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Some Remarks on Wittgenstein’s Philosophy of Mathematics
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...
| Published in: | Open Journal of Philosophy |
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| ISSN: | 2163-9434 2163-9442 |
| Published: |
Scientific Research Publishing, Inc.
2020
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| Online Access: |
Check full text
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| 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. |
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| Keywords: |
Wittgenstein, Philosophy of Mathematics, Rules, Number Systems, Theorem and Proof |
| College: |
Faculty of Humanities and Social Sciences |
| Issue: |
01 |
| Start Page: |
45 |
| End Page: |
65 |