Languages with self-reference II : Knowledge, belief, and modality

Negative results of Montague and Thomason have diverted research in propositional attitudes away from syntactic ("first-order") approaches, encouraging modal formalisms instead, especially in representing epistemic notions. We show that modal logics are on no firmer ground than first-order ones when equally endowed with substitutive self-reference. Nonetheless, there may still be remedies, hinging in part upon a distinction between "dynamic" and "static" notions of provability and belief (an earlier version of this paper emphasized a somewhat different distinction).