Talk (Work in Progress): Elio La Rosa (MCMP)

Title:

Unrestricted Connexivity in Minimal Choice-functional Frames, over Classical Logic

Abstract:

Connexive principles trace back to the earliest accounts of conditionals. Still, they remain difficult to formally reconstruct, since basic conditional principles are often incompatible with connexive ones over classical logic. This puts into question the very possibility of formulating a well-behaved, fully connexive conditional over an unrestricted classical base validating substitutivity of equivalents. In this talk, I reconsider this possibility, and develop a new conditional logic CX that achieves more than expected. CX combines what I call minimal choice-functional Segerberg frames with a new semantic clause for the conditional. As a result, it defines a hyper- and strongly connexive conditional validating conditional identity, modus ponens and excluded middle, and invalidating the paradoxes of material implication, strengthening of antecedents, explosion and implosion. The trade-off concerns the distribution of antecedents over conjunction, which only holds for possible antecedents in CX on pain of inconsistency. This, however, comes as expected, given the partially non-vacuist interpretation of impossible antecedents in CX.