Wittgenstein on Mathematics

Severin Schroeder, Schroeder Severin

$315

Hardback

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English

Acumen Publishing Ltd
30 December 2020

Western philosophy, from c 1900 -; Philosophy of mathematics

Series: Wittgenstein's Thought and Legacy

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.

By: Severin Schroeder, Schroeder Severin
Imprint: Acumen Publishing Ltd
Country of Publication: United Kingdom
Dimensions: Height: 229mm, Width: 152mm,
Weight: 630g
ISBN: 9781844658626
ISBN 10: 1844658627
Series: Wittgenstein's Thought and Legacy
Pages: 238
Publication Date: 30 December 2020
Audience: College/higher education , Primary
Format: Hardback
Publisher's Status: Active

Severin Schroeder is Associate Professor of Philosophy at the University of Reading. He has published three monographs on Wittgenstein: Wittgenstein: The Way Out of the Fly Bottle (2006), Wittgenstein Lesen (2009), and Das Privatsprachen-Argument (1998). He is the editor of Wittgenstein and Contemporary Philosophy of Mind (2001) and Philosophy of Literature (2010).