What an Average Semantics Needs

Christopher Kennedy and Jason Stanley

This paper investigates the semantics of sentences that express numerical averages, focusing initially on cases such as The average American has 2.3 children, which have been argued by Chomsky and others to provide evidence against the hypothesis that natural language semantics includes a reference relation holding between words and objects in the world. We develop a fully general and independently justified compositional semantics in which such constructions are assigned truth conditions that are about amounts rather than individuals. We show that this account crucially involves the relation of "parasitic scope", discussed in most detail by Barker (2007), and consider the implications of average sentences for the implementation of this relation in a theory of the syntax-semantics interface.