Sentences with definite plurals display a property known as 'homogeneity': (1a) is true if John read (roughly) all of the books, (1b) is true if he read none of the books. If he read half of the books, neither sentence is true.
I will argue that homogeneity and non-maximality (i.e. tolerance for irrelevant exceptions) should be linked, as both of these properties are shared by a variety of constructions (plurals, conditionals, generics), and present a theory on which non-maximality is a pragmatic phenomenon that arises from the interaction of a trivalent semantics with pragmatic principles.
A number of welcome empirical predictions of this approach will be explored, including some that arise from a more detailed view on what exactly homogeneity consists in for various classes of predicates.