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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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DOI (Published version): 10.4236/ojpp.2020.101005

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
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URI: https://cronfa.swan.ac.uk/Record/cronfa53147
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first_indexed 2020-01-08T13:49:23Z
last_indexed 2020-10-28T04:06:05Z
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spelling 2020-10-27T14:37:41.1135266 v2 53147 2020-01-08 Some Remarks on Wittgenstein’s Philosophy of Mathematics d86a8b1f7833763cea35d2b88386d0d4 Richard Startup Richard Startup true false 2020-01-08 FGSEN 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. Journal Article Open Journal of Philosophy 10 01 45 65 Scientific Research Publishing, Inc. 2163-9434 2163-9442 Wittgenstein, Philosophy of Mathematics, Rules, Number Systems, Theorem and Proof 3 1 2020 2020-01-03 10.4236/ojpp.2020.101005 COLLEGE NANME Science and Engineering - Faculty COLLEGE CODE FGSEN Swansea University 2020-10-27T14:37:41.1135266 2020-01-08T10:15:22.9274338 Faculty of Science and Engineering School of Biosciences, Geography and Physics - Geography Richard Startup 1 53147__16232__2c138951ae3a47109513d9c23a774fe4.pdf 53147.pdf 2020-01-08T10:18:11.1485335 Output 356640 application/pdf Version of Record true Released under the terms of a Creative Commons Attribution International License (CC-BY). true eng https://creativecommons.org/licenses/by/4.0/
title Some Remarks on Wittgenstein’s Philosophy of Mathematics
spellingShingle Some Remarks on Wittgenstein’s Philosophy of Mathematics
Richard Startup
title_short Some Remarks on Wittgenstein’s Philosophy of Mathematics
title_full Some Remarks on Wittgenstein’s Philosophy of Mathematics
title_fullStr Some Remarks on Wittgenstein’s Philosophy of Mathematics
title_full_unstemmed Some Remarks on Wittgenstein’s Philosophy of Mathematics
title_sort Some Remarks on Wittgenstein’s Philosophy of Mathematics
author_id_str_mv d86a8b1f7833763cea35d2b88386d0d4
author_id_fullname_str_mv d86a8b1f7833763cea35d2b88386d0d4_***_Richard Startup
author Richard Startup
author2 Richard Startup
format Journal article
container_title Open Journal of Philosophy
container_volume 10
container_issue 01
container_start_page 45
publishDate 2020
institution Swansea University
issn 2163-9434
2163-9442
doi_str_mv 10.4236/ojpp.2020.101005
publisher Scientific Research Publishing, Inc.
college_str Faculty of Science and Engineering
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hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Biosciences, Geography and Physics - Geography{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Biosciences, Geography and Physics - Geography
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description 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.
published_date 2020-01-03T04:05:59Z
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