David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Studia Logica 101 (3):601-617 (2013)
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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References found in this work BETA
Hartry H. Field (2008). Saving Truth From Paradox. Oxford University Press.
Saul A. Kripke (1975). Outline of a Theory of Truth. Journal of Philosophy 72 (19):690-716.
Stewart Shapiro (1991). Foundations Without Foundationalism: A Case for Second-Order Logic. Oxford University Press.
Stephen Yablo (1993). Paradox Without Self--Reference. Analysis 53 (4):251-252.
Citations of this work BETA
David Ripley (2015). The Yablo Paradox: An Essay on Circularity By Roy T. Cook. Analysis 75 (3):523-525.
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