One of the main arguments intended to show that content externalism undermines the privileged access thesis is the ‘slow switching argument’, originally proposed by Boghossian (1989). In this argument, it is supposed that a subject is unknowingly switched back and forth between Earth and Twin Earth: then it is claimed that, given externalism, when the subject is on Earth thinking that water is wet, he cannot know the content of his thought a priori, for he cannot, by mere reflection, rule out the relevant alternative hypothesis that he is on Twin Earth thinking that twater is wet. One of the controversies surrounding this argument stems from the fact that it is not clear which epistemological principle underlies it. Here, I examine two suggestions made in the literature as to what that underlying principle might be. I argue that neither of these suggested principles is plausible, and thus that the slow switching argument never gets off the ground.