We offer a general framework for theorizing about the structure of knowledge and belief in terms of the comparative normality of situations compatible with one’s evidence. The guiding idea is that, if a possibility is sufficiently less normal than one’s actual situation, then one can know that that possibility does not obtain. This explains how people can have inductive knowledge that goes beyond what is strictly entailed by their evidence. We motivate the framework by showing how it illuminates knowledge about the future, knowledge of lawful regularities, knowledge about parameters measured using imperfect instruments, the connection between knowledge, belief, and probability, and the dynamics of knowledge and belief in response to new evidence.

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