Contradictory Belief and Epistemic Closure Principles

Kripke’s puzzle has put pressure on the intuitive idea that one can believe that Superman can fly without believing that Clark Kent can fly. If this idea is wrong then many theories of belief and belief ascription are built from faulty data. I argue that part of the proper analysis of Kripke’s puzzle refutes the closure principles that show up in many important arguments in epistemology, e.g. if S is rational and knows that P and that P entails Q, then if she considers these two beliefs and Q, she is in a position to know that Q.