Identity and the formation of the notion of object

Abstract

The principle of the identity of indiscernibles says that two things that are indiscernible - that share all their properties - are one and the same thing. The principle was clearly formulated, and gained immense philosophical importance in Leibniz's thought. Turned round to read that identity is sufficient for indiscernibility, it seems compelling, and in this version it is connected with the principle of the substitutivity of identicals - that two terms which denote the same thing are substitutable for one another in any context salva veritate. We shall not concern ourselves here with this latter principle, but confine our attention to the original formulation -that indiscernibility is sufficient for identity. The exact interpretation of the principle in Leibniz's philosophy is not entirely clear. It sometimes appears as a sort of empirical generalization. But this surely does not exhaust its meaning, for it is obviously connected with same of Leibniz's central metaphysical doctrines such as the notion of a (complete) individual concept, or the principle of sufficient reason. In fact, most commentators regard the principle as 'analytic', or 'logically necessary'. 1 In this paper I shall not try to re-interpret the principle and its exact meaning in Leibniz; I shall completely ignore its metaphysical background, and its systematic status in his theory. I shall rather present a partial explication of the principle in more modern logical terminology, by which I shall contend that the principle is not analytic, that it is not "true by definition" or anything of the kind (sections II-IV), and yet that it is a necessary and a priori truth (sections V-VI). Under this particular interpretation the argument that the principle is not analytic is based on the difference between the notions of identity and indiscernibility, and the fact that identifying them in a particular language, is a step of great conceptual