Moore's proof of an external world is a piece of reasoning whose premises, in context, are true and warranted and whose conclusion is perfectly acceptable, and yet immediately seems flawed. I argue that neither Wright's nor Pryor's readings of the proof can explain this paradox. Rather, one must take the proof as responding to a sceptical challenge to our right to claim to have warrant for our ordinary empirical beliefs, either for any particular empirical belief we might have, or for belief in the existence of an external world itself. I show how Wright's and Pryor's positions are of interest when taken in connection with Humean scepticism, but that it is only linking it with Cartesian scepticism which can explain why the proof strikes us as an obvious failure.