Transparent quantification into hyperpropositional attitudes de dicto

Abstract

We prove how to validly quantify into hyperpropositional contexts de dicto in Transparent Intensional Logic. Hyperpropositions are sentential meanings and attitude complements individuated more finely than up to logical equivalence. A hyperpropositional context de dicto is a context in which only co-hyperintensional propositions can be validly substituted. A de dicto attitude ascription is one that preserves the attributee’s perspective when one complement is substituted for another. Being an extensional logic of hyperintensions, Transparent Intensional Logic validates all the rules of extensional logic, including existential quantification. Yet the rules become more exacting when applied to hyperintensional contexts. The rules apply to only some types of entities, because the existence of only some types of entities is entailed by a hyperpropositional attitude de dicto. The insight that the paper offers is how a particular logic of hyperintensions is capable of validating quantifying-in in a principled and rigorous manner. This result advances the community-wide understanding of how to logically manipulate hyperintensions.