Wittgenstein and concept‐extension in mathematics
I begin by attempting to get a perspicuous overview of what Wittgenstein means by saying that a mathematical proof forms concepts. I then distinguish these sorts of cases from those we might call concept‐extending proofs, which, rather than introducing new concepts, function to enrich those concepts...
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| Published in | Philosophical investigations Vol. 48; no. 3; pp. 333 - 348 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Oxford
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01.07.2025
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| ISSN | 0190-0536 1467-9205 1467-9205 |
| DOI | 10.1111/phin.12457 |
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| Abstract | I begin by attempting to get a perspicuous overview of what Wittgenstein means by saying that a mathematical proof forms concepts. I then distinguish these sorts of cases from those we might call concept‐extending proofs, which, rather than introducing new concepts, function to enrich those concepts that have already been given a home in our mathematical practice. At the same time, I also want to argue that the line between these two sorts of proofs is not always clear and will sometimes be blurred. I go on to compare paradigmatic examples of each, concluding with a case in which it is not immediately clear whether we ought to all the proof concept‐forming or extending. This last section includes a discussion of Sorin Bangu's recent account of Wittgenstein on mathematical proof. |
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| AbstractList | I begin by attempting to get a perspicuous overview of what Wittgenstein means by saying that a mathematical proof forms concepts. I then distinguish these sorts of cases from those we might call concept‐extending proofs, which, rather than introducing new concepts, function to enrich those concepts that have already been given a home in our mathematical practice. At the same time, I also want to argue that the line between these two sorts of proofs is not always clear and will sometimes be blurred. I go on to compare paradigmatic examples of each, concluding with a case in which it is not immediately clear whether we ought to all the proof concept‐forming or extending. This last section includes a discussion of Sorin Bangu's recent account of Wittgenstein on mathematical proof. |
| Author | Wheeler, Samuel J. |
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| Cites_doi | 10.1111/phin.12379 10.1007/978-3-030-48481-1 10.4324/9781003056904 10.1111/phin.12413 10.1093/pq/pqad111 10.1111/1467-9205.00144 10.1111/phin.12335 |
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| Copyright | 2025 The Author(s). published by John Wiley & Sons Ltd. 2025. This work is published under Creative Commons Attribution License~https://creativecommons.org/licenses/by/3.0/ (the "License"). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. |
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| References | 2023; 75 2023; 46 2021; 45 2022 2011 2020 1976 2009 1974 1983 1982 2024; 13 2024; 47 2001; 24 1969 1958 1979 1966 Wittgenstein L. (e_1_2_6_17_1) 1982 Wittgenstein L. (e_1_2_6_18_1) 1983 Wheeler Samuel J. (e_1_2_6_11_1) 2024; 13 e_1_2_6_10_1 Säätelä S. (e_1_2_6_6_1) 2011 Wittgenstein L. (e_1_2_6_19_1) 1958 e_1_2_6_9_1 e_1_2_6_8_1 Wittgenstein L. (e_1_2_6_13_1) 1976 e_1_2_6_5_1 e_1_2_6_4_1 e_1_2_6_7_1 Wittgenstein L. (e_1_2_6_20_1) 1979 Wittgenstein L. (e_1_2_6_12_1) 1966 Wittgenstein L. (e_1_2_6_16_1) 2009 Wittgenstein L (e_1_2_6_14_1) 1969 e_1_2_6_3_1 e_1_2_6_2_1 Wittgenstein Ludwig (e_1_2_6_15_1) 1974 |
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| Title | Wittgenstein and concept‐extension in mathematics |
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