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Dummett's objection to the ontological route to intuitionistic logic: a rejoinder

Abstract : In ‘The philosophical basis of intuitionistic logic’, Michael Dummett discusses two routes towards accepting intuitionistic rather than classical logic in number theory, one meaning-theoretical (his own) and the other ontological (Brouwer and Heyting's). He concludes that the former route is open, but the latter is closed. I reconstruct Dummett's argument against the ontological route and argue that it fails. Call a procedure ‘investigative’ if that in virtue of which a true proposition stating its outcome is true exists prior to the execution of that procedure; and ‘generative’ if the existence of that in virtue of which a true proposition stating its outcome is true is brought about by the execution of that procedure. The problem with Dummett's argument then is that a particular step in it, while correct for investigative procedures, is not correct for generative ones. But it is the latter that the ontological route is concerned with.
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https://hal-cnrs.archives-ouvertes.fr/hal-03738910
Contributor : Mark Van Atten Connect in order to contact the contributor
Submitted on : Tuesday, July 26, 2022 - 4:51:59 PM
Last modification on : Wednesday, July 27, 2022 - 3:46:12 AM

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Mark van Atten. Dummett's objection to the ontological route to intuitionistic logic: a rejoinder. Inquiry, Taylor & Francis (Routledge), 2022, 65 (6), pp.725-742. ⟨10.1080/0020174X.2019.1651091⟩. ⟨hal-03738910⟩

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