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This paper motivates and develops a semantics for epistemic modals and other epistemic vocabulary. If we start by studying the behavior of simple nested modals, we can naturally build a theory that explains the interaction of epistemic modals and indicative conditionals, together with other distinctive data not sufficiently appreciated by extant theories. The semantics I defend constitutes a dramatic alternative to standard truth conditional theories, as it assigns sets of probability measures rather than sets of worlds as sentential semantic values. I argue that what my theory lacks in conservatism is made up for by its strength; combined with a novel pragmatics, my semantics accounts for a wide range of useful empirical judgments.