The aim of this article is to determine how useful to us are the notes from the late work of Ludwig Wittgenstein, On Certainty, in dealing with one of the modern sceptical problems. By determining the usefulness I have in mind whether or not his thoughts and descriptions of everyday linguistic practice help solve the sceptical problem and, if so, in what way. The sceptical problem in question is the Cartesian argument about the external world – the argument of ignorance. We will endeavour to show that if we accept Wittgenstein’s remarks as adequate descriptions of epistemic practice, they will help to make it possible to block the argument in question. However, there arise questions of whether Wittgenstein’s descriptions of epistemic practice are adequate, on the one hand, and whether the sceptical claims about the external world really spring from this practice, on the other hand. I hold the view that these questions are basically empirical. This has the relatively unusual consequence that the worth of Wittgenstein’s thoughts, as well as the cogency of the problem of the external world, cannot be judged in a purely philosophical way.