Title: Parts of a whole: Distributivity as a bridge between aspect and measurement
Committee: Cleo Condoravdi (advisor), Aravind Joshi (committee chair), Maribel Romero, Florian Schwarz (with special thanks to Tony Kroch)
Why can I tell you that I "slept for five hours" but not that I "slept in five hours"? Why can you say that there are "five pounds of books" or "more books than needed" in this package if it contains several books, but not "five pounds of book" or "more book than needed" if it contains only one? What keeps you from using "sixty degrees of water" to tell me the temperature of the water in your pool when you can use "sixty inches of water" to tell me its height? And what goes wrong when I suggest to you that we should "each have lunch together"?
It is common in semantics to explain the constraints on these constructions by appealing to concepts from separate domains: atelicity, plural and mass reference, monotonicity of measurement, distributivity. This dissertation moves beyond this compartmentalized view to argue that the constructions illustrated above -- measure adverbials, pseudopartitives, comparatives, and distributive constructions -- are in fact systematically related, and that the concepts just mentioned capture the same thing viewed from different angles. Known and novel parallels across these domains are subsumed under a generalized notion of distributivity: a predicate that holds of a certain entity or event is presupposed to hold of its parts along a certain dimension and down to a certain granularity. This notion is made formally precise within the framework of mereological semantics (Link 1983, Krifka 1998). By abstracting over the temporal parameter of the subinterval property, a classical formalization of atelicity (Bennett and Partee 1972), we gain the means to express a single constraint that characterizes the properties of distributive constructions in this new, generalized sense and that predicts a wide range of facts across different domains, including the judgments above. This constraint not only subsumes existing characterizations of aspect and monotonicity by Dowty, Link, Krifka, and Schwarzschild, but also surpasses them in terms of descriptive accuracy.
The emerging picture is one in which a large class of constructions impose an identical distributivity presupposition that is relativized to two parameters. The first one is dimension: a thematic role in the case of "each", time or space in the case of "for"-adverbials, measure functions in the case of partitives and comparatives. The second parameter is granularity: atomicity in count domains, context-dependent size in nonatomic domains such as mass, time, space and scales of measurement.