  Leibniz also follows Aristotle (cf. Metaphysics IV.3), in placing great emphasis on the Principle of Identity or the Principle of Contradiction (PC). PC states simply that “a proposition cannot be true and false at the same time, and that therefore  A is A and cannot be not A”  (G VI 355/AG 321). According to Leibniz, the primary truths of his metaphysical system are identities, but, in a striking move, he combines PC with PIN and asserts in Primary Truths that “all remaining truths are reduced to primary truths with the help of definitions, that is, through the resolution of notions” (A VI iv 1644/AG 31). Furthermore, the combination of PC and PIN will mean that, since in any true proposition the predicate is contained explicitly or implicitly within the subject, this is so for all affirmative truths, whether they be universal or particular, necessary or contingent. Leibniz will use this seemingly innocuous principle to draw profoundly strong metaphysical conclusions about the nature of substance and modality.