Yablo’s Paradox, a Coinductive Language and Its Semantics

  • Shunsuke Yatabe
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7856)

Abstract

We generalize the framework of Barwise and Etchmendy’s “the liar” to that of coinductive language, and focus on two problems, the mutual identity of Yablo propositions coded by hypersets in ZFA and the difficulty of constructing semantics. We define a coding as a game theoretic syntax and semantics, which can be regarded as a version of Austin semantics.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [A88]
    Aczel, P.: Non-well-founded sets. CSLI publications (1988)Google Scholar
  2. [BE87]
    Barwise, J., Etchemendy, J.: The Liar: An Essay in Truth and Circularity. Oxford University Press (1987)Google Scholar
  3. [BM96]
    Barwise, J., Moss, L.: Vicious Circles. CSLI publications (1996)Google Scholar
  4. [C93]
    Coquand, T.: Infinite Objects in Type Theory. In: Barendregt, H., Nipkow, T. (eds.) TYPES 1993. LNCS, vol. 806, pp. 62–78. Springer, Heidelberg (1994)CrossRefGoogle Scholar
  5. [HH05]
    Halbach, V., Horsten, L.: The deflationist’s axioms for truth. In: Beal, J.C., Armour-Garb, B. (eds.) Deflationism and Paradox. Oxford Universoty PressGoogle Scholar
  6. [L01]
    Leitgeb, H.: Theories of truth which have no standard models. Studia Logica 68, 69–87 (2001)MathSciNetMATHCrossRefGoogle Scholar
  7. [L04]
    Leitgeb, H.: Circular languages. Journal of Logic, Language and Information 13, 341–371 (2004)MathSciNetMATHCrossRefGoogle Scholar
  8. [Mc85]
    McGee, V.: How truthlike can a predicate be? A negative result. Journal of Philosophical Logic 17, 399–410 (1985)MathSciNetCrossRefGoogle Scholar
  9. [Mo08]
    Moss, L.S.: Coalgebra and Circularity (2008) (preprint)Google Scholar
  10. [P97]
    Priest, G.: Yablo’s paradox. Analysis 57, 236–242 (1997)MathSciNetMATHCrossRefGoogle Scholar
  11. [V04]
    Viale, M.: The cumulative hierarchy and the constructible universe of ZFA. Mathematical Logic Quarterly 50(1), 99–103 (2004)MathSciNetMATHCrossRefGoogle Scholar
  12. [Yab93]
    Yablo, S.: Paradox Without Self-Reference. Analysis 53, 2251–2252 (1993)MathSciNetCrossRefGoogle Scholar
  13. [Yab06]
    Yablo, S.: Circularity and Paradox. In: Bolander, Hendricks, Pedersen (eds.) Self-Reference. CSLI Publications, StanfordGoogle Scholar
  14. [Ynf03]
    Yanofsky, N.S.: A Universal Approach to Self-Referential Paradoxes, Incomplete-ness and Fixed Point (2003) (preprint)Google Scholar
  15. [Yat12]
    Yatabe, S.: A constructive naive set theory and infinity (preprint)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Shunsuke Yatabe
    • 1
  1. 1.Graduate School of LettersKyoto UniversityJapan

Personalised recommendations