Leibniz on Possible Worlds

Logicians frequently make reference to the Leibnizian idea that a proposition is a necessary truth if and only if it is true of all possible worlds when defining logical truth in terms of interpretations or models. The same idea is usually mentioned in discussions of the semantics of modal logics. However, on further observations it becomes apparent that the concepts of “possible world” employed by modern investigators are quite different from that of Leibniz himself; and although perhaps this is all to the good, there may be some interest in considering what the effect would be if a more strictly Leibnizian approach were followed. The chapter describes certain features of the Leibnizian conceptual framework and attempts to incorporate them in the semantics of a formalized language. Specifically, the formal system discussed in the chapter is a first order monadic predicate calculus with identity and necessity and also with individual constants that do not in all cases denote. A similar system without the modal operator is considered in the chapter in an auxiliary way.