In a famous passage from Outlines of Pyrrhonism, Sextus Empiricus presents four different accounts of the conditional in increasing strength. Contemporary analogues have been identified (subject to various degrees of controversy) for the first three, but the last, which even fails to satisfy A>A, has proved elusive. In this talk, I discuss ways of modeling this heterodox conditional. Taking a cue from Sextus, I regard the characteristic feature of this conditional as one of proper (conceptual) containment and approach it using the framework of containment logic. Different implementations of this approach are discussed and evaluated both for their historical and technical merits. In the course of the talk, I will discuss (among other things) the relationship between Sextus’ third and fourth accounts, how Kripke semantics can be and has been used to deepen our understanding of various ancient conditionals, and how ancient notions of containment might yield interesting new (old) perspectives on contemporary containment logic.
Saul Kripke Center, Young Scholars Series: Yale Weiss, “Sextus Empiricus’ Fourth Conditional and Containment Logic”