Many have thought that it is impossible to rationally persuade an external world skeptic that we have knowledge of the external world. This paper aims to show how this could be done. I argue, while appealing only to premises that a skeptic could accept, that it is not rational to believe external world skepticism, because doing so commits one to more extreme forms of skepticism in a way that is self-undermining. In particular, the external world skeptic is ultimately committed to believing a proposition P while believing that she shouldn’t believe P, an irrational combination of beliefs. Suspending judgment on skepticism is also problematic, for similar reasons; and, I argue, rational dilemmas are not possible; so, we should believe that skepticism is false.