Infinite Liar in a (Modal) Finitistic Setting

  • Michał Tomasz Godziszewski
  • Rafal UrbaniakEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11600)


Yablo’s paradox results in a set of formulas which (with local disquotation in the background) turns out consistent, but \(\omega \)-inconsistent. Adding either uniform disquotation or the \(\omega \)-rule results in inconsistency. One might think that it doesn’t arise in finitary contexts. We study whether it does. It turns out that the issue turns on how the finitistic approach is formalized.


Axiomatic theories of truth Paradoxes Yablo’s paradox Finitism Potential infinity 


  1. 1.
    Godziszewski, M.T.: Yablo sequences in potentially infinite domains and partial semantics (2018). [submitted]Google Scholar
  2. 2.
    Hamkins, J.D., Linnebo, Ø.: The modal logic of set-theoretic potentialism and the potentialist maximality principles. Rev. Symb. Logic (2018, to appear)., arXiv:1708.01644
  3. 3.
    Ketland, J.: Yablo’s paradox and \(\omega \)-inconsistency. Synthese 145, 295–302 (2005)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Mostowski, M.: On representing concepts in finite models. Math. Logic Q. 47, 513–523 (2001)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Mostowski, M.: On representing semantics in finite models. In: Rojszczak, A., Cachro, J., Kurczewsk, G. (eds.) Philosophical Dimensions of Logic and Science, pp. 15–28. Kluwer Academic Publishers, Dordrecht (2001)Google Scholar
  6. 6.
    Mostowski, M., Zdanowski, K.: FM-representability and beyond. In: Cooper, S.B., Löwe, B., Torenvliet, L. (eds.) CiE 2005. LNCS, vol. 3526, pp. 358–367. Springer, Heidelberg (2005). Scholar
  7. 7.
    Mostowski, M.: Truth in the limit. Rep. Mathe. Logic 51, 75–89 (2016)MathSciNetzbMATHGoogle Scholar
  8. 8.
    Priest, G.: Yablo’s paradox. Analysis 57, 236–242 (1997)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Urbaniak, R.: Potential infinity, abstraction principles and arithmetic (Leśniewski style). Axioms 5(2), 18 (2016)CrossRefGoogle Scholar
  10. 10.
    Yablo, S.: Paradox without self-reference. Analysis 53, 251–252 (1993)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.University of WarsawWarsawPoland
  2. 2.University of GdańskGdańskPoland
  3. 3.Ghent UniversityGhentBelgium

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