  In §8 of the Discourse on Metaphysics, Leibniz gives one of his most important accounts of the nature of individual substance. There he claims that the Aristotelian idea that a substance is that which is the subject of predication and which cannot be predicated of something else is insufficient for a true analysis of the nature of substance. He next appeals to the PC and the PIN: in every true predication, the concept of the predicate is contained in the concept of the subject. “Since this is so,” Leibniz claims, “we can say that the nature of an individual substance or of a complete being is to have a notion so complete that it is sufficient to contain and to allow us to deduce from it all the predicates of the subject to which this notion is attributed” (A VI iv 1540/AG 41). In other words, x is a substance if and only if x has a complete individual concept (CIC), that is, a concept that contains within it all predicates of x past, present, and future. The CIC, then, serves to individuate substances; it is able to pick out its bearer from an infinity of other finite created substances. Leibniz gives as an example Alexander the Great. The concept of Alexander contains being a King, being a student of Aristotle, conquering Darius and Porus, and so on. Now, “God, seeing Alexander's individual notion or haecceity, sees in it at the same time the basis and reason for all the predicates which can be said truly of him” (A VI iv 1540–41/AG 41). Leibniz's invocation of the Scotist notion of a haecceity is intriguing. What Leibniz is telling us is that Alexander's thisness is determined by the sum of his qualitative properties. Moreover, we can see a metaphysical aspect to this logical conception of substance: the complete individual concept of a substance is the notion or essence of the substance as it known by the divine understanding.