Speaker: Brian Buccola (McGill University) Time: Wednesday, October 8, 3:30-5pm (note exceptional time!) Location: 32-D461 Title: Global semantic constraints: the case of van Benthem’s problem
Any adjectival theory of numeral modifiers faces a challenge known as van Benthem’s problem (van Benthem, 1986), whereby non-upward-monotone quantifiers like “fewer than three” give rise to inadequate truth conditions. I propose a novel solution based on general economy principles for LF availability: certain LFs are generated by the grammar but unavailable (blocked) by virtue of (i) their semantic equivalence to LFs of syntactically simpler sentences, and (ii) the simultaneous availability of other, non-trivial LFs. The equivalence check is shown to rely crucially on the distributivity-collectivity properties of the predicates, in particular on whether the predicates distribute to at least some (not necessarily every) subpart (not necessarily atomic). The proposal therefore makes strong predictions regarding the interpretations of sentences with negative (and other) quantifiers and various predicates along the distributive-collective spectrum, which I show are borne out.