Reply to Øystein Linnebo and Stewart Shapiro
In reply to Linnebo, I defend my analysis of Tait's argument against the use of classical logic in set theory, and make some preliminary comments on Linnebo's new argument for the same conclusion. I then turn to Shapiro's discussion of intuitionistic analysis and of Smooth Infinitesim...
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| Format: | Journal article |
| Language: | English |
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Routledge
2018
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| _version_ | 1797094866149179392 |
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| author | Rumfitt, I |
| author_facet | Rumfitt, I |
| author_sort | Rumfitt, I |
| collection | OXFORD |
| description | In reply to Linnebo, I defend my analysis of Tait's argument against the use of classical logic in set theory, and make some preliminary comments on Linnebo's new argument for the same conclusion. I then turn to Shapiro's discussion of intuitionistic analysis and of Smooth Infinitesimal Analysis (SIA). I contend that we can make sense of intuitionistic analysis, but only by attaching deviant meanings to the connectives. Whether anyone can make sense of SIA is open to doubt: doing so would involve making sense of mathematical quantities (infinitesimals) whose relationship to zero and to one another is inherently indeterminate. |
| first_indexed | 2024-03-07T04:19:53Z |
| format | Journal article |
| id | oxford-uuid:caabc48d-adea-49cb-a219-bd1c2ecf7146 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T04:19:53Z |
| publishDate | 2018 |
| publisher | Routledge |
| record_format | dspace |
| spelling | oxford-uuid:caabc48d-adea-49cb-a219-bd1c2ecf71462022-03-27T07:09:01ZReply to Øystein Linnebo and Stewart ShapiroJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:caabc48d-adea-49cb-a219-bd1c2ecf7146EnglishSymplectic Elements at OxfordRoutledge2018Rumfitt, IIn reply to Linnebo, I defend my analysis of Tait's argument against the use of classical logic in set theory, and make some preliminary comments on Linnebo's new argument for the same conclusion. I then turn to Shapiro's discussion of intuitionistic analysis and of Smooth Infinitesimal Analysis (SIA). I contend that we can make sense of intuitionistic analysis, but only by attaching deviant meanings to the connectives. Whether anyone can make sense of SIA is open to doubt: doing so would involve making sense of mathematical quantities (infinitesimals) whose relationship to zero and to one another is inherently indeterminate. |
| spellingShingle | Rumfitt, I Reply to Øystein Linnebo and Stewart Shapiro |
| title | Reply to Øystein Linnebo and Stewart Shapiro |
| title_full | Reply to Øystein Linnebo and Stewart Shapiro |
| title_fullStr | Reply to Øystein Linnebo and Stewart Shapiro |
| title_full_unstemmed | Reply to Øystein Linnebo and Stewart Shapiro |
| title_short | Reply to Øystein Linnebo and Stewart Shapiro |
| title_sort | reply to oystein linnebo and stewart shapiro |
| work_keys_str_mv | AT rumfitti replytoøysteinlinneboandstewartshapiro |