David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Mind 115 (460):947-956 (2006)
The project of antirealism is to construct an assertibility semantics on which (1) the truth of statements obeys a recognition condition so that (2) counterexamples are forthcoming to the law of the excluded third and (3) intuitionistic formal predicate logic is provably sound and complete with respect to the associated notion of validity. Using principles of intuitionistic mathematics and employing only intuitionistically correct inferences, we show that prima facie reasonable formulations of (1), (2), and (3) are inconsistent. Therefore, it should not be assumed that the project of anti-realism as it bears upon intuitionistic mathematics and logic can be accomplished.
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W. Dean & H. Kurokawa (2010). From the Knowability Paradox to the Existence of Proofs. Synthese 176 (2):177 - 225.
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