Principle that, where P and Q are propositions, if we know that P, and know that P logically entails Q, we know that Q.
Sometimes said to support skepticism, because if I know that, for example, I am holding a pen, and know that if I am holding a pen I am not merely dreaming that I am doing so, then (by the principle) I know that I am not merely dreaming this: but, it is alleged, I cannot know that I am not dreaming because even if I were, things would still appear just as they do.
Therefore, I cannot know that I am really holding a pen.
Also see the theory of relative alternatives which has been used to answer this.
J Dancy, An Introduction to Contemporary Epistemology (1985)
Most epistemological theories involve a closure principle and many skeptical arguments assume a closure principle. … Nozick, in Philosophical Explanations, advocated that, when considering the Gettier problem, the least counter-intuitive assumption we give up should be epistemic closure.