Abstract: Formal theories of knowledge, belief, and partial belief usually make the idealizing assumption that an agent's knowledge or beliefs are closed under logical consequence—that knowers or believers are logically omniscient. This paper aims to clarify the nature of and motivation for this idealization. It is argued that it is more difficult than is sometimes supposed to give an adequate representation of belief or knowledge that avoids this idealization. Different ways of distinguishing implicit from explicit belief are distinguished. It is argued that while one can avoid logical omniscience by building linguistic structure into the contents of belief and knowledge, this fails to address the underlying problem, which is a problem about the accessibility or availability of information to influence action.

Keywords: belief, explicit belief, idealization, implicit belief, knowledge, logical omniscience,