Studia Logica

, Volume 101, Issue 3, pp 601–617 | Cite as

Yablo’s Paradox in Second-Order Languages: Consistency and Unsatisfiability



Stephen Yablo [23,24] introduces a new informal paradox, constituted by an infinite list of semi-formalized sentences. It has been shown that, formalized in a first-order language, Yablo’s piece of reasoning is invalid, for it is impossible to derive falsum from the sequence, due mainly to the Compactness Theorem. This result casts doubts on the paradoxical character of the list of sentences. After identifying two usual senses in which an expression or set of expressions is said to be paradoxical, since second-order languages are not compact, I study the paradoxicality of Yablo’s list within these languages. While non-paradoxical in the first sense, the second-order version of the list is a paradox in our second sense. I conclude that this suffices for regarding Yablo’s original list as paradoxical and his informal argument as valid.


Paradoxicality Consistency Ω-Inconsistency Second-order languages Unsatisfiability Finiteness 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Barrio E.: Theories of truth without Standard Models and Yablo’s sequences. Studia Logica 96, 375–391 (2010)CrossRefGoogle Scholar
  2. 2.
    Belnap N., Gupta A.: The Revision Theory of Truth. MIT Press, Cambridge (1993)Google Scholar
  3. 3.
    Benacerraf P., Wright C.: Skolem and the Skeptic. Proceedings of the Aristotelian Society, Supplementary Volume 56, 85–115 (1985)Google Scholar
  4. 4.
    Bolander, T., V. F. Hendricks, and S. A. Pedersen (eds.), Self-Reference, CSLI Publications, Stanford, 2004.Google Scholar
  5. 5.
    Cook R.T.: Patterns of paradox. The Journal of Symbolic Logic 69(1), 767–774 (2004)Google Scholar
  6. 6.
    Cook R.T.: There are non-circular paradoxes (but Yablo’s Isn’t One of Them!). The Monist 89(1), 118–149 (2006)CrossRefGoogle Scholar
  7. 7.
    Dedekind, R., Was sind und was sollen die zahlen?, in William B. Ewald (ed.), From Kant to Hilbert: A Source Book in the Foundations of Mathematics, Oxford University Press, Oxford, 1996, pp. 787–832.Google Scholar
  8. 8.
    Ewald W.B.: (ed.), From Kant to Hilbert: A Source Book in the Foundations of Mathematics. Oxford University Press, New York (1996)Google Scholar
  9. 9.
    Field H.: Saving Truth from Paradox. Oxford University Press, New York (2008)CrossRefGoogle Scholar
  10. 10.
    Forster, T., The significance of Yablo’s paradox without self-reference,, 1996.
  11. 11.
    Halbach V.: Axiomatic Theories of Truth. Cambridge University Press, New York (2011)CrossRefGoogle Scholar
  12. 12.
    Hardy J.: Is Yablo’s paradox liar-like?. Analysis 55(3), 197–198 (1995)CrossRefGoogle Scholar
  13. 13.
    Ketland J.: Bueno and Colyvan on Yablo’s paradox. Analysis 64, 165–172 (2004)CrossRefGoogle Scholar
  14. 14.
    Ketland J.: Yablo’s paradox and ω-inconsistency. Synthese 145, 295–307 (2005)CrossRefGoogle Scholar
  15. 15.
    Kripke S.: Outline of a theory of truth. The Journal of Philosophy 72, 690–716 (1975)CrossRefGoogle Scholar
  16. 16.
    Leitgeb H.: Theories of truth which have no standard models. Studia Logica 68, 69–87 (2001)CrossRefGoogle Scholar
  17. 17.
    Leitgeb H.: What is a self-referential sentence? Critical remarks on the alleged (non-)circularity of Yablos paradox. Logique and Analyse 177, 3–14 (2002)Google Scholar
  18. 18.
    Priest G.: The structure of the paradoxes of self-reference. Mind 103, 25–34 (1994)CrossRefGoogle Scholar
  19. 19.
    Priest G.: Yablo’s paradox. Analysis 57, 236–242 (1997)CrossRefGoogle Scholar
  20. 20.
    Shapiro S.: Foundations Without Foundationalism: A Case for Second-Order Logic. Oxford University Press, New York (1991)Google Scholar
  21. 21.
    Sorensen R.A.: Yablo’s paradox and kindred infinite liars. Mind 107, 137–155 (1998)CrossRefGoogle Scholar
  22. 22.
    Tennant N.: On paradox without self-reference. Analysis 55, 199–207 (1995)CrossRefGoogle Scholar
  23. 23.
    Yablo S.: Truth and reflexion. Journal of Philosophical Logic 14, 297–349 (1985)CrossRefGoogle Scholar
  24. 24.
    Yablo S.: Paradox without self-reference. Analysis 53, 251–252 (1993)CrossRefGoogle Scholar
  25. 25.
    Yablo, S., Circularity and paradox, in T. Bolander, V. F. Hendricks, and S. A. Pedersen (eds.), Self-Reference, CSLI Publications, Stanford, 2004, pp. 139–157.Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.Department of PhilosophyUniversity of Buenos AiresBuenos AiresArgentina

Personalised recommendations