KANT'S ANTITHESIS OF DOGMATISM AND CRITICISM. 199 simple concepts into a single notion would be possible and legitimate. In such a case, though you would not be en- titled to say that a triangle is a non-triangle, there would be nothing to prevent your saying that a triangle is a parallelo- gram. For if some one urged that a triangle is definable as a three-sided figure while a parallelogram has four sides, and that three-sidedness and four-sidedness are incompatible, one would have to ask : How, unless " simple " concepts have relations of fixed incompatibility inter se, can I know that what has three sides cannot have four sides ? It could not be merely because the two concepts are two, i.e., merely distinct ; for three-sidedness and whiteness are also distinct, yet no objection arises when I define a figure as a white triangle. If there are incompatibilities anywhere in defini- tions, they must inhere in the original elements, the primary concepts, of which the definition is made up ; and if there were, contrariwise, no such original incompatibilities self- evident, not capable of being demonstrated by further de- finition, and not to be confused with mere non-identity everything under heaven in the way of a definition would be permissible. In asserting, then, that definitions are not arbitrary, Leibniz plainly points to the affirmation of ultimate repugnancies to coinherence between distinct and positive concepts ; and thus to the affirmation that synthetic relations of incompossibility, on the one hand, of necessary coexistence, on the other are to be found, in some cases, between the ultimate and irreducible ideas upon which our thinking finally depends. 1 As regards Leibniz, then, we must sum up the case thus :^ He sought to give definiteness and self -evidence to the method to be used in philosophical construction, by reducing thei grounds of all a priori reasoning to a single principle. But in his treatment of this principle he fell into a twofold and inconsistent doctrine. On the one hand, in the pursuit of extreme rigour and simplicity in the definition of his ultimate j criterion of truth, he tended to reduce it to the useless and ; trivial principle of the mere self-identity of concepts. But j on the other hand, in another part of his imperfectly con- catenated system, he plainly implied that there exist syn- thetic relations of compatibility and incompatibility between ; several distinct concepts, and that by the elucidation of . these relations, important and significant truths a priori may be discovered. And in the form of this open choice between 1 This point has already been clearly set forth by Mr. Russell (Philo- sophy of Leibniz, loc. tit.}.
