Frege, Thomae, and Formalism
Mathematical formalism is the the view that numbers are “signs” and that arithmetic is like a game played with such signs. Frege’s colleague Thomae defended formalism using an analogy with chess, and Frege’s critique of this analogy has had a major influence on discussions in analytic philosophy ab...
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| Format: | Article |
| Language: | English |
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MULPress
2023-05-01
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| Series: | Journal for the History of Analytical Philosophy |
| Online Access: | https://jhaponline.org/jhap/article/view/5366 |
| _version_ | 1797834407953825792 |
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| author | Richard Lawrence |
| author_facet | Richard Lawrence |
| author_sort | Richard Lawrence |
| collection | DOAJ |
| description |
Mathematical formalism is the the view that numbers are “signs” and that arithmetic is like a game played with such signs. Frege’s colleague Thomae defended formalism using an analogy with chess, and Frege’s critique of this analogy has had a major influence on discussions in analytic philosophy about signs, rules, meaning, and mathematics. Here I offer a new interpretation of formalism as defended by Thomae and his predecessors, paying close attention to the mathematical details and historical context. I argue that for Thomae, the formal standpoint is an algebraic perspective on a domain of objects, and a “sign” is not a linguistic expression or mark, but a representation of an object within that perspective. Thomae exploits a shift into this perspective to give a purely algebraic construction of the real numbers from the rational numbers. I suggest that Thomae’s chess analogy is intended to provide a model for such shifts in perspective.
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| first_indexed | 2024-04-09T14:37:28Z |
| format | Article |
| id | doaj.art-ed7d6ee740f54bc494ba0243be841f36 |
| institution | Directory Open Access Journal |
| issn | 2159-0303 |
| language | English |
| last_indexed | 2024-04-09T14:37:28Z |
| publishDate | 2023-05-01 |
| publisher | MULPress |
| record_format | Article |
| series | Journal for the History of Analytical Philosophy |
| spelling | doaj.art-ed7d6ee740f54bc494ba0243be841f362023-05-03T13:00:02ZengMULPressJournal for the History of Analytical Philosophy2159-03032023-05-01112Frege, Thomae, and FormalismRichard Lawrence0University of Vienna Mathematical formalism is the the view that numbers are “signs” and that arithmetic is like a game played with such signs. Frege’s colleague Thomae defended formalism using an analogy with chess, and Frege’s critique of this analogy has had a major influence on discussions in analytic philosophy about signs, rules, meaning, and mathematics. Here I offer a new interpretation of formalism as defended by Thomae and his predecessors, paying close attention to the mathematical details and historical context. I argue that for Thomae, the formal standpoint is an algebraic perspective on a domain of objects, and a “sign” is not a linguistic expression or mark, but a representation of an object within that perspective. Thomae exploits a shift into this perspective to give a purely algebraic construction of the real numbers from the rational numbers. I suggest that Thomae’s chess analogy is intended to provide a model for such shifts in perspective. https://jhaponline.org/jhap/article/view/5366 |
| spellingShingle | Richard Lawrence Frege, Thomae, and Formalism Journal for the History of Analytical Philosophy |
| title | Frege, Thomae, and Formalism |
| title_full | Frege, Thomae, and Formalism |
| title_fullStr | Frege, Thomae, and Formalism |
| title_full_unstemmed | Frege, Thomae, and Formalism |
| title_short | Frege, Thomae, and Formalism |
| title_sort | frege thomae and formalism |
| url | https://jhaponline.org/jhap/article/view/5366 |
| work_keys_str_mv | AT richardlawrence fregethomaeandformalism |