In this paper, I give a semantic account of the grammaticality of the negative particle not with noun phrases in English. On the way to developing my solution, I explore a few previous attempts at this problem, including an extension of Horn’s discussion of the availability of NEG-Q readings (Horn, 1989) and Barwise and Cooper’s treatment of this phenomenon within the generalized quantifiers approach (Barwise & Cooper, 1981). I will show that while both of these approaches provide interesting insights, neither approach is an adequate solution. My solution focuses on the nature of the complement of the noun phrase. After a thorough investigation of a large data set, I conclude that negation of a noun phrase is possible if and only if the size of the complement of the noun phrase is representable by a continuous set of values, and the noun phrase contains no other aspect of its meaning that can be negated.