If, then, Spinoza's definitions correspond to the definitions of geo- metry, i.e., if his method is a geometrical one, the definitions presuppose a system in which the things defined are elements, and apart from a reference to this system there can be no- legitimate demonstration. Now while it is legitimate for a special science, which does not propose to answer ultimate questions, to make postulates presupposing a system within which the objects of the science are inter-related, such a procedure is inconsistent with the purpose of an absolute philosophy. In order to expound the meaning of the universe ordine geometrico you must begin with a definition of the universe, just as in order to expound the meaning of a geometrical figure, you must begin with a definition of the figure. But while there are other geometrical figures by the aid of which the meaning of the figure defined may be further expounded, there is no other through which the meaning of the universe may be set forth. Either the definition must already include and express the whole of the properties of the thing defined, in which case it must say everything that is to be said, or it must express some property from which nothing further can be deduced except by the aid of other considerations, in which case it is inadequate as a definition. Spinoza, however, contends that while it is perhaps true in the case of very simple things or entia rationis (including geometrical figures) that the definition of the thing, apart from its relation to other things, yields only one property, this is untrue as regards real things. " For from this alone, that I define God as a Being to whose essence belongs existence, I infer several of His properties ; namely, that He necessarily exists, that He is one, immutable, 1 Ep. 82, Van Vloten and Land (71 in Bruder). 1