A Soft Defence of Mathematical Platonism

Abstract

In this paper, I provide a soft defence of the Platonist conception of mathematics, which posits mathematical objects as having substantial and necessary meaning independent of human constructions or compulsions. I defend the Platonist account of mathematics against two interpretations of Wittgenstein's theory of mathematics. The first interpretation, which I term the 'Independent Instantiation' interpretation, maintains that mathematical claims only have meaning within a linguistic framework, and thus correspond to no generalizable essences. The second, the "Psychological Predilection" interpretation, argues that humans are psychologically, rather than socially compelled to accept mathematical claims, but still rejects any metaphysical necessity in mathematics. I accuse the first interpretation of committing the genetic fallacy and failing to account for our ability to apply mathematics in new ways. The second interpretation I claim to be neither true nor false, but nonsensical by Wittgenstein's own standards, leaving us to find criteria other than truth for choosing a theory of mathematics.