Wittgenstein on Mathematics
eBook - ePub

Wittgenstein on Mathematics

Severin Schroeder

  1. 238 pages
  2. English
  3. ePUB (mobile friendly)
  4. Available on iOS & Android
eBook - ePub

Wittgenstein on Mathematics

Severin Schroeder

Book details
Table of contents
Citations

About This Book

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 Gödel's incompleteness theorems.

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Information

Publisher
Routledge
Year
2020
ISBN
9781000318296
Edition
1
Topic
Mathematics
Subtopic
Arithmetic
Index
Mathematics

Table of contents

    Citation styles for Wittgenstein on Mathematics

    APA 6 Citation

    Schroeder, S. (2020). Wittgenstein on Mathematics (1st ed.). Taylor and Francis. Retrieved from https://www.perlego.com/book/2015131/wittgenstein-on-mathematics-pdf (Original work published 2020)

    Chicago Citation

    Schroeder, Severin. (2020) 2020. Wittgenstein on Mathematics. 1st ed. Taylor and Francis. https://www.perlego.com/book/2015131/wittgenstein-on-mathematics-pdf.

    Harvard Citation

    Schroeder, S. (2020) Wittgenstein on Mathematics. 1st edn. Taylor and Francis. Available at: https://www.perlego.com/book/2015131/wittgenstein-on-mathematics-pdf (Accessed: 25 September 2021).

    MLA 7 Citation

    Schroeder, Severin. Wittgenstein on Mathematics. 1st ed. Taylor and Francis, 2020. Web. 25 Sept. 2021.