Mathematics, time, and confirmation

Abstract

This dissertation discusses two issues about abstract objects: their role in scientific theories, and their relation to time. Chapter 1, "Why Apply Mathematics?" argues that scientific theories are not about the mathematics that is applied in them, and defends this thesis against the Quine-Putnam Indispensability Argument. Chapter 2, "Scientific Ontology," is a critical study of W. V. Quine's claim that metaphysics and mathematics are epistemologically on a par with natural science. It is argued that Quine's view relies on a unacceptable account of empirical confirmation. Chapter 3, "Prior and the Platonist," demonstrates the incompatibility of two popular views about time: the "Platonist" thesis that some objects exist "outside" time, and A. N. Prior's proposal for treating tense on the model of modality. Chapter 4, "What has Eternity Ever Done for You?" argues against the widely held view that abstract objects exist eternally ("outside" time), and presents a defense of the rival view that they exist sempiternally (at all times)