Radical scepticism is the view that it is impossible to know very much. One dominant type of sceptical argument appeals to what is known as a sceptical hypothesis. This is a scenario that is indistinguishable from normal life but in which one is radically deceived (e.g. the possibility that one is a disembodied brain floating in a vat of nutrients being ‘fed’ one’s experiences by supercomputers). For this to generate sceptical consequences, we also need the closure principle, which roughly holds that if you know one proposition (e.g. that you are sitting at a computer typing), and know that it entails a second proposition (e.g. that you are not a brain in a vat), then you also know that second proposition. One way of responding to the sceptical argument is thus to deny this principle, and therefore hold that one can know ‘everyday’ propositions (e.g. that you are sitting at a computer) even while being unable to know anti-sceptical propositions (e.g. that you are not a brain in a vat). If one wishes to retain the closure principle, then one possibility is to opt for the view that we can know the denials of sceptical hypotheses. We also consider the contextualist response to the sceptical problem. This holds that knowledge is a radically context-sensitive notion. On this view, while the sceptic is right to contend, relative to her very demanding epistemic standards, that we are unable to know very much, this claim is consistent with our possessing lots of knowledge relative to the more relaxed standards in operation in normal contexts. One problem facing this proposal is that it is not obvious that the sceptical argument does trade on high epistemic standards in this way.