Pablo Cobreros

Tolerant, Classical, Strict

In this paper we investigate a semantics for first-order logic originally proposed by R. van Rooij to account for the idea that vague predicates are tolerant, that is, 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 to model similarity, 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. We characterize the space of consequence relations definable in terms of those and discuss the kind of solution this gives to the sorites paradox. We discuss some applications of the framework to the pragmatics and psycholinguistics of vague predicates, in particular regarding judgments about borderline cases.

Vagueness, Truth and Permissive Consequence

We say that a sentence A is a permissive consequence of a set of premises Γ whenever, if all the premises of Γ hold up to some standard, then A holds to some weaker standard. In this paper, we focus on a three-valued version of this notion, which we call strict-to-tolerant consequence, and discuss its fruitfulness toward a unified treatment of the paradoxes of vagueness and self-referential truth. For vagueness, st-consequence supports the principle of tolerance; for truth, it supports the requisit of transparency. Permissive consequence is non-transitive, however, but this feature is argued to be an essential component to the understanding of paradoxical reasoning in cases involving vagueness or self-reference.

Tolerance and Mixed Consequence in the S'valuationist Setting

In a previous paper (see ‘Tolerant, Classical, Strict’, henceforth TCS) we investigated a semantic framework to deal with the idea that vague predicates are tolerant, namely that small changes do not affect the applicability of a vague predicate even if large changes do. Our approach there rests on two main ideas. First, given a classical extension of a predicate, we can define a strict and a tolerant extension depending on an indifference relation associated to that predicate. Second, we can use these notions of satisfaction to define mixed consequence relations that capture non-transitive tolerant reasoning. Although we gave some empirical motivation for the use of strict and tolerant extensions, making use of them commits us to the view that sentences of the form ‘

Pragmatic Interpretations of Vague Expressions: Strongest Meaning and Nonmonotonic Consequence

{p {\vee} {\neg} p}

Supervaluationism and Fara's Argument concerning Higher-Order Vagueness

’ and ‘

Comparing Some Substructural Strategies Dealing with Vagueness

{p {\wedge} {\neg} p}