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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| Summary: | 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. |
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