Benjamin Marschall PhD

May 1^st until September 30^th, 2021

Affiliation: University of Cambridge

Research for a study about:

Quine’s Philosophy of Mathematics

What is Quine’s philosophy of mathematics, and how does it differ from Carnap’s? It is natural to expect the differences to be quite severe. In Carnap’s account of mathematics the notion of analyticity plays a major role, after all, which Quine famously rejected. Furthermore the indispensability argument for mathematical Platonism is frequently ascribed to Quine, whereas Carnap is not generally thought of as a Platonist. It is thus tempting to describe the historical development as a move from Carnapian conventionalism to Quinean realism about mathematics. This is indeed how the story is often told, but I think that it paints a misleading picture. The aim of my project is to gain a better understanding of Quine’s philosophy of mathematics, which, on closer inspection, turns out to be largely continuous with that of Carnap. Two issues that I will focus on specifically are 1) Quine’s conception of ontology and its relationship to truth, and 2) his attitude towards Gödel’s incompleteness theorems.