Radical skepticism relies on the hypothesis that one could be completely cut off from the external world. In this paper, I argue that this hypothesis can be rationally motivated by means of a conceivability argument. Subsequently, I submit that this conceivability argument does not furnish a good reason to believe that one could be completely cut off from the external world. To this end, I show that we cannot adequately conceive scenarios that verify the radical skeptical hypothesis. Attempts to do so fall prey to one or another of three pitfalls: they end up incomplete, reveal a deep contradiction or recreate a non-skeptical hypothesis. I use these results to improve upon Pritchard’s recent attempt at undercutting radical skepticism.