Abstract

There is a gap in explaining the interrelationships between Wittgenstein’s philosophy of mathematics and the other areas of his thought in the intermediate period. With special attention paid to Wittgenstein’s philosophy of mathematics, this thesis is meant as a first step in outlining some of these important interconnections. Chapter 1 sets the stage by presenting Wittgenstein’s views in the philosophy of mathematics in the Tractatus, with a focus on his analysis of infinity. Chapter 2 outlines the principal aspects of Wittgenstein’s philosophy of mathematics, and the phenomenological language and its demise. Against the background of the Tractatus, the phenomenological language, and Wittgenstein’s relationship with the Vienna Circle, Chapter 3 reconstructs the development of the verification principle, before examining the extensive application he makes of it to the philosophy of mathematics. Chapter 4 examines Wittgenstein’s analyses of infinity, with special attention given to how his evolving views either contain the seeds of later insights or exemplify more general aspects of his philosophy. In Chapters 5 and 6, the results of the previous chapter are considered in relation to two important topics in Wittgenstein’s thought: inductive proof and set theory, respectively. The discussion of Wittgenstein’s views on inductive proof culminates in outlining how they influenced his philosophy of mathematics and philosophy generally. The examination of Wittgenstein’s views on set theory concludes with a re-evaluation of an important debate within Wittgenstein studies on the extent of Wittgenstein’s criticisms of set theory. The conflict arises as the result of an unduly narrow focus on (seemingly) contradictory elements of Wittgenstein’s philosophy of mathematics, but disappears with a comprehensive understanding of Wittgenstein’s mature philosophy of mathematics.