  Leibniz has a very distinctive notion of truth, one which underlies much of his metaphysics. But this notion of truth goes back to Aristotle's Organon (cf. Posterior Analytics I.4), as Leibniz himself says, and it is also present in Arnauld and Nicole's Logic, or the Art of Thinking (Book IV, Chapter 6). As Leibniz puts it in a letter to Arnauld, “in every true affirmative proposition, whether necessary or contingent, universal or particular, the notion of the predicate is in some way included in that of the subject. Praedicatum inest subjecto; otherwise I do not know what truth is” (G II 56/L 337). As he tells us in the Primary Truths and the Discourse on Metaphysics, many things follow from the Predicate-in-Notion Principle (PIN), including what he believes to be the correct analysis of necessity and contingency.