Journal of Logic, Language and Information

, Volume 22, Issue 1, pp 23–31 | Cite as

Equiparadoxicality of Yablo’s Paradox and the Liar

  • Ming Hsiung


It is proved that Yablo’s paradox and the Liar paradox are equiparadoxical, in the sense that their paradoxicality is based upon exactly the same circularity condition—for any frame \({\mathcal{K}}\), the following are equivalent: (1) Yablo’s sequence leads to a paradox in \({\mathcal{K}}\); (2) the Liar sentence leads to a paradox in \({\mathcal{K}}\); (3) \({\mathcal{K}}\) contains odd cycles. This result does not conflict with Yablo’s claim that his sequence is non-self-referential. Rather, it gives Yablo’s paradox a new significance: his construction contributes a method by which we can eliminate the self-reference of a paradox without changing its circularity condition.


Circularity Equiparadoxical Liar paradox T-schema Yablo’s paradox 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Beall J. C. (2001) Is Yablo’s paradox non-circular?. Analysis 61: 176–187CrossRefGoogle Scholar
  2. Bolander, T. (2003). Logical theories for agent introspection. PhD thesis, Technical University of Denmark.Google Scholar
  3. Bueno O., Colyvan M. (2003) Paradox without satisfaction. Analysis 63: 152–156CrossRefGoogle Scholar
  4. Bueno O., Colyvan M. (2003) Yablos paradox and referring to infinite objects. Australasian Journal of Philosophy 81: 402–412CrossRefGoogle Scholar
  5. Bueno, O., & Colyvan, M. (2011): Yablo paradox rides again: A reply to Ketland.
  6. Butler, J. (2008). An infinity of undecidable sentences.
  7. Cook R. T. (2004) Patterns of paradox. Journal of Symbolic Logic 69: 767–774CrossRefGoogle Scholar
  8. Cook R. T. (2006) There are non-circular paradoxes (But Yablo’s Isn’t One of Them!). The Monist 89: 118–149CrossRefGoogle Scholar
  9. Hsiung M. (2009) Jump Liars and Jourdain’s card via the relativized T-scheme. Studia Logica 91: 239–271CrossRefGoogle Scholar
  10. Ketland J. (2005) Yablo’s paradox and ω-inconsistency. Synthese 145: 295–302CrossRefGoogle Scholar
  11. Leitgeb H. (2005) What truth depends on. Journal of Philosophical Logic 34: 155–192CrossRefGoogle Scholar
  12. Löwe, B. (2006). Revision forever!. In H. Schärfe, P. Hitzler & P. Øhrstrøm (Eds.), Conceptual structures: inspiration and application 14th international conference on conceptual structures, ICCS. Lecture notes in computer science (pp. 22–36). Berlin: Springer.Google Scholar
  13. Priest G. (1997) Yablo’s paradox. Analysis 57: 236–242CrossRefGoogle Scholar
  14. Schlenker P. (2007) The elimination of self-reference: Generalized Yablo-series and the theory of truth. Journal of Philosophical Logic 36: 251–307CrossRefGoogle Scholar
  15. Schlenker P. (2007) How to eliminate self-reference: A précis. Synthese 158: 127–138CrossRefGoogle Scholar
  16. Sorensen R. (1998) Yablo’s paradox and kindred infinite liars. Mind 107: 137–155CrossRefGoogle Scholar
  17. Yablo S. (1985) Truth and reflection. Journal of Philosophical Logic 14: 297–349CrossRefGoogle Scholar
  18. Yablo S. (1993) Paradox without self-reference. Analysis 53: 251–252Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2012

Authors and Affiliations

  1. 1.School of Politics and AdministrationSouth China Normal UniversityGuangzhouPeople’s Republic of China

Personalised recommendations