On the Optimality of Vagueness: "Around", "Between", and the Gricean Maxims
This addresses a foundational problem in linguistics and philosophy of language regarding the utility of vagueness, though it is incremental as it builds on existing frameworks like Rational Speech Act models.
The paper tackles the problem of why ordinary language uses vague expressions like 'around', arguing that they offer an optimal tradeoff between truthfulness and informativeness in contexts of imperfect information, showing that vague sentences can be more informative than precise ones by conveying indirect probabilistic information.
Why is ordinary language vague? We argue that in contexts in which a cooperative speaker is not perfectly informed about the world, the use of vague expressions can offer an optimal tradeoff between truthfulness (Gricean Quality) and informativeness (Gricean Quantity). Focusing on expressions of approximation such as "around", which are semantically vague, we show that they allow the speaker to convey indirect probabilistic information, in a way that can give the listener a more accurate representation of the information available to the speaker than any more precise expression would (intervals of the form "between"). That is, vague sentences can be more informative than their precise counterparts. We give a probabilistic treatment of the interpretation of "around", and offer a model for the interpretation and use of "around"-statements within the Rational Speech Act (RSA) framework. In our account the shape of the speaker's distribution matters in ways not predicted by the Lexical Uncertainty model standardly used in the RSA framework for vague predicates. We use our approach to draw further lessons concerning the semantic flexibility of vague expressions and their irreducibility to more precise meanings.