The material and the suppositional conditional

This paper defines a precise sense in which the material conditional analysis (MCA) is a successful heuristic for deductive reasoning with a suppositional conditional, interpreted by means of trivalent semantics. Both accounts generate the same theorems and valid deductive inferences in a large fragment of the conditional language. However, the suppositional analysis gives a more attractive treatment of conditional negation and the probability of conditionals. Therefore, this paper inverts Williamson's claim that suppositional reasoning is a heuristic for valid reasoning with conditionals (on his account, given by MCA). Similarly, the logic C2 of Stalnaker's possible-world semantics for conditionals is interpreted as approximating probability-preserving inference with suppositional conditionals.