Parts of a Whole: Distributivity as a Bridge between Aspect and Measurement
This book uses mathematical models of language to explain why there are certain gaps in language: things that we might expect to be able to say but can't. For instance, why can we say I ran for five minutes but not *I ran all the way to the store for five minutes? Why is five pounds of books acceptable, but *five pounds of book not acceptable? What prevents us from saying *sixty degrees of water to express the temperature of the water in a swimming pool when sixty inches of water can express its depth? And why can we not say *all the ants in my kitchen are numerous? The constraints on these constructions involve concepts that are generally studied separately: aspect, plural and mass reference, measurement, and distributivity. In this book, Lucas Champollion provides a unified perspective on these domains, connects them formally within the framework of algebraic semantics and mereology, and uses this connection to transfer insights across unrelated bodies of literature and formulate a single constraint that explains each of the judgments above.
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adnominal adverbial algebraic closure algebraic semantics analysis anaphoric applies assume assumption atelic predicates atomic bought two sausages Champollion Chapter collective predicates constraint context count nouns covert distributivity cumulative readings cumulative reference definition denotation dimension parameter discussed in Section DIST distance-distributive items distributive constructions distributive items distributive predicates distributive reading distributivity operator divisive reference domain Dowty entails event predicate events whose agents example for-adverbials formal granularity parameter group nouns hour implicature individuals interpretation intervals intuition involve reference jeweils John pushed carts Kratzer Krifka Landman Lasersohn lexical cumulativity mass nouns meaning postulates measure functions mereological minimal-parts problem Moltmann nonatomic distributivity noun phrases overt parthood phrasal distributivity presupposition proposal pseudopartitives relation requirement runtime salient Schwarzschild 1996 sentence spatial strata theory strata-based approach stratified reference subevents subgroups subinterval property sum event syntactic temporal thematic roles theme thirty zebras universal quantifier verb phrase Zimmermann 2002b