Ockham's doctrine of intuitive cognition lies at the heart of his epistemology. As Philotheus Boehner and Sebastian Day have quite rightly observed, one of the central aims of this doctrine is to answer the question how the intellect can have certain knowledge of contingent states of affairs (including the existence or non-existence of material particulars). A number of scholars, including Etienne Gilson and Anton Pegis, have charged, however, that far from achieving this goal, Ockham's doctrine (and especially what he says about the logical possibility of intuitive cognition of non-existents) leads to scepticism. Coming to Ockham's defense, Boehner and Day have rejected these criticisms as resting on misinterpretations of Ockham. I believe Boehner and Day have done much to clarify what Ockham actually meant. I should like to reopen the discussion, however, because I believe not all the consequences of Oekham's doctrine have been accurately drawn.