 It is an important and controversial question whether the necessary propositions are all and only the epistemically necessary (a priori) ones, or whether the extensions of the two concepts can come apart. One possible reason for thinking that the notions are coextensive derives from a very natural picture of information and inquiry. On this picture, all information about the world is information about which of all possible worlds is realized (i.e., about where in the space of all possible worlds the actual world is located). My total information about the world can be identified with the set of possible worlds that I cannot rule out on the basis of my empirical evidence and ideal reasoning. As I gather more and more empirical evidence, I can progressively narrow down the range of possibilities. Suppose, for example, that I am ignorant of the current weather conditions. The worlds compatible with my evidence include some where the weather is good and others where it is bad. A look out of the window at the rain provides information about the matter. I can now narrow down the set of possibilities by excluding all possible worlds with fine weather. On this account, a proposition \(P\) is epistemically necessary for \(A\) just in case \(P\) is true in all possible worlds that cannot be ruled out on the basis of \(A\)’s empirical evidence and ideal reasoning. \(P\) is a priori just in case it is epistemically necessary for a possible agent who has no empirical evidence. Since such an agent cannot rule out any possible worlds, a proposition is a priori just in case it is true in all possible worlds. In other words, the a priori propositions are all and only the necessary  propositions.[3]