Chris Kennedy

This talk investigates the semantics of sentences that express numerical averages, such as (1)-(3).

1. Although we did not measure this in our study, I can say from other work the average German sees his doctor 13 times a year, the average Swiss sees his doctor 7.5 times a year and the average Briton 3.5 times. (British National Corpus)
2. Another study, by British researchers, stated that men had 12.7 heterosexual partners in their lifetimes on  average and women had 6.5. (New York Times, 8.12.07)
3. NYU has reported that the 53 teens have lost an average of half of their excess weight over the past year, and that’s truly excellent, considering that their average weight was 297 pounds at the beginning! (July 7, 2007 post to www.fitnessblogonline.com)

We begin with a discussion of the use of 'average' in definite descriptions, as in (1), which has been argued by Chomsky, Hornstein and others to provide an argument against the hypothesis that natural language semantics includes a reference relation mapping words to objects in the world. We then develop an analysis in which the definite construction in (1), the adverbial construction in (2) and the nominal construction in (3) all involve truth conditions that are about amounts rather than individuals, and involve interpretive operations that are independently necessary for other, related constructions (in particular comparatives and prenominal 'same/different').  Finally, we show both how our analysis defuses the arguments against a reference relation that have been presented on the basis of (1), and that an empirically adequate account of the full range of sentences that describe numerical averages supports two more general conclusions about the syntax-semantics interface. First, numerals must be able to take scope independently of the nouns they modify. Second, it is not always the case that the function created by abstracting over the base position of a scope-bearing element composes with the scopal term (as in e.g. Heim and Kratzer 1998); instead, this function may compose with a third element intervening between the scopal term and its base position.