Tracing back to at least Frege, genuine higher-orderism sharply distinguishes between objects and categorically distinct higher-order entities and the expressions that denote them. Against the background of this view, Frege himself felt compelled to regard numbers as objects rather than higher-level entities—concepts, in Frege’s terminology—because number words in arithmetical contexts appear to function as object-denoting expressions. In this paper, I argue that, from the perspective of natural language semantics, a case can be made that number words in such contexts function as concept-denoting rather than object-denoting expressions and that, consequently, numbers should be conceived of as concepts rather than objects. In developing this argument, I will develop a novel semantic analysis of expressions like ‘the number of Mars’ moons’ as higher-order definite descriptions. Moreover, the view developed in this paper will shed new light on so-called easy arguments for the existence of numbers.