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Why is ordinary language vague? We argue that in contexts in which acooperative speaker is not perfectly informed about the world, the use of vagueexpressions can offer an optimal tradeoff between truthfulness (GriceanQuality) and informativeness (Gricean Quantity). Focusing on expressions ofapproximation such as "around", which are semantically vague, we show that theyallow the speaker to convey indirect probabilistic information, in a way thatcan give the listener a more accurate representation of the informationavailable to the speaker than any more precise expression would (intervals ofthe form "between"). That is, vague sentences can be more informative thantheir precise counterparts. We give a probabilistic treatment of theinterpretation of "around", and offer a model for the interpretation and use of"around"-statements within the Rational Speech Act (RSA) framework. In ouraccount the shape of the speaker's distribution matters in ways not predictedby the Lexical Uncertainty model standardly used in the RSA framework for vaguepredicates. We use our approach to draw further lessons concerning the semanticflexibility of vague expressions and their irreducibility to more precisemeanings.

On the Optimality of Vagueness: "Around", "Between", and the Gricean Maxims