According to epistemological disjunctivism (ED), in paradigmatic cases of perceptual knowledge, a subject, S, has perceptual knowledge that p in virtue of being in possession of reasons for her belief that p which are both factive and reflectively accessible to S. It has been argued that ED is better placed than both knowledge internalism and knowledge externalism to undercut underdetermination-based skepticism. I identify several principles that must be true if ED is to be uniquely placed to attain this goal. After that, I use those principles to formulate a diachronic skeptical argument. This argument yields the counterintuitive conclusion that understanding a global skeptical hypothesis is all it takes for a rational subject to lose all her perceptual knowledge of the world. Next, I show that a popular Austinian move must reject one or another of the principles that underlie ED. I close by delineating a novel strategy that can block the diachronic skeptical argument while preserving all the principles. The key idea is that perceptual knowledge is grounded in primitive, perceptual and recognitional abilities. This view sheds new light on some puzzling features of global skepticism that have been noted by Descartes and Hume, among others.