Supervaluationism and Logical Consequence: A Third Way

Abstract

It is often assumed that the supervaluationist theory of vagueness is committed to a global notion of logical consequence, in contrast with the local notion characteristic of modal logics. There are, at least, two problems related to the global notion of consequence. First, it brings some counterexamples to classically valid patterns of inference. Second, it is subject to an objection related to higher-order vagueness. This paper explores a third notion of logical consequence, and discusses its adequacy for the supervaluationist theory. The paper proceeds in two steps. In the first step, the paper provides a deductive notion of consequence for global validity using the tableaux method. In the second step, the paper provides a notion of logical consequence which is an alternative to global validity, and discusses i) whether it is acceptable to the supervaluationist and ii) whether it plays a better role in a theory of vagueness in the face of the problems related to the global notion.

Tolerant, Classical, Strict

“…Two is the maximum number of steps that ensure tolerance, however. 4 Consider, for instance, a T-model M with four elements a, b , c, d…”

“…This means that all premises of a standard sorites 4 What if we wanted to validate only the 1-step version of tolerance, and not the 2-step version? A possibility is to ask for similarity relations to be reflexive, but not necessarily to be symmetric.…”

Paraconsistent vagueness: a positive argument

“…Some authors, however, hold a supervaluationist-like treatment of vagueness but endorse local consequence instead (for exampleVarzi 2007 andAsher et al 2009; see myCobreros (2010a) for discussion on Varzi's arguments). I hold that supervaluationism is committed to a third alternative between local and global consequence (inCobreros 2008Cobreros , 2010b. In order to concentrate on the arguments in this paper I leave the discussion of this issue for a better occasion, but just two quick remarks on the strategy of linking supervaluationism to local consequence.…”

Vague Analysis

“…For notions of supervaluationist validity distinct from these, seeVarzi (2007) andCombreros (2008).9 The "respect" here is that the tolerance principle is not denied-the principle is not false, on the threevalued approach.…”