The Shape of Modified Numerals

The pattern of implicatures of modified numeral `more than n' depends on the roundness of n. Cummins, Sauerland, and Solt (2012) present experimental evidence for the relation between roundness and implicature patterns, and propose a pragmatic account of the phenomenon. More recently, Hesse and Benz (2020) present more extensive evidence showing that implicatures also depend on the magnitude of n and propose a novel explanation based on the Approximate Number System (Dehaene 1999). Despite the wealth of experimental data, no formal account has yet been proposed to characterize the full posterior distribution over numbers of a listener after hearing `more than n'. We develop one such account within the Rational Speech Act framework, quantitatively reconstructing the pragmatic reasoning of a rational listener. We show that our pragmatic account correctly predicts various features of the experimental data.