  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.
