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4 - Prolegomena to Any Future Inconsistent Mathematics

from Part II - How to Face the Paradoxes?

Published online by Cambridge University Press:  08 October 2021

Zach Weber
Zach Weber
Affiliation:
University of Otago, New Zealand
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Summary

This chapter looks at the constraints on a logic for inconsistentmathematics. Curry’s paradox is presented in several forms,leading to problems for conditionals and validity. Grisin’sparadox and the Hinnion–Libert paradox lead to problems foridentity (equality) and the axiom of set extensionality. Inresponse, a broadly substructural response is recommended, where allforms of “contraction” are dropped, and a“relevant” logic is adopted to preserveextensionality. This leads to presentation of the official logicused in the second half of the book, and its main properties areoutlined, including some further methodological considerations forworking without contraction.

Keywords

Curry’s paradoxGrisin’s paradoxconditionalscontractionsubstructural logicextensionalityidentity
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Paradoxes and Inconsistent Mathematics , pp. 110 - 148
Publisher: Cambridge University Press
Print publication year: 2021

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