Walter Dean (Department of Philosophy - University of Warwick)

The unification of the paradoxes of truth and vagueness has been a topic of recurrent philosophical interest (e.g. McGee 1990, Tappenden 1993, Field 2003/2008). I will present a sequence of observations which illustrate how the liar and sorites paradoxes are formally related, culminating in the claim that they give rise to similar sorts of mathematical incompleteness phenomena. A central tool will be the use of the arithmetized completeness theorem to provide interpretations of putatively paradoxical notions within the language of first-order arithmetic.

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