198 ARTHUR O. LOVEJOY : even in mathematics ; and metaphysics, possessing no means -of demonstration except the Principle of Contradiction, would indeed be condemned to perpetual sterility. We must, then, recognise this blunder in Leibniz's treat- ment of the Principle of Contradiction. By describing the judgments based upon that principle as " identical" by re- garding the relation between subject and predicate in such judgments as purely analytical, and then further treating both concepts as ultimately "simple" notions he undeni- ably destroys by implication the possibility of constructive metaphysics ; and by his confused thinking upon the point he is, unquestionably, largely responsible for Kant's aberra- tions in the matter of the distinction between synthetical and analytical judgments. But on the other hand, one must repeat that Leibniz intended no such result. He fully meant his Principle of Contradiction to be a positive and constructive principle ; and if he habitually employs the sort of language that I have quoted, implying that there are no necessary relations between any two distinct simple concepts except that of bare non-identity, it is also true that there is an essential and frequently reiterated point in the Leibnitian system which implies exactly the contrary. This is to be seenl in Leibniz's doctrine of definition. Definition consists in form- " ing a complex idea by the conjunction, in a single meaning, of several simple ideas or of less complex ideas which are ultimately resolvable into simple ones. The contrary process, j as we have already seen, is analysis the taking apart of the " complex which definition puts together, and so the eventual discovery of the simple conceptual elements of which it is composed. Leibniz, now, on the one hand, always insists that the analysis of a definition must bring us to such simple and indefinable concepts ; but on the other hand, he con- stantly insists that definition is not an arbitrary process but is always (when legitimately performed) limited from the outset by the requirement that the notions united shall be " compossible," compatible with one another. 1 But these two contentions taken together are equivalent to the asser- tion that there may subsist, even between ultimately simple and indefinable concepts, relations of incompatibility. For if there were no such relations of ultimate incompatibility, definitions ivould be arbitrary, and any conjunction of positive 1 Gerhardt iii., 443 : " Les definitions ne sont point arbitraires, et on ne peut point former les idees comme Ton veut. Car il faut que ces idees qu'on pretend former soyent veritables, c'est-a-dire, possibles, et que les ingrediens qu'on y met soyent compatibles entre eux." So fre- quently elsewhere.
