Adaptive Fregean Set Theory

Abstract

This paper defines provably non-trivial theories that characterize Frege’s notion of a set, taking into account that the notion is inconsistent. By choosing an adaptive underlying logic, consistent sets behave classically notwithstanding the presence of inconsistent sets. Some of the theories have a full-blown presumably consistent set theory T as a subtheory, provided T is indeed consistent. An unexpected feature is the presence of classical negation within the language.

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Acknowledgements

Part of the ideas and results were presented in conferences. My gratitude goes (i) to the audience of the 5th World Congress on Universal Logic (Istanbul, Turkey, 20–30 June 2015) for questions and suggestions, especially to Graham Priest with whom I also corresponded on the matter afterwards; (ii) to the attentive and helpful audience of an \(\exists \)ntia et Nomin \(\forall \) Workshop (Krakow, Poland, 9–11 September 2015); and (iii) to both referees for pointing out ways to improve the paper.

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Correspondence to Diderik Batens.

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Batens, D. Adaptive Fregean Set Theory. Stud Logica 108, 903–939 (2020). https://doi.org/10.1007/s11225-019-09882-1

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Keywords

  • Fregean set theories
  • Adaptive logics
  • Content guidance
  • Paraconsistency