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IS CANTOR’S THEOREM A DIALETHEIA? VARIATIONS ON A PARACONSISTENT APPROACH TO CANTOR’S THEOREM

Part of: Philosophical aspects of logic and foundations General logic Set theory

Published online by Cambridge University Press:  29 June 2023

UWE PETERSEN
UWE PETERSEN*
Affiliation:
ALTONAER STIFTUNG FÜR PHILOSOPHISCHE GRUNDLAGENFORSCHUNG (ASFPG) EHRENBERGSTR. 27, 22767 HAMBURG, GERMANY
*
E-mail: uwe.petersen@asfpg.de
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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.

Keywords

Cantor’s theoremparaconsistent logicdialetheiasunrestricted abstraction

MSC classification

Primary: 03A05: Philosophical and critical 03B53: Paraconsistent logics 03E70: Nonclassical and second-order set theories
Type
Research Article
Information
The Review of Symbolic Logic , First View , pp. 1 - 18
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of The Association for Symbolic Logic

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References

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