Inferentialism and Connexivity

This paper investigates the relationships between two claims about conditionals that are often discussed separately. One is the claim that conditionals express inferences, in the sense that a conditional holds when its consequent can be inferred from its antecedent. The other is the claim that conditionals intuitively obey the characteristic principles of connexive logic. Following a line of thought that goes back to Chrysippus, we suggest that these two claims may coherently be understood as distinct manifestations of a single and more basic idea, namely, that a conditional holds when its antecedent is incompatible with the negation of its consequent. The account of conditionals we propose is based precisely on this idea.