Varzi on Supervaluationism and Logical Consequence Pablo Cobreros University of Navarra pcobreros@unav.es Though it is standardly assumed that supervaluationism applied to vagueness is committed to global validity, Achille Varzi (2007) argues that the supervaluationist should take seriously the idea of adopting local validity instead. Varzi’s motivation for the adoption of local validity is largely based on two objections against the global notion: that it brings some counterexamples to classically valid rules of inference and that it is inconsistent with unrestricted higher-order vagueness. In this discussion I review these objections and point out ways to address them not considered in Varzi’s paper. 1. Supervaluationism and logical consequence The supervaluationist theory interprets vagueness as a matter of under- determination of meaning. A vague expression like ‘bald’ can be made precise in several ways consistent with the use we make of it. Where Peter is a borderline case of ‘bald’, the sentence ‘Peter is bald’ will be true on some ways of making ‘bald’ precise and false on others. Since each way of making ‘bald’ precise is consistent with our use, our use does not decide the correct way of making that term precise. As a consequence, the truth-value of the sentence ‘Peter is bald’ is left unsettled. The fact that supervaluationism is a truth-gap theory is conveyed in the slogan that ‘truth is supertruth’: a sentence f is true in an interpretation just in case it is true in every admissible precisification (admissible ways of making the language precise) in that interpret- ation. Falsity is defined as truth of the negation. Truth-value gaps are allowed under this reading of ‘truth’. It is standardly assumed that logical consequence is a matter of necessary preservation of truth. Since for the supervaluationist truth is supertruth, logical consequence in the supervaluationist theory should preserve truth in all precisifications. More explicitly, a sentence f is a logical consequence of a set of sentences À just in case for every Mind, Vol. 120 . 479 . July 2011 ß Cobreros 2011 doi:10.1093/mind/fzq069 Advance Access publication 30 November 2010 Downloaded from https://academic.oup.com/mind/article/120/479/833/1131924 by guest on 02 May 2023