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  • 4 - Prolegomena to Any Future Inconsistent Mathematics

  • from Part II - How to Face the Paradoxes?
  • Zach Weber, University of Otago, New Zealand
  • Book:
    Paradoxes and Inconsistent Mathematics
    Published online:
    08 October 2021
    Print publication:
    21 October 2021, pp 110-148

  • 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.