The Ramsey Test for Conditionals and Iterated Theory Change

The Ramsey Test interprets conditionals as reflecting changes of theories (or beliefs): A>B is accepted in T iff B is accepted in the minimal revision of T necessary to accommodate A. More than 20 years ago, the Ramsey test has come under heavy attack. A series of impossibility theorems ("triviality theorems") seemed to show that given standard models of theory change, the Ramsey test cannot serve as a viable analysis of conditionals. But later various authors have come to its defence, arguing that it is rather the standard AGM-type models of theory change that are mistaken. In this talk I argue that the reason for the fact that the situation is still somewhat unclear lies in an overly postulational approach to the analysis of the meaning of conditionals, and that the interpretation of (nested) conditionals should instead be studied in terms of constructive models of (iterated) theory change.

A crucial question has always been whether it is possible to use the Ramsey Test for the interpretation of conditionals and still satisfy the Preservation Condition according to which the original theory T should be fully retained after a revision by information consistent with T. Among the most natural models for iterated belief change, I shall identify a unique solution that indeed allows us to combine the Ramsey test with Preservation in languages containing only non-nested conditionals A>B. It is shown, however, that this solution fails Preservation for nested conditionals of the form A>(B>C). I argue that by looking at the constructve models, we can understand why it has been wrong to expect that Preservation holds in languages containing nested conditionals.