Wittgenstein on Mathematics av Severin Schroeder

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<P>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 <I>Tractatus</I> 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 <I>calculus view</I> and the <I>grammar view</I>. 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