Formal systems for knowledge and belief, from Lemmon and Hintikka to present day Belief Revision systems, have often been described as models of "ideal rational agents." From the first, there has been extensive controversy about the validity of the models. A series of topics have given focus to the controversy. They include distinguishing knowing from believing, formalising positive and negative introspection, omniscience of various kinds, the contrast between finite and infinite, and contradictory belief. We consider the extent to which a range of formal models of knowledge and belief are reasonable and realistic. We conclude with comments on the persistence of unreal models and the lack of discussion of their structure.
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