We use imperatives to refute a naïve analysis of update potentials (force-operators attaching to sentences), arguing for a dynamic analysis of imperative force as restrictable, directed, and embeddable. We propose a dynamic, non-modal analysis of conditional imperatives, as a counterpoint to static, modal analyses. Our analysis retains Kratzer's analysis of if-clauses as restrictors of some operator, but avoids typing it as a generalized quantifier over worlds (against her), instead as a dynamic force operator. Arguments for a restrictor treatment (but against (...) a quantificational treatment) are mustered, and we propose a novel analysis of update on conditional imperatives (and an independently motivated revision of the standard ordering-semantics for root modals that makes use of it). Finally, we argue that imperative force is embeddable under an operation much like dynamic conjunction. (shrink)

Quantifier expressions like “many” and “at least” are part of a rich repository of words in language representing magnitude information. The role of numerical processing in comprehending quantifiers was studied in a semantic truth value judgment task, asking adults to quickly verify sentences about visual displays using numerical or proportional quantifiers. The visual displays were composed of systematically varied proportions of yellow and blue circles. The results demonstrated that numerical estimation and numerical reference information are fundamental in encoding the meaning (...) of quantifiers in terms of response times and acceptability judgments. However, a difference emerges in the comparison strategies when a fixed external reference numerosity is used for numerical quantifiers, whereas an internal numerical criterion is invoked for proportional quantifiers. Moreover, for both quantifier types, quantifier semantics and its polarity biased the response direction. Overall, our results indicate that quantifier comprehension involves core numerical and lexical semantic properties, demonstrating integrated processing of language and numbers. (shrink)