Subject-Matter and Intensional Operators II: Applications to the Theory of Topic-Sensitive Intentional Modals

Abstract

In frameworks in which topic-theoretic considerations—e.g., tracking subject-matter or topic—are given equal importance with veridical considerations, assigning topics to formulae in a satisfactory way is of critical importance. While intuitions are more-or-less solid for extensional formulae in a propositional language, arriving at a compelling account of the subject-matter of intensional formulae, i.e., formulae including intensional operators, is more challenging. This paper continues previous work on modeling topics of intensional formulae in William Parry’s logic of analytic implication, adapting the general techniques to the framework of topic-sensitive intentional modals (TSIMs) championed by Francesco Berto and his collaborators. As illustrations, we introduce variations on Berto and Peter Hawke’s logic of knowability relative to information ($\pmb {\textsf{KRI}}$), including a refinement sensitive to topic-theoretic distinctions between knowledge and belief and a refinement capable of internalizing its own properties. Finally, subsystems of Aybüke Ozgun and Berto’s logic of plain hyperintensional belief ($\pmb {\textsf{PHB}}$) are introduced in which fine-grained distinctions in subject-matter are possible.