Research on the semantics of number has been strongly influenced by the distri bution of overt number morphology in English. As is well know, number can be expressed on nouns and on verbs in English. In example (1), overt plural morphol ogy is present in both places.(1)The books- [PL] were-[pL] lying on the table.All research on plurality has assumed the the [pI]-feature on the noun is interpreted in some way. Bennett (1974) was the first to propose a semantics of number along these lines, and this assumption has been adopted by all subsequent research. Fur thermore most research has followed Bennett to assume that the [PI]-feature on the verb remains uninterpreted in English, and is a reflex of syntactic agreement with the subject. 1 A contemporary version of Bennett's proposal (e.g. Chierchia 1998b, Schwarzschild 1996) assigns to the singular noun book a set of individuals as its extension, while the extension of the plural noun books includes groups of these in dividuals (and, for Schwarzschild, atomic individuals, as well). These denotations are illustrated in (2): 2 (2) a.[book] = {a, b, c} b.[books] = {aEBbEBc, aEBb, aEBc, ... } However, in many languages, overt plural morphology is also found on the determiner as shown by the German example (3a) . Even in English plurality is also expressed on demonstrative determiners as in (3b). In this paper, I will argue that even German does not express morpholog ically the [PI]-feature that is interpreted. I propose that there is another syntactic head above the determiner, which I call the ¢-head, and that the only semantically contentful number features are contained in this head. Furthermore, I will argue that [PI] on nouns is not interpreted, but is a reflex of syntactic agreement with a ¢-head, just like [PI] on adjectives, verbs, and determiners. There have to be two agreement processes, one to establish agreement in the DP between N, A, D, and the ¢-head. The other one to establish agreement between the finite verb and a ¢P in the subject position.I first present my proposal in all detail, and then present two arguments