Idealizing, a speaker endorses or rejects a (declarative) sentence S in a situation s based on how she understands S and represents s. But relatively little is known about how speakers represent situations. Linguists can construct and test initial models of semantic competence, by supposing that sentences have representation-neutral truth conditions, which speakers represent somehow; cf. Marr's (1982) Level One description of a function computed, as opposed to a Level Two description of an algorithm that computes outputs given inputs. But this leaves interesting questions unsettled. One would like to find cases in which S can be held fixed, while modifying s in ways that have predictable effects on the nonlinguistic cognitive systems recruited to evaluate S. Extant work in perceptual psychology offers opportunities for eliciting judgments from speakers in highly controlled settings where something is known about the cognitive systems that speakers recruit when endorsing or rejecting a target sentence. In such settings, behavioral data can reveal aspects of how the human language system interfaces with other systems of cognition that are presumably shared with other species. As an illustration, we focus on the quantificational word “most” and how perception of numerosity is related to the meaning of “Most of the dots are blue,” in the hope that studies of other perceptual systems may provide analogous opportunities for investigating how words are related to prelinguistic representations.