‘Is knowledge impossible?’ considers an influential argument that purports to show that we do not know much of what we take ourselves to know. If this argument works, then it licenses a radical sceptical doubt. It first looks at Descartes’s formulation of radical scepticism—Cartesian scepticism—which employs an important theoretical innovation known as a radical sceptical hypothesis. The closure principle is also discussed along with the radical sceptical paradox. If this radical sceptical argument works, then we not only lack knowledge of much of what we believe, but we do not even have any good epistemic reasons for believing what we do.