Certain and Uncertain Inference with Indicative Conditionals
This provides a unified account for semantics and epistemology of indicative conditionals, addressing foundational issues in logic and language, but it is incremental as it builds on prior trivalent frameworks.
The paper tackles the problem of defining truth conditions and probability for natural language indicative conditionals by developing a trivalent semantics, resulting in two logics: one for certain premises and another for uncertain premises, with applications to puzzles like McGee's.
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.