Strengthened, and weakened, by belief

This paper discusses a set of observations, many of which are novel, concerning differences between the adjectival modals certain and possible and their adverbial counterparts certainly and possibly. It argues that the observations can be derived from a standard interpretation of certain/certainly as universal and possible/possibly as existential quantifiers over possible worlds, in conjunction with the hypothesis that the adjectives quantify over knowledge and the adverbs quantify over belief. The claims on which the argument relies include the following: (i) knowledge implies belief, (ii) agents have epistemic access to their belief, (iii) relevance is closed under speakers' belief, and (iv) commitment is pragmatically inconsistent with explicit denial of belief.