Wittgenstein on Mathematics

This book offers a detailed account and discussion of Ludwig Wittgenstein-s philosophy of mathematics. In Part I, the stage is set with a brief presentation of Frege-s logicist attempt to provide arithmetic with a foundation and Wittgenstein-s criticisms of it, followed by sketches of Wittgenstein-s early views of mathematics, in the Tractatus and in the early 1930s. Then (in Part II), Wittgenstein-s mature philosophy of mathematics (1937-44) is carefully presented and examined. Schroeder explains that it is based on two key ideas: the calculus view and the grammar view. On the one hand, mathematics is seen as a human activity - calculation - rather than a theory. On the other hand, the results of mathematical calculations serve as grammatical norms. The following chapters (on mathematics as grammar; rule-following; conventionalism; the empirical basis of mathematics; the role of proof) explore the tension between those two key ideas and suggest a way in which i