Adam Hogan

I propose that Leibniz did not state Leibniz’s Law, the logically and metaphysically robust principle that is typically understood as the following biconditional: ∀x ∀y [(x = y) ↔ ∀P (Px ↔ Py)]. To arrive at this conclusion, I examine the three principles that have become associated with Leibniz’s Law: the Substitutivity Principle (salva veritate), the Indiscernibility of Identicals, and the Identity of Indiscernibles. I show that Leibniz intended salva veritate as a semantic principle, never explicitly stated the Indiscernibility of Identicals, and understood the Identity of Indiscernibles as a metaphysical principle. In the debate about Leibniz’s Law, I focus on four commentators: (1) W. V. O. Quine’s construal of salva veritate as the Indiscernibility of Identicals, (2) Nicholas Rescher’s contention that both the Identity of Indiscernibles and salva veritate may be construed as Leibniz’s Law, (3) Fred Feldman’s argument that Leibniz did not state a law or definition of identity, but only a criterion of identity for concepts, and (4) Edwin Curley’s response to Feldman, that Feldman’s assumptions, along with passages in Leibniz, show Leibniz did state Leibniz’s Law. I argue that Feldman’s position is not completely correct but can be amended with insights from Quine, Rescher, and Curley and by reference to Leibniz’s Complete Concept Theory.