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Some Remarks on Wittgenstein’s Philosophy of Mathematics / Richard, Startup

Open Journal of Philosophy, Volume: 10, Issue: 01, Pages: 45 - 65

Swansea University Author: Richard, Startup

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Abstract

Drawing mainly from the Tractatus Logico-Philosophicus and his middle period writings, strategic issues and problems arising from Wittgenstein’s philosophy of mathematics are discussed. Topics have been so chosen as to assist mediation between the perspective of philosophers and that of mathematicia...

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Published in: Open Journal of Philosophy
ISSN: 2163-9434 2163-9442
Published: Scientific Research Publishing, Inc, 2020
Online Access: Check full text

URI: https://cronfa.swan.ac.uk/Record/cronfa53147
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Abstract: Drawing mainly from the Tractatus Logico-Philosophicus and his middle period writings, strategic issues and problems arising from Wittgenstein’s philosophy of mathematics are discussed. Topics have been so chosen as to assist mediation between the perspective of philosophers and that of mathematicians on their developing discipline. There is consideration of rules within arithmetic and geometry and Wittgenstein’s distinctive approach to number systems whether elementary or transfinite. Examples are presented to illuminate the relation between the meaning of an arithmetical generalisation or theorem and its proof. An attempt is made to meet directly some of Wittgenstein’s critical comments on the mathematical treatment of infinity and irrational numbers.
Keywords: Wittgenstein, Philosophy of Mathematics, Rules, Number Systems, Theorem and Proof
Issue: 01
Start Page: 45
End Page: 65