Wittgenstein on Mathematics (Wittgenstein's Thought and Legacy)

By: Severin Schroeder

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Synopsis: 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.

Book Quality:: Publisher Quality
Book Size:: 238 Pages
ISBN-13:: 9781000318296
Related ISBNs:: 9781844658626, 9780367683283, 9781003056904, 9780367522056, 9781844658633
Publisher:: Taylor and Francis
Date of Addition:: 12/30/20
Copyrighted By:: Severin Schroeder, The right of Severin Schroeder to be identified as author of this work has been asserted by him in accordance with sections
Adult content:: No
Language:: English
Has Image Descriptions:: No
Categories:: Nonfiction, Philosophy
Submitted By:: Bookshare Staff
Usage Restrictions:: This is a copyrighted book.