Studia Logica

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

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

Article

Abstract

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.

Keywords

Paradoxicality Consistency Ω-Inconsistency Second-order languages Unsatisfiability Finiteness 

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Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.Department of PhilosophyUniversity of Buenos AiresBuenos AiresArgentina

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