Theoretical linguistics postulates abstract structures that successfully explain key aspects of language. However, the precise relation between abstract theoretical ideas and empirical data from language use is not always apparent. Here, we propose to empirically test abstract semantic theories through the lens of probabilistic pragmatic modelling. We consider the historically important case of quantity words (e.g., `some', `all'). Data from a large-scale production study seem to suggest that quantity words are understood via prototypes. But based on statistical and empirical model comparison, we show that a probabilistic pragmatic model that embeds a strict truth-conditional notion of meaning explains the data just as well as a model that encodes prototypes into the meaning of quantity words.