DOES ASSERTIBILITY SATISFY THE S4 AXIOM

‘Assertible’ abbreviates ‘warrantedly assertible’ throughout. (AA) is the result of reading in the S4 axiom of modal logic p → p as ‘it is assertible that’, or of substituting those words for ‘one knows that’ in the KK schema ‘If one knows that P, then one knows that one knows that P’. This paper argues that (AA) has false consequences. Some clarifications: Assertibility depends on circumstances; it is gained or lost as the available evidence changes. Thus (AA) has implicit generality both over circumstances and in the schematic variable ‘P’. ‘P’ is replaceable by declarative sentences, which may have features sensitive to the circumstances, e.g. tense (as in the third occurrence of ‘is’ in (AA)). The circumstances are the