Formalism 25
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866916958574739456 |
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| author | Katz, Mikhail G. Kuhlemann, Karl Sanders, Sam Sherry, David |
| author_facet | Katz, Mikhail G. Kuhlemann, Karl Sanders, Sam Sherry, David |
| contents | Abraham Robinson's philosophical stance has been the subject of several recent studies. Erhardt following Gaifman claims that Robinson was a finitist, and that there is a tension between his philosophical position and his actual mathematical output. We present evidence in Robinson's writing that he is more accurately described as adhering to the philosophical approach of Formalism. Furthermore, we show that Robinson explicitly argued {against} certain finitist positions in his philosophical writings. There is no tension between Robinson's mathematical work and his philosophy because mathematics and metamathematics are distinct fields: Robinson advocates finitism for metamathematics but no such restriction for mathematics. We show that Erhardt's analysis is marred by historical errors, by routine conflation of the generic and the technical meaning of several key terms, and by a philosophical {parti pris}. Robinson's Formalism remains a viable alternative to mathematical Platonism. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_14811 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Formalism 25 Katz, Mikhail G. Kuhlemann, Karl Sanders, Sam Sherry, David History and Overview 00A30, 01A60, 03A05 Abraham Robinson's philosophical stance has been the subject of several recent studies. Erhardt following Gaifman claims that Robinson was a finitist, and that there is a tension between his philosophical position and his actual mathematical output. We present evidence in Robinson's writing that he is more accurately described as adhering to the philosophical approach of Formalism. Furthermore, we show that Robinson explicitly argued {against} certain finitist positions in his philosophical writings. There is no tension between Robinson's mathematical work and his philosophy because mathematics and metamathematics are distinct fields: Robinson advocates finitism for metamathematics but no such restriction for mathematics. We show that Erhardt's analysis is marred by historical errors, by routine conflation of the generic and the technical meaning of several key terms, and by a philosophical {parti pris}. Robinson's Formalism remains a viable alternative to mathematical Platonism. |
| title | Formalism 25 |
| topic | History and Overview 00A30, 01A60, 03A05 |
| url | https://arxiv.org/abs/2502.14811 |