Identity, quantification and sortals

Abstract

The topic of this thesis is the exploration of the relations between first-order quantification and identity and between identity conditions and sortals. In the first chapter, I will formulate a version of the thesis that quantification involves identity. I will formulate two principles that together entail this thesis and defend those principles from the arguments against them in the literature. In the second chapter, I will turn to the sortalist idea that the answers to identity questions depend on the identity conditions provided by sortal terms and point out the tension between two sortalist theses and their application in the standard semantics. Then, I will develop a version of situation semantics for first-order logic by adapting Fine’s truth-maker semantics for propositional logic. Finally, I will argue that when the sortalist theses are applied in this semantics, the tension evaporates. In the third chapter, I will apply the semantics that I developed to the thesis that identity conditions can be taken as abstraction principles and to the thesis of sortal essentialism. I will show that the semantics that I developed is a versatile tool that can shed light on the problems involving identity that can arise in other branches of philosophy, for example, in philosophy of mathematics and modal metaphysics.