196 ARTHUR O. LOVEJOY : follows from the logical principle : " Dans toute verite, uni- verselle ou singuliere, necessaire ou contingente, le predicat est contenu dans le sujet ". But while Leibniz thus makes all judgments analytical in a sense, it is also true that he fully recognises a distinction corresponding to Kant's distinction- bet ween analytic and synthetic judgments. Some predicates are contained in their subjects essentially and inextricably, so- that, lacking those predicates, the subject would cease to fee- itself, would become an inconceivability ; in other words, the concept, as a whole, is made up of a complex of attributes, some one or more of which are inconceivable without the others. In other cases the inclusion of the given predicate with the several other predicates that make up the essence-- (or definition) of the subject is purely accidental ; the several attributes do not coinhere of necessity. In the latter cases, the connexion of predicate with subject can only be known a posteriori ; the former class constitute the field where a priori reasoning is legitimate, and where necessary and eternal truths are to be looked for. It is, of course, true that Leib- niz called propositions of this class identical propositions, their distinguishing mark being that their opposites involved self-contradiction. But by identity Leibniz did not really in- tend to mean mere tautology, and by contradiction he does not always signify merely verbal contradiction. It was, in- deed, difficult for him to make out how he could mean any- thing else ; but he was, none the less, firmly persuaded that the Grund des Widerspruches is no empty and sterile maxim,, but the fruitful source of important insights ; and he especially (if not always very successfully) exerted himself to prove its- positive utility. Thus he remarks (Gerhardt vii., p. 299) that though there may seem to bs nothing but a coccy sinus- inutilis in identical propositions, yet levi mutatione utilia inde axiomata nascuntur. This, to be sure, is a somewhat no/if way of putting it, and the examples which follow are hardly con- vincing ; but it all shows Leibniz's unwillingness to take his- principle in its strict and narrow sense. There are, more- over, he maintains, two distinct kinds of judgment included within its range of application : (1) identical judgments, of which the opposite is formally self-contradictory, e.g., A is A ; (2) judgments virtualiter identicae, of which the opposite can be seen to involve contradiction only per terminorum intellec- tum et resolutionem that is, only by an examination of the whole implicit connotation of the terms involved, showing" that the two notions are ' incompossible '. It is chiefly these latter, or " virtually identical," judgments which constitute the substance of our demonstrative knowledge, and especially
