Strict finitism refuted?
In his paper 'Wang's Paradox', Michael Dummett provides an argument for why strict finitism in mathematics is internally inconsistent and therefore an untenable position. Dummett's argument proceeds by making two claims: (1) Strict finitism is committed to the claim that there ar...
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| Format: | Journal article |
| Language: | English |
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2007
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| _version_ | 1797065145730465792 |
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| author | Magidor, O |
| author_facet | Magidor, O |
| author_sort | Magidor, O |
| collection | OXFORD |
| description | In his paper 'Wang's Paradox', Michael Dummett provides an argument for why strict finitism in mathematics is internally inconsistent and therefore an untenable position. Dummett's argument proceeds by making two claims: (1) Strict finitism is committed to the claim that there are sets of natural numbers which are closed under the successor operation but nonetheless have an upper bound; (2) Such a commitment is inconsistent, even by finitistic standards. In this paper I claim that Dummett's argument fails. I question both parts of Dummett's argument, but most importantly I claim that Dummett's argument in favour of the second claim crucially relies on an implicit assumption that Dummett does not acknowledge and that the strict finitist need not accept. ©2007 The Aristotelian Society. |
| first_indexed | 2024-03-06T21:24:28Z |
| format | Journal article |
| id | oxford-uuid:429aa918-37ec-4e7e-9640-6b68ef5bd1ac |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T21:24:28Z |
| publishDate | 2007 |
| record_format | dspace |
| spelling | oxford-uuid:429aa918-37ec-4e7e-9640-6b68ef5bd1ac2022-03-26T14:50:28ZStrict finitism refuted?Journal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:429aa918-37ec-4e7e-9640-6b68ef5bd1acEnglishSymplectic Elements at Oxford2007Magidor, OIn his paper 'Wang's Paradox', Michael Dummett provides an argument for why strict finitism in mathematics is internally inconsistent and therefore an untenable position. Dummett's argument proceeds by making two claims: (1) Strict finitism is committed to the claim that there are sets of natural numbers which are closed under the successor operation but nonetheless have an upper bound; (2) Such a commitment is inconsistent, even by finitistic standards. In this paper I claim that Dummett's argument fails. I question both parts of Dummett's argument, but most importantly I claim that Dummett's argument in favour of the second claim crucially relies on an implicit assumption that Dummett does not acknowledge and that the strict finitist need not accept. ©2007 The Aristotelian Society. |
| spellingShingle | Magidor, O Strict finitism refuted? |
| title | Strict finitism refuted? |
| title_full | Strict finitism refuted? |
| title_fullStr | Strict finitism refuted? |
| title_full_unstemmed | Strict finitism refuted? |
| title_short | Strict finitism refuted? |
| title_sort | strict finitism refuted |
| work_keys_str_mv | AT magidoro strictfinitismrefuted |