Semantic values as latent parameters: Testing a fixed threshold hypothesis for cardinal readings of few & many

Abstract Certain uses of vague quantifiers few and many intuitively compare a true quantity to a priori expectations about that quantity. A concrete proposal for the truth conditions of such readings stipulates a contextually-stable threshold on a contextually-variable representation of a priori expectations (Clark, H. H. 1991. Words, the world, and their possibilities. In Lockhead G. R. & Pomerantz J. R. (eds.), The perception of structure: Essays in honor of Wendell R Garner, 263–277. Washington, DC: American Psychological Association; Fernando, T. & H. Kamp. 1996. Expecting many. In Galloway T. & Spence J. (eds.), Proceedings of SALT VI, 53–68. Ithaca, NY: Cornell University.) The main goal of this paper is to introduce data-driven computational modeling as a means to implement and test complex semantic theories of this kind, which may be hard to assess based on solitary introspection of meaning intuitions. Based on an empirical measure of a priori expectations, we use Bayesian inference to estimate likely values of the latent threshold parameters given empirical data from production and comprehension tasks. We demonstrate how posterior inference and statistical model comparison can help assess the plausibility of the fixed threshold hypothesis.