This essay is a reconstruction and defense of Davidson's argument against the intelligiblity of the notion of conceptual scheme. After presenting a brief clarification of Davidson's argument in ‘On the Very Idea of a Conceptual Scheme’, I turn to reconstructing Davidson's argument. Unlike many commentators, and occasionally Davidson, who hold that the motive force of the argument is the Principle of Charity (or the denial of the Third Dogma), I argue that there is a further principle which underlies the argument. This principle I call the Strong Discrimination Principle.