Dummett argued that T-theories cannot serve as adequate theories of meaning since they do not give an account of what it is to possess the concepts that speakers associate with a language's primitive terms. Although I agree with orthodoxy that Dummett's original argument fails to establish that T-theories are inadequate theories of meaning, I provide another argument that yields Dummett's conclusion. I suggest that some T-theories are adequate in ways that T-theories as standardly conceived are not, but the adequate T-theories cannot be stated in natural language, and they are, in a certain sense, equivalent to theories of meaning that explain concept possession.