{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,11,6]],"date-time":"2024-11-06T05:24:16Z","timestamp":1730870656379,"version":"3.28.0"},"reference-count":18,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2023,6,29]],"date-time":"2023-06-29T00:00:00Z","timestamp":1687996800000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":["cambridge.org"],"crossmark-restriction":true},"short-container-title":["The Review of Symbolic Logic"],"published-print":{"date-parts":[[2024,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The present note was prompted by Weber\u2019s approach to proving Cantor\u2019s 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\u2019s 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\u2019s three-valued logic of paradox and cut free Gentzen calculi this, <jats:italic>a fortiori<\/jats:italic>, has an impact on any paraconsistent set theory built on Priest\u2019s logic of paradox.<\/jats:p>","DOI":"10.1017\/s1755020323000187","type":"journal-article","created":{"date-parts":[[2023,6,29]],"date-time":"2023-06-29T07:54:00Z","timestamp":1688025240000},"page":"860-877","update-policy":"http:\/\/dx.doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":0,"title":["IS CANTOR\u2019S THEOREM A DIALETHEIA? 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