Some opponents of the incommensurability thesis, such as Davidson and Rorty, have argued that the very idea of incommensurability is incoherent and that the existence of alternative and incommensurable conceptual schemes is a conceptual impossibility. If true, this refutes Kuhnian relativism and Kantian scepticism in one fell swoop. For Kuhnian relativism depends on the possibility of alternative, humanly accessible conceptual schemes that are incommensurable with one another, and the Kantian notion of a realm of unknowable things-in-themselves gives rise to the possibility of humanly inaccessible schemes that are incommensurable with even our best current or future science. In what follows we argue that the possibility of incommensurability of either the Kuhnian or the Kantian variety is inescapable and that this conclusion is forced upon us by a simple consideration of what is involved in acquiring a concept. It turns out that the threats from relativism and scepticism are real, and that anyone, including Davidson himself, who has ever defended an account of concept acquisition is committed to one or the other of these two possibilities.1