Unrestricted Connexive Conditionals, over Classical Logic

Organizzato da: Melissa Antonelli, Guido Gherardi, Eugenio Orlandelli
Con: Elio La Rosa

Connexive principles trace back to the earliest accounts of conditionals, but have proven difficult to formally reconstruct given their contraclassicality. This fact calls into question the very possibility of a semantics that (1) validates all connexive and some basic conditional principles unrestrictedly (2) over a classical extensional base, and that (3) remains compatible with both desiderata of the general literature on conditionals and a notion of connection. I show how to achieve this by a new conditional logic, CX, that combines 'minimal total choice-functional’ Segerberg frames with a new semantic clause for conditionals expressing connections at world-witnesses for antecedents. The conditionals of CX are hyper- and strongly connexive, validate identity and Modus Ponens and invalidate the paradoxes of material implication and antecedent strengthening, but also explosion and implosion. Simplification and distribution over conjunction, however, only hold for possible antecedents. This is as expected consequence of CX's non-vacuist interpretation of impossible antecedents, and I will argue that from a pragmatic point of view this restriction may not be as problematic as it seems.