One notable line of argument for epistemic relativism appeals to considerations to do with non-neutrality: in certain dialectical contexts—take for instance the famous dispute between Galileo and Cardinal Bellarmine concerning geocentrism—it seems as though a lack of suitably neutral epistemic standards that either side could appeal to in order to resolve their first-order dispute is itself—as Rorty influentially thought—evidence for epistemic relativism. In this essay, my aim is first to present a more charitable reformulation of this line of reasoning, one (...) that is framed not merely in terms of the availability of epistemic norms that are suitably neutral between interlocutors, but in terms of the availability of what I call Archimedean metanorms. Once this more charitable line of argument is developed, I show how, even though it avoids problems that face ‘non-neutrality’ versions of the argument, it nonetheless runs into various other problems that appear ultimately intractable and, further, that the strategy in question gives us no decisive reason to draw the relativist’s conclusion rather than the Pyrrhonian sceptic’s. (shrink)