Closure Principles

A dispute in epistemology has arisen over whether some class of things epistemic (things known or justified, for example) is closed under some operation involving the notion of what follows deductively from members of this class. Very few philosophers these days believe that if you know that p, and p entails q, then you know that q. But many philosophers think that something weaker holds, for instance that if you know that p, and p entails q, then you are in a position to know that p, or if you know that p and you competently deduce p from q, then you know that q. However there are some considerations tracing back to Wittgenstein's On Certainty and some early work by Fred Dretske that suggests even these weaker principles are false.