Certain and Uncertain Inference with Indicative Conditionals

This paper develops a trivalent semantics for the truth conditions and the probability of the natural language indicative conditional. Our framework rests on trivalent truth conditions first proposed by W. Cooper and yields two logics of conditional reasoning: (i) a logic C of inference from certain premises; and (ii) a logic U of inference from uncertain premises. But whereas C is monotonic for the conditional, U is not, and whereas C obeys Modus Ponens, U does not without restrictions. We show systematic correspondences between trivalent and probabilistic representations of inferences in either framework, and we use the distinction between the two systems to cast light, in particular, on McGee's puzzle about Modus Ponens. The result is a unified account of the semantics and epistemology of indicative conditionals that can be fruitfully applied to analyzing the validity of conditional inferences.