Voting and vagueness

Abstract

How to handle vagueness? One way is to introduce the machinery of acceptable sharpenings, and reinterpret truth as truth-in-all-sharpenings (supervaluationism) or truth-in-some-sharpenings (subvaluationism). A major selling point has been the conservativism of the resulting systems with respect to classical theoremhood and inference. Supervaluationism and subvaluationism possess interesting formal symmetries, a fact that has been used to argue for the subvaluationist approach. However, the philosophical motivation behind each is a different matter. Subvaluationism comes with a standard story (due to Stanislaw Jaśkowski) that is difficult to sign up to. In this paper, I make use of a variant of Putnam's well-known idea of linguistic deference, and some results in voting theory, to answer this criticism of subvaluationism. The acceptability intuitions of each member of a linguistic community amount to their voting for one or more acceptable sharpenings, with truth then characterised as truth-in-a-(contextually-determined)-sufficiency-of-sharpenings. This produces a family of logical systems that are close relations of subvaluationism, share its conservatism results, yet have stronger philosophical foundations in the workings of externalist content.