Much literature in syntax has assumed that all noun phrases are categorically headed by the determiner or the noun, with well-formedness categorial in nature. In this paper I develop a theory of noun phrase structure in which both categories project noun phrases, arguing that this better fits the indeterminacy of the criteria often cited for determining headedness (Zwicky, 1985, inter alia). The only categorial differences between determiners and nouns are their semantics and selectional restrictions, and the conditions that determine well-formedness are semantic in nature. Specifically, a well-formed noun phrase must have some restrictive semantics associated with nouns coupled with some operational semantics associated with determiners (e.g. as a generalized quantifier), and from this I show how we can derive structural well-formedness. Thus the need for categorial well-formedness is nullified, providing an analysis with greater cross-linguistic import, being compatible with languages without determiners.