Program


Pablo Cobreros (Univ. of Navarra), Paul Egré (IJN), David Ripley (IJN), Robert van Rooij (ILLC, Amsterdam)

Tolerant, Classical, Strict


In this paper we investigate a semantic framework originally defined by van Rooij (2010) to account for the idea that vague predicates are tolerant, namely for the principle that if x is P, then y should be P whenever y is similar enough to x.  The semantics, which makes use of indifference relations in order to capture the notion of similarity relevant for the application of vague predicates, rests on the interaction of three notions of truth: the classical notion, and two dual notions simultaneously defined in terms of it, which we call tolerant truth and strict truth. Basically, a vague predicate P is said to hold tolerantly of an object x provided there is an object y similar enough to x in the relevant respects that satisfies P classically. Dually, a vague predicate is said to hold strictly of an object provided it holds classically of all objects that are similar enough in the relevant respects.

In the first part of the paper, we explain how the semantics allows us to validate the tolerance principle and to solve the sorites paradox. We characterize, in particular, the space of consequence relations definable on the basis of the notions of classical, strict and tolerant truth at hand. We present and discuss some correspondences and differences between our approach and other approaches used to deal with vagueness (in particular supervaluationism, subvaluationism, and many-valued logics).

A specificity of the notion of tolerant truth we get is that it is paraconsistent: in particular, it implies that borderline cases are tolerantly P and not P (while they are neither strictly P nor strictly not P). We argue for the plausibility of this conception. In particular, we discuss how the framework can be used to accommodate the recent experimental data by Ripley (2009) and Alxatib and Pelletier (2010) regarding the way subjects respond to classical contradictions and tautologies for borderline cases. If time permits, we will also discuss the connection between the present framework and other characterizations of borderline cases based on the notion of similarity, in particular Douven et al.'s recent topological approach.