Generative approaches to grammar take an Aristotelean view of syntactic categories. Expressions are either a member of a category or they are not, and every member of a category has the same status. Mixed category constructions, which show evidence of being a member of more than one syntactic category at the same time, can raise serious problems for this viewpoint. For example, the word near behaves in many respects like a typical English adjective, yet also shows many properties typical of prepositions. This leads Ross (1972) and others to argue for a categorical continuum, with typical adjectives standing at one end, typical prepositions at the other, and words like near somewhere in the middle. On the other hand, Newmeyer (1998) argues instead that there are in fact (at least) two words near in English - one an adjective and one a preposition - and there is no need for gradient category membership. In this talk, we present the results of quantitative experiments designed to test Newmeyer's hypothesis on the basis of a large collection of English text. We find that there is indeed a strong association among adjectival properties and a strong association among prepositional properties. That is, as Newmeyer would predict, individual occurrences of near tend to either be adjectival or prepositional, but not both. However, this is only a tendency. Intermediate forms, which show a mixture of prepositional and adjectival properties, are well attested, and in fact are not even particularly rare. On the basis of this evidence, it appears that neither Ross's nor Newmeyer's analyses are fully consistent with the facts. Instead, it seems that there is a need for some notion of a categorial prototype which represents a preference for canonical forms while still allowing occurrences of mixed forms.