Interface Transparency and the Psychosemantics of most

This paper proposes and defends an Interface Transparency Thesis concerning how linguistic meanings are related to the cognitive systems that are used to evaluate sentences for truth/falsity: a declarative sentence S is semantically associated with a canonical procedure for determining whether S is true (cf. Dummett 1973, Horty 2007); and while this procedure need not be used as a verification strategy, competent speakers are biased towards strategies that directly reflect canonical specifications of truth conditions. Evidence in favor of this hypothesis comes from a psycholinguistic experiment examining adult judgments concerning ‘Most of the dots are blue’. This sentence is true if and only if the number of blue dots exceeds the number of nonblue dots. But this leaves many issues unsettled—e.g., how the second cardinality is specified for purposes of understanding and/or verification: via the nonblue things, given a restriction to the dots, as in ‘|{x: Dot(x) & ~Blue(x)}|’; via the blue things, given the same restriction, and subtraction from the number of dots, as in ‘|{x: Dot(x)}| − |{x: Dot(x) & Blue(x)}|’; etc. We obtained evidence in favor of the second hypothesis. Participants saw displays of between 2 and 5 colors of dots for 150ms, with between 5 and 17 dots per color. Ratios of blue to non-blue dots ranged between 1:2 and 7:8, with half the trials containing more blue dots and half containing more nonblues. Results indicated use of the Approximate Number System (Dehaene 1997) in verification, with accuracy unaffected by the number of colors. Psychophysical modeling suggests that the number of nonblue dots was specified via subtraction, and that sentences of the form ‘Most Δs are β’ have corresponding meanings, with truth conditions canonically specified along the following lines: |{x: Δ(x) & β(x)}| > |{x: Δ(x)}| − |{x: Δ(x) & β(x)}|.