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Wittgenstein on Rule-Following and the Foundations of Mathematics

by Severin Schroeder

  • Hardback
  • Publisher: Routledge
  • 15.7 x 23.6 x 2.2 cm

£162.26

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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 it can be resolved. Finally, there are chapters analysing and defending Wittgenstein's provocative views on Hilbert's Formalism and the quest for consistency proofs and on G del's incompleteness theorems.
Wittgenstein on Rule-Following and the Foundations of Mathematics and Sacred And The Profane
Sacred And The ProfaneWittgenstein on Rule-Following and the Foundations of Mathematics

  • Author

    Severin Schroeder

  • Book Format

    Hardcover

  • Publisher

    Routledge

  • Published

    October 2019

  • Weight

    486g

  • Dimensions

    15.7 x 23.6 x 2.2 cm

  • ISBN

    9781844658626

  • ISBN-10

    1844658627

  • Eden Code

    4888477

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