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Curry’s Paradox and ω -Inconsistency

Abstract

In recent years there has been a revitalised interest in non-classical solutions to the semantic paradoxes1. In this paper I show that a number of logics are susceptible to a strengthened version of Curry’s paradox. This can be adapted to provide a proof theoretic analysis of the ω-inconsistency in Łukasiewicz’s continuum valued logic, allowing us to better evaluate which logics are suitable for a naïve truth theory. On this basis I identify two natural subsystems of ukasiewicz logic which individually, but not jointly, lack the problematic feature.

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References

  1. Beall J. (2009) Spandrels of Truthgtr. Oxford University Press, USA

    Book  Google Scholar 

  2. Brady, R., Universal Logic. CSLI Publications, 2006.

  3. Brady R.T. (1983) The simple consistency of a set theory based on the logic CSQ. Notre Dame Journal of Formal Logic 24(4): 431–449

    Article  Google Scholar 

  4. Cintula P. (2007) Hájek P, Horcík R., Formal systems of fuzzy logic and their fragments. Annals of Pure and Applied Logic 150(1–3): 40–65

    Article  Google Scholar 

  5. Field H. (2008) Saving Truth from Paradox. Oxford University Press, USA

    Book  Google Scholar 

  6. Hájek, P., Metamathematics of Fuzzy Logic, Springer, 1998.

  7. Hajek P., Paris J., Shepherdson J. (2000) The liar paradox and fuzzy logic. Journal of Symbolic Logic 65(1): 339–346

    Article  Google Scholar 

  8. Priest, G., In contradiction: A Study of the Transconsistent, Oxford University Press, 2006.

  9. Restall G. (1992) Arithmetic and truth in Lukasiewicz’s infinitely valued logic. Logique et Analyse 140: 303–312

    Google Scholar 

  10. Restall G. (1993) How to be really contraction free. Studia Logica 52(3): 381–391

    Article  Google Scholar 

  11. Restall, G., An Introduction to Substructural Logics, Routledge, 2000.

  12. Rogerson S., Butchart S. (2002) Naïve comprehension and contracting implications. Studia Logica 71(1): 119–132

    Article  Google Scholar 

  13. Rogerson S., Restall G. (2004) Routes to triviality. Journal of Philosophical Logic 33(4): 421–436

    Article  Google Scholar 

  14. Shaw-Kwei M., Logical paradoxes for many-valued systems. Journal of Symbolic Logic 37–40, 1954

Download references

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Correspondence to Andrew Bacon.

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Presented by Jacek Malinowski

1 See, for example, [ 1,2,5].

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Bacon, A. Curry’s Paradox and ω -Inconsistency. Stud Logica 101, 1–9 (2013). https://doi.org/10.1007/s11225-012-9373-3

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  • DOI: https://doi.org/10.1007/s11225-012-9373-3

Keywords

  • Contractionless logic
  • ω-Inconsistency
  • Łukasiewicz logic
  • Curry’s paradox
  • Naïve truth theory