Why is our 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 gives the
listener a more accurate representation of the information available to the
speaker than any more precise expression would (intervals of the form
"between"). 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. Our model
differs in substantive ways from the Lexical Uncertainty model often used
within the RSA framework for vague predicates