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IS CANTOR’S THEOREM A DIALETHEIA? VARIATIONS ON A PARACONSISTENT APPROACH TO CANTOR’S THEOREM
Published online by Cambridge University Press: 29 June 2023
Abstract
The present note was prompted by Weber’s approach to proving Cantor’s theorem, i.e., the claim that the cardinality of the power set of a set is always greater than that of the set itself. While I do not contest that his proof succeeds, my point is that he neglects the possibility that by similar methods it can be shown also that no non-empty set satisfies Cantor’s theorem. In this paper unrestricted abstraction based on a cut free Gentzen type sequential calculus will be employed to prove both results. In view of the connection between Priest’s three-valued logic of paradox and cut free Gentzen calculi this, a fortiori, has an impact on any paraconsistent set theory built on Priest’s logic of paradox.
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- © The Author(s), 2023. Published by Cambridge University Press on behalf of The Association for Symbolic Logic