, Volume 195, Issue 11, pp 5007–5019 | Cite as

An entirely non-self-referential Yabloesque paradox

  • Jesse M. Butler


Graham Priest (Analysis 57:236–242, 1997) has argued that Yablo’s paradox (Analysis 53:251–252, 1993) involves a kind of ‘hidden’ circularity, since it involves a predicate whose satisfaction conditions can only be given in terms of that very predicate. Even if we accept Priest’s claim that Yablo’s paradox is self-referential in this sense—that the satisfaction conditions for the sentences making up the paradox involve a circular predicate—it turns out that there are paradoxical variations of Yablo’s paradox that are not circular in this sense, since they involve satisfaction conditions that are not recursively specifiable, and hence not recognizable in the sense required for Priest’s argument. In this paper I provide a general recipe for constructing infinitely many (in fact, continuum-many) such noncircular Yabloesque paradoxes, and conclude by drawing some more general lessons regarding our ability to identify conditions that are necessary and sufficient for paradoxically more generally.


Yablo paradox Circularity Recursive function Self-reference 



An early version of this paper was presented by Jesse M. Butler at the 2009 APA Central Division Meeting in Chicago, Illinois, where Roy T. Cook was the commentator. Sadly, Jesse passed away in 2013 before publishing this work, and Professor Cook graciously volunteered to oversee the refereeing and revision process for the paper. Jesse’s widow—Ivana Simic—would like to gratefully acknowledge all the work Professor Cook has put in to help prepare the paper for publication, despite the fact that it was written more than 10 years ago and that a lot has happened in the discourse on Yablo’s paradox since. Thanks are also owed to two anonymous referees for exceptionally helpful comments.


  1. Barrio, E. (2010). Theories of truth without standard models and Yablo’s sequences. Studia Logica, 96, 377–393.CrossRefGoogle Scholar
  2. Cook, R. (2014). The Yablo paradox: An essay on circularity. Oxford: Oxford University Press.CrossRefGoogle Scholar
  3. Ketland, J. (2005). Yablo’s Paradox and \(\omega \)-inconsistency. Synthese, 145, 295–302.CrossRefGoogle Scholar
  4. Leitgeb, H. (2002). What is a self-referential sentence? Critical remarks on the alleged (non)-circularity of Yablo’s paradox. Logique et Analyse, 177, 3–14.Google Scholar
  5. Picollo, L. (2013). Yablo’s paradox in second-order languages: Consistency and unsatisfiability. Studia Logica, 101, 601–613.CrossRefGoogle Scholar
  6. Priest, G. (1997). Yablo’s paradox. Analysis, 57, 236–242.CrossRefGoogle Scholar
  7. Sorensen, R. (1998). Yablo’s paradox and kindred infinite liars. Mind, 107, 137–155.CrossRefGoogle Scholar
  8. Urbaniak, R. (2009). ”Leitgeb, “About”, Yablo”, Logique et Analyse, 52(207), 239–254.Google Scholar
  9. Yablo, S. (1993). Paradox without self-reference. Analysis, 53, 251–252.CrossRefGoogle Scholar

Copyright information

© Springer Nature B.V. 2017

Authors and Affiliations

  1. 1.GainesvilleUSA

Personalised recommendations