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Description: Recent debate over the semantics and pragmatics of epistemic modals has focused on intuitions about cross-contextual truth-value assessments. In this paper, we advocate for a different approach to evaluating theories of epistemic modals. Our strategy focuses on judgments of the incompatibility of two different epistemic possibility claims, or two different truth value assessments of a single epistemic possibility claim. We subject the predictions of existing theories to empirical scrutiny, and argue that existing contextualist and relativist theories are unable to account for the full pattern of observed judgments. As a way of illustrating the theoretical upshot of these results, we conclude by developing a novel theory of epistemic modals that is able to predict the results.