**Speaker**: Adele Mortier (MIT)

**Time**: Friday October 4, 2pm

**Location**: 32-D461

**Abstract**: Numerical approximation expressions are expressions of the form “around n”, “approximately n”, where n is a number. They can include an explicit unit, and the n can be decimal or a round number.

(1) Around 15 people came to the party

(2) Sue ran around 6 miles

(3) The film’s average rating is around 3.5

Numerical approximation is challenging as it is used very commonly in everyday conversations, without apparent problems. Yet these expressions seem to carry inherent vagueness: is (1) felicitous if 15 people came? What about 21 people? 22? Is 20 more probable than 22? This might suggest that people tend to enrich their interpretation using the context as well as their knowledge of the world to get more precise inferences. We make the assumption that such inferences rely on classical pragmatic processes, very much alike scalar implicatures (granularity implicatures, [Cummins et al., 2012]). We also argue that these inferences can be modeled, if not explained, by probabilistic Bayesian reasoning (some variants of the RSA, [Kennedy, 2007, Lassiter and Goodman, 2013]). To back up this theory, we present experimental data about the probabilistic inferences drawn by people facing numerical approximation expressions (round numbers, no unit). The most basic results corroborate prevalent intuitions about numerical approximation (symmetry of the distribution, granularity effects). More refined (and disputable) results seem to support the hypothesis that a vague expression like “around” differs from a more exact (but underspecified) expression like “between”, as they do not give rise to the same kind of subjective probability distribution (posterior). However, another experiment would be needed to better control for unwanted order effects between items, because they are likely to explain a huge part of the observed variability.Your feedback is of course very welcome!