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What an Average Semantics Needs

The mystery of (1a-b) is that it seems that they can be true, even though there is no person in the world that is the reference of the noun phrases the average American and the average Freddie Voter, and no person in the world that has 2.3 children. (1c) makes a similar point, though in a somewhat different fashion: while the property of seeing one’s doctor 7.5 times per year is not incoherent in the same way as the property of having 2.3 children, the truth of (1c) does not commit us to the existence of any individuals who actually have this property. Both linguists and philosophers have used average sentences to draw dramatic conclusions of various sorts. For example, Norbert Hornstein and Noam Chomsky have used this class of sentences to argue that semantic theory does not exploit a reference relation, a relation between words and things (Hornstein 1984, Chomsky 2000). Similarly, some philosophers have used these sentences to argue that singular reference is not ontologically committing. Such conclusions are far too hasty. Those who based dramatic conclusions about the nature of semantics or ontological commitment on average sentences are unfairly exploiting the lack of a compositional semantics for sentences of this sort. In this paper, we provide the first such semantics. Moreover, we show that within the referential approach to semantics one can provide a detailed compositional semantics of these constructions that reveals much of specific linguistic interest. Specifically, average sentences provide new evidence that the compositional system of natural language must allow for the possibility that the nuclear scope of of a scope-taking term may serve as the argument of a third expression, rather than the scope-taking term itself, a relation that Barker (2007) refers to as PARASITIC SCOPE.