Distributivity, lexical semantics, and world knowledge
Keywords: Linguistics.

A predicate is understood distributively if it is inferred to be individually true of each member of a plural subject, nondistributively if not. "Alice and Bob smiled" conveys that Alice smiled and Bob smiled (distributive); "Alice and Bob met" conveys that they met jointly (nondistributive); "Alice and Bob opened the window" can describe a situation in which they each did so (distributive), or one in which they did so only jointly (nondistributive). These facts raise a compositional semantics question and a lexical semantics question. The compositional semantics question has been discussed widely: how should these sentences be represented semantically? To what extent should such representations capture inferences about distributivity? The lexical semantics question has received less attention: which predicates are understood in which ways? Certainly these inferences are grounded in the events described by these predicates (smile is distributive because people have their own faces and can only smile individually); but which further predicates behave like "smile", like "meet", or like "open the window", and why? To make progress on the lexical semantics question, this dissertation presents the Distributivity Ratings Dataset, over 2300 verb phrases (built from the verbs of Levin 1993) rated for their distributivity potential by online annotators. This dataset provides evidence consistent with a series of far-reaching hypotheses: that predicates describing the action of an individual body or mind ("smile", "faint", "swallow a pill") are distributive given that individuals have their own bodies and minds; that predicates describing inherently multilateral actions ("meet", "gather") are nondistributive given that individuals such as Alice cannot carry out these actions unilaterally; that causative predicates ("open a window", describing an action where the subject causes the object to change) can (but need not) be nondistributive given that multiple individuals' actions may be jointly but not individually sufficient to cause a result; and finally, that predicates with incremental objects (objects whose parts correspond to the parts of the event described by the predicate, as in "eat the pizza") can also be nondistributive, given that each member of a plural subject might carry out the verb event on a different portion of the object, only jointly adding up to the whole. Turning from verb phrases to adjectives, the dissertation draws on tools from measurement theory to argue that a gradable adjective's potential for distributivity depends on the nature of the scale associated with it (assuming that gradable adjectives relate individuals to "degrees" along a scale). A predicative adjective can be understood nondistributively (as when "the boxes are heavy" conveys that the boxes are jointly but not individually heavy) if the scale associated with the adjective behaves "positively" with respect to concatenation: if the weight of two boxes together exceeds the weight of each one. That way, the contextual standard for what counts as "heavy" can be set in such a way that two boxes together exceed it, while each box individually falls short of it — nondistributive, because heavy is true of the two boxes together, but not of each one alone. Other adjectives are not associated with scales that behave in this way, explaining why they are only understood distributively: "the boxes are new" conveys that each box is new (distributive), not that they are new jointly, because two boxes together are no newer than each one. In sum, this dissertation puts forward a series of large-scale generalizations about how the distributivity potential of various verbal and adjectival predicates is derived from the nature of the events and properties that they describe. Turning to the compositional semantics question, the dissertation advocates for an underspecified semantic representation in which a predicate is true of each cell of a contextually supplied cover (set of subparts) of its plural subject. All inferences about distributivity are framed as inferences about which cover(s) to entertain, given what is known about the event or property described by the predicate and how the members of the subject can participate in it. This semantic analysis does not explain anything on its own, but becomes explanatory when combined with a predictive analysis of which predicates can be understood in which ways. In this way, the compositional semantics question and the lexical semantics question are framed as complements to one another: an underspecified compositional representation is supplemented with an articulated theory of how a predicate's distributivity potential depends on the nature of the event or state it describes. While distributivity has traditionally been studied as a topic for compositional semantics, it is defined by the observation that different predicates ("smile", "meet", "open the window"; "heavy", "new") act differently from one another, making it a lexical semantics topic from the start. This dissertation aims to illuminate it by treating it as one.