Essays on indiscernibility

Abstract

This Thesis is a collection of essays on qualitatively indiscernible entities, i.e. entities which agree with respect to all the qualitative properties they instantiate. In Chapter 1 I introduce various accounts of indiscernibility, and provide a review of the relevant literature. Chapter 2 is dedicated to Leibniz’s principle of the Identity of Indiscernibles, the claim that indiscernibility suffices for numerical identity. I argue that if certain assumptions about identity criteria are accepted, the weakest non-trivial interpretation of the principle is one restricted solely to qualitative properties. In Chapter 3 I present a new counterexample to the Identity of Indiscernibles. In Chapter 4 I argue that Anti-Haecceitism, the claim that there are no maximal possibilities which differ only with respect to the non-qualitative possibilities they include, entails that the Identity of Indiscernibles holds of necessity. In Chapter 5 I propose a new account of qualitative properties, according to which a property is qualitative if and only if it is invariant under any identity assignment — where an identity assignment is a function from individuals and worlds to identities. In Chapter 6 I argue that singular reference to indiscernible individuals is possible, and show how current theories of Arbitrary Reference allow for a successful analysis of this phenomenon. In Chapter 7 I defend Arbitrary Reference against a popular objection, and advance a new probabilistic account of Arbitrary Reference. Finally, in Chapter 8, I show that singular reference to entities to which identity does not apply is impossible.