Does vagueness exclude knowledge? After arguing for an affirmative answer to this question, I consider a fascinating objection. Barnett offers purported counterexamples to the following: Vagueness as to whether p entails that nobody knows whether p. These putative counterexamples, were they successful, would establish that standard accounts of vagueness are mistaken. I defend three central theses: First, whenever it is vague whether p competent speakers would be ambivalent about whether p when considering whether p, and such ambivalence would exclude knowledge (...) of whether p. Second, it is impossible for there to be vagueness regarding which of two polar opposite mental states obtains when only one of such states obtains. Finally, this type of impossibility constitutes evidence for dualism; i.e., the thesis that mental states are neither identical to physical states nor obtain in virtue of the obtaining of physical states. (shrink)