According to Duncan Pritchard, there are two kinds of radical sceptical problem; the closure-based problem, and the underdetermination-based problem. He argues that distinguishing these two problems leads to a set of desiderata for an anti-sceptical response, and that the way to meet all of these desiderata is by supplementing a form of Wittgensteinian contextualism with disjunctivist views about factivity. I agree that an adequate response should meet most of the initial desiderata Pritchard puts forward, and that some version of Wittgensteinian (...) contextualism shows the most promise as a starting point for this, but I argue, contra Pritchard, that the addition of disjunctivism is unnecessary and potentially counter-productive. If we draw on lessons from Michael Williams's inferential contextualism then it is both possible, and preferable, to meet the most important of Pritchard's desiderata, undercutting both closure-based and underdetermination-based sceptical problems in a unified way, without the need to resort to disjunctivism. (shrink)