In Alexander Miller (ed.), Language, Logic,and Mathematics: Themes from the Philosophy of Crispin Wright. Oxford University Press (forthcoming)

Ian Rumfitt
Oxford University
In his essay ‘“Wang’s Paradox”’, Crispin Wright proposes a solution to the Sorites Paradox (in particular, the form of it he calls the ‘Paradox of Sharp Boundaries’) that involves adopting intuitionistic logic when reasoning with vague predicates. He does not give a semantic theory which accounts for the validity of intuitionistic logic (and the invalidity of stronger logics) in that area. The present essay tentatively makes good the deficiency. By applying a theorem of Tarski, it shows that intuitionistic logic is the strongest logic that may be applied, given certain semantic assumptions about vague predicates. The essay ends with an inconclusive discussion of whether those semantic assumptions should be accepted.
Keywords Sorites Paradox  Wang's Paradox  Paradox of Sharp Boundaries  Intuitionistic logic  Topological semantics  Open sets  Regualr open sets  Alfred Tarski  Crispin Wright  Michael Dummett
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References found in this work BETA

Vagueness.Timothy Williamson - 1994 - London and New York: Routledge.
Wang's Paradox.Michael Dummett - 1975 - Synthese 30 (3-4):201--32.
On the Coherence of Vague Predicates.Crispin Wright - 1975 - Synthese 30 (3-4):325--65.
Concepts Without Boundaries.R. M. Sainsbury - 1996 - In Rosanna Keefe & Peter Smith (eds.), Vagueness: A Reader. MIT Press. pp. 186-205.

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