This book offers a detailed account and discussion of Ludwig Wittgensteinâs philosophy of mathematics. In Part I the stage is set with a brief presentation of Fregeâs logicist attempt to provide arithmetic with a foundation and Wittgensteinâs criticisms of it followed by sketches of Wittgensteinâs early views of mathematics in the Tractatus and in the early 1930s. Then (in Part II) Wittgensteinâs 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 â calculation â 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 it can be resolved. Finally there are chapters analysing and defending Wittgensteinâs provocative views on Hilbertâs Formalism and the quest for consistency proofs and on GÃdelâs incompleteness theorems. . Language: English