The Persistence of Counterexample: Re-examining the Debate Over Leibniz Law

Abstract

Are there good reasons to reject the principle of the Identity of Indiscernibles as a necessary truth? Refutations seem to abound, the most common of which appeal to considerations of symmetry. But just as numerous are defenses of the principle. Of course, any argument that the identity of indiscernibles is (or fails to be) necessarily true must be examined against an assumed background theory of universals.' A change in the theory may well result in a different assessment of whether indiscernibility with respect to those universals is sufficient for identity. Opponents in the debate have expressed much concern over what univerals there are-one admitting only a subset of the other's universals. This paper contends that a more fundamental issue concerns what the opponents take a universal to be. We distinguish two non-overlapping theories of universals, Logical Realism and Natural Realism, and show that much of the debate conflates these frameworks.