Abstract: Semantic theories are supposed to be theories of meaning, so ascriptions of meaning should play a role in guiding and constraining our semantic theories. To play this role, however, we need to know the meaning of “means” itself. In this paper I develop a semantics for the verb “means,” as it is used to specify the meanings of natural language expressions. According to the view I propose—which I call the type-polymorphism view—the type of “means” is flexible, and shifts to accept whatever type of expression occurs in its complement. I formalize this view in a system that extends standard type theory to accommodate polymorphism: System F. I go on to argue that proponents of higher-order approaches to natural language semantics—who state their semantic theories in a higher-order metalanguage—can and should see themselves as stating their semantic theories using the verb “means.” But this approach is not available to proponents of first-order, model-theoretic approaches to semantic theorizing. As a consequence, I argue, only higher-order approaches are genuinely offering theories of meaning.