One of the success stories in formal semantics is the analysis of NPs as generalized quantifiers, which can be traced back from Barwise & Cooper (1981) via Montague to Frege. The great attraction of this analysis is that it allows for a compositional analysis of the meariing of noun phrases that is consistent with independently motivated assumptions about their syntax. For example, Barwise and Cooper analyze NPs like every bay, a bay, three bays and n0 bay as having the syntactic structure [Det N], and interpretations as second-order predicates, as follows: