Epistemic Conditionals and Conditional Epistemics

There has been a murder in the mansion. There are, and we all know that this is so, only three suspects: the gardener, the driver, and the butler. We believe, and we have our reasons for so believing, that if the gardener did not do it, then the driver did. We share belief in this particular conditional, and this conditional is of a particular kind. It is what Quine calls an ‘‘ordinary indicative’’ conditional (so-called because such conditionals are typically expressed in the indicative mood). We could, just as well, call them ordinary epistemic conditionals since, intuitively anyway, they express some conditional connection about epistemic possibilities. Either way, these ‘‘ordinary’’ conditionals have proved to be rather extraordinary. 1 There are two kinds of obstacles to a satisfying theory about indicatives, and these two classes of obstacles mirror a distinction within the class of epistemic conditionals. A plausible pragmatic constraint on indicatives is that they carry a presupposition that their antecedents might be true. Let us call indicatives which meet this presupposition—i.e., indicatives whose antecedents are consistent with our picture of the world—open indicatives or open epistemic conditionals. But the pragmatic constraint on indicatives can be cancelled; some indicatives have antecedents the belief in which would require us to revise our epistemic states. The well-known example due to Ernest Adams (1975) illustrates this fact: I believe that Oswald killed Kennedy, but I also believe the indicative conditional If Oswald didn’t kill Kennedy, then someone else did. 2 Let us call indicatives of this latter sort belief-contravening indicatives or belief-contravening epistemic conditionals. The first kind of obstacle to a comprehensive understanding of indicatives is specific to the belief-contravening indicatives. Frank Ramsey (1931) suggested, in a famous footnote, that the basic structure to reasoning about