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An axiomatic version of Fitch’s paradox. (English) Zbl 1284.03141
Summary: A variation of Fitch’s paradox is given, where no special rules of inference are assumed, only axioms. These axioms follow from the familiar assumptions which involve rules of inference. We show (by constructing a model) that by allowing that possibly the knower doesn’t know his own soundness (while still requiring he be sound), Fitch’s paradox is avoided. Provided one is willing to admit that sound knowers may be ignorant of their own soundness, this might offer a way out of the paradox.

03B42 Logics of knowledge and belief (including belief change)
Full Text: DOI
[1] Carlson, T. J., Knowledge, machines, and the consistency of reinhardt’s strong mechanistic thesis, Annals of Pure and Applied Logic, 105, 51-82, (2000) · Zbl 0973.03019
[2] Chow, T. Y., The surprise examination or unexpected hanging paradox, The American Mathematical Monthly, 105, 41-51, (1998) · Zbl 0917.03001
[3] Duc, H. N. (2001). Resource-bounded reasoning about knowledge. Ph.D. thesis, University of Leipzig. · Zbl 0989.68142
[4] Fitch, F., No article title, A logical analysis of some value concepts. The Journal of Symbolic Logic, 28, 135-142, (1963) · Zbl 0943.03599
[5] Halpern, J.; Moses, Y., Taken by surprise: the paradox of the surprise test revisited, Journal of Philosophical Logic, 15, 281-304, (1986) · Zbl 0614.03005
[6] Kritchman, S.; Raz, R., The surprise examination paradox and the second incompleteness theorem, Notices of the American Mathematical Society, 57, 1454-1458, (2010) · Zbl 1261.03159
[7] Salerno, J., Introduction to knowability and beyond, Synthese, 173, 1-8, (2010) · Zbl 1213.03010
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