Abstract

If we consider Wittgenstein's career as a whole, it appears that he wrote more on the philosophy of logic and mathematics than any other subject. Yet his writings on these subjects have exerted little influence. Indeed, the tide of response to Remarks on the Foundations of Mathematics, which contains the bulk of his latest views of mathematics, has been for the most part overwhelmingly negative. Given his later emphasis on the context-bound character of language, mathematics and logic--where language apparently operates in an maximally precise, clear and general way--represent two of the most difficult cases for Wittgenstein to confront. My thesis aims to defend Wittgenstein from the charges of benighted arrogance traditionally levelled against him. I argue that Wittgenstein's later discussions of mathematics form a central part of a larger philosophical project, internally related to Philosophical Investigations and shaping in specific ways Wittgenstein's reaction to both scepticism and accounts of the nature of logical and mathematical truth. I see Wittgenstein criticizing the unreflective use of mathematical tools in philosophy, not offering a competing philosophy of mathematics. ;Too few of Wittgenstein's readers have been willing to offer detailed exegesis of his writing . This has made it difficult to understand how the aphoristic style of his late writing bears on the philosophical problems being discussed. On my view, the quality of Wittgenstein's writing is intrinsic to his later conception of the nature of logic, mathematics and philosophy. Line by line engagement with his texts is thus imperative in order to achieve an understanding of his philosophical objectives and criticisms. My dissertation offers as a paradigm of such reading a detailed exegesis and criticism of the opening five sections of Remarks on the Foundations of Mathematics. ;I briefly explore in some detail the origin and genesis of Wittgenstein's interest in rule-following, from its roots in the Tractatus's conception of logical syntax. This background illuminates Wittgenstein's later conception of logical truth and his criticisms of Frege's and Russell's arguments for logicism. To explore these criticisms, I focus on Wittgenstein' s discussions of the Frege-Russell definition of "Number" in "logical" terms. Placed in their appropriate philosophical and historical context, Wittgenstein's seemingly outrageous remarks about the nature of proof, mathematical logic and the foundations of mathematics do not simply betray his ignorance. Nor do they commit him to a revisionist attitude toward mathematical practice. Rather, they raise fundamental questions about the philosophical presuppositions lying behind attempts to bring particular mathematical results to bear in philosophy