This paper presents an account of the semantics of copular be as displayed in its behaviour in be +AP configurations. I begin by arguing against the Partee/Dowty distinction between a semantically null be of predication and a thematically relevant agentive be, and I propose that there is one semantically relevant verb whose grammatical role is to turn an AP predicate into a verbal one. The denotation of be must thus be a function from denotations of Adjective Phrases to denotation of Verb Phrases. I argue that these denotations are crucially different in kind: verbs (and thus VPs) denote eventualities, which are count entities and which are temporally locatable, while adjectives (and thus APs) denote mass entities, which are states and which are not temporally locatable. Be thus denotes a locating function which maps from the mass to the count domain, and is the analogue of the 'packaging' function in the nominal domain. After a comparison between the mass/count distinction in the verbal and nominal domains, I show how this theory accounts for properties of be in small clause and progressive constructions which have hitherto been explained by positing a so-called agentive be.