Must rational thinkers have consistent sets of beliefs? I shall argue that it can be rational for a thinker to believe a set of propositions known to be inconsistent. If this is right, an important test for a theory of rational belief is that it allows for the right kinds of inconsistency. One problem we face in trying to resolve disagreements about putative rational requirements is that parties to the disagreement might be working with different conceptions of the relevant attitudes. (...) My aim is modest. I hope to show that there is at least one important notion of belief such that a thinker might rationally hold a collection of beliefs (so understood) even when the thinker knows their contents entail a contradiction. (shrink)