Dynamic Formal Epistemology

Abstract

In the general framework which takes conditional probability functions as a primitive notion, we prove two triviality results about the possibility of defining the probability Pr(A > B,Γ) of a counterfactual as the probability of the consequent B after some revision of the probability function that puts the probability of the antecedent A to 1. The paper is divided in three parts. In the first part, we present the context in which this research takes place and provide the formal tools we will use in the two other parts. In the second part, we present our first triviality result: Any probability revision process that satisfies the identity Pr(A>B,Γ)=PrA(B,Γ) for all Pr, A, B and Γ (where PrA) is any revision of the probability distribution Pr which sets PrA(A,Γ)=1) is trivial in a sense that will be specified. Finally, in the third part, we prove another triviality result: Any probability revision process that satisfies the identity Pr(A>B,Γ)=PrA(B,Γ∗A) for all Pr, A, B and Γ (where Γ∗A is a revision of the background Γ in the light of A) is also trivial.