Page:The World as Will and Idea - Schopenhauer, tr. Haldane and Kemp - Volume 1.djvu/97

THE WORLD AS IDEA. 55 really different concepts, each of them, or at least one of them, contains something which the other does not contain; this is the relation in which every subject stands to its predicate. The recognition of this relation is called judgment. The representation of these spheres by means of figures in space, is an exceedingly happy idea. It first occurred to Gottfried Plouquet, who used squares for the purpose. Lambert, although later than him, used only lines, which he placed under each other. Euler carried out the idea completely with circles. Upon what this complete analogy between the relations of concepts, and those of figures in space, ultimately rests, I am unable to say. It is, however, a very fortunate circumstance for logic that all the relations of concepts, according to their possibility, i.e., a priori, may be made plain in perception by the use of such figures, in the following way: —

(1.) The spheres of two concepts coincide: for example the concept of necessity and the concept of following from given grounds, in the same way the concepts of Ruminantia and Bisulca (ruminating and cloven-hoofed animals), also those of vertebrate and red-blooded animals (although there might be some doubt about this on account of the annelida): they are convertible concepts. Such concepts are represented by a single circle which stands for either of them.

(2.) The sphere of one concept includes that of the other.