Vagueness Is Rational under Uncertainty

We seek to show that some properties of vague scalar adjectives are consequences of rational communication. Theories of vagueness are usually directed at a cluster of traditional philosophical desiderata: how vagueness fits into a theory of truth (or metaphysics), the sorites, and related issues. These are important, and we will have more to say about some of them, but we also seek to refocus the analysis of vagueness, moving away from consideration of abstract philosophical problems, and towards consideration of the problems faced by ordinary language users. It is our contention that it is by considering the latter that the former can best be understood. Using standard mathematical tools, we suggest that, given a certain model of communication, what have typically been taken to be puzzles in the truth conditions of vague expressions, should just be expected consequences of communication under uncertainty. The most basic criterion for any successful semantic theory is that it should establish when sentences are true, and when they are false. This is a tall order as regards sentences involving vague predicates. Some scholars settle for giving definite truth values for only a subset of conditions in the world, or for abandoning truth in favor of some notion of acceptability. We have no a priori argument against theories which attribute partial or fuzzy truth conditions to vague sentences, and no a priori argument against theories stated in terms of acceptability, but prefer to retain classical semantics. W e will not claim that it is always possible to specify objective boolean truth values for every vague sentence even with complete knowledge of the utterance situation and speaker, but we will offer a theory which allows that every vague sentence has a boolean truth value, and we will offer a theory of how speakers can and must approximate it.