Since the most promising path to a solution to the problem of skepticism regarding perceptual knowledge seems to rest on a sharp distinction between perceiving and inferring, I begin by clarifying and defending that distinction. Next, I discuss the chief obstacle to success by this path, the difficulty in making the required distinction between merely logical possibilities that one is mistaken and the ‘real’ (Austin) or ‘relevant’ (Dretske) possibilities which would exclude knowledge. I argue that this distinction cannot be drawn in the ways Austin and Dretske suggest without begging the questions at issue. Finally, I sketch and defend a more radical way of identifying ‘relevant’ possibilities that is inspired by Austin's controversial suggestion of a parallel between saying ‘I know’ and saying ‘I promise’: a claim of knowledge of some particular matter is relative to a context in which questions about the matter have been raised.