9 November: Brad Shubert
“Fully Truth-Functional Modal Logic”
Abstract: Modal logic (the logic of possibility and necessity) is commonly understood as being non-truth-functional or, at best, only partially truth-functional. If so, this would mean we cannot make sense of modal claims using only truth-tables. Many-valued logic is entirely truth-functional but employs more truth-values than the classical division — true and false. This difference contributes to a common understanding of modal logic and many valued logic as distinct kinds of logic. In this paper I will demonstrate one method by which any normal modal logic can be expressed without loss as a many-valued logic and will thus make the case that modal logic can be understood as fully truth-functional after all. Throughout this discussion I will reflect on the notion of truth generally, as these techniques will suggest a broadening of what we ordinarily mean when we say of a statement that it is true or false.
This talk will assume only a minimal background in logic (e.g. a first course in symbolic logic)