Astract

I present an untyped theory of knowledge and truth that solves the knower paradoxes of Kaplan and Montague from the 1960's. The underlying idea is (1) to formalize the principle of veracity (that whatever is known is true) more precisely, and (2) to embrace self-reference in the spirit of the Friedman-Sheard theory of truth and its associated revision semantics. It turns out that this facilitates expedient reasoning with common-knowledge predicates defined by self-referential formulas obtained by Gödel diagonalization. A generalization of the revision semantics to modalities (formalized as predicates) due to Johannes Stern is employed. Apart from answering questions of consistency, this opens up for philosophical insights on the meaning of sentences involving iterations of knowledge and truth, such as ' "Kim knows A" is true' and 'Kim knows "Kim knows A" '.

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