Scalar predicates and negation: Punctual semantics and interval interpretations
Many linguists and philosophers hold the view that scalar lexical items are downward bounded semantically and upward bounded only pragmatically via implicatures a Ia Grice. This approach, called by Anscombre and Ducrot (1983) the minimalist view, has been controversial for some twenty years. In this paper, I will examine the minimalist argumentation and will show it to be ill-founded in the case of nuimber names, both empirically and logically. I will then propose another account of their scalar behavior which will preserve the results that motivated the minimalist view, while ascribing a more adequate lexical meaning to scalar predicates in general.