Subject-matter and intensional operators I:conditional-agnostic analytic implication

Although logical settings are typically concerned with tracking alethic considerations, frameworks exist in which topic-theoretic considerations—e.g., tracking subject-matter or topic—are given equal importance. Intuitions about extending topic through a propositional language are generally straightforward for extensional cases. For a number of reasons, arriving at a compelling account of the subject-matter of intensional operators—such as intensional conditionals—is a more difficult task. In particular, the framework of topic-sensitive intentional modals (TSIMs) championed by Francesco Berto and his collaborators leave the topics of intensional formulae undefined, which artificially constricts the expressivity of the theory. This paper proposes an approach to fill in this lacuna, emphasizing an analogous problem in Parry-style containment logics. In this setting, the approach receives a proof-of-concept through the introduction of a natural and general family of subsystems of Parry’s PAI—with sound and complete axiomatizations—that allow a fine degree of control over the topics of intensional conditionals

The Subject-Matter of Intensional Conditionals

We consider the matter of how intensional conditional connectives contribute to the subject-matter of sentences in which they appear. We review Kit Fine’s model theory for William Parry’s logic of analytic implication and some preliminary suggestions made by Fine to address the influence of intensional connectives on subject-matter. After outlining some thoughts on an appropriate formalization, we modify Fine’s model theory to give a more natural account and show how severalsemantic conditions are characterized by individual axioms