Leibniz's argument for the identity of indiscernibles in his correspondence with Clarke

Abstract

The Principle of Identity of Indiscernibles, which says that there are no two particulars having in common all their properties, occupies an important part in Leibniz’s metaphysics. This principle, however, is normally held not to be necessarily true; indeed Max Black’s [2, p. 83] possibility of a world consisting of two exactly similar spheres consists of a refutation of the necessity of the Identity of Indiscernibles. And some results in quantum physics imply that the principle is false even in the actual world (French [6], French and Redhead [7]). Leibniz believed in the Identity of Indiscernibles because he thought it followed from other principles of his metaphysics. In particular, in a letter to Clarke Leibniz infers the Identity of Indiscernibles from the Principle of Sufficient Reason (L V, 21).2 Specifically Leibniz there attempts to derive the Identity of Indiscernibles from an application of the Principle of Sufficient Reason to God’s act of creation, namely that God has a reason to create the world he creates. Since the Leibnizian God governs his act of creation by the Principle of the Best, according to which God wills only what is best, the reason he creates the world he creates is that it is the best possible world. Thus, although Leibniz does not say so explicitly, the Principle of the Best plays a part in his derivation of the Identity of Indiscernibles from the Principle of Sufficient Reason in his letters to Clarke.3

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