Probabilities of Conditionals

Both conditionals and probabilities have been the subject of lively philosophical debate. Lately their interaction has been in the limelight, through the disputed thesis that Ρ(Α→Β)=P (Β/Α), the probability of the conditional is the conditional probability (of consequent on antecendent). This thesis is tenable for the Stalnaker conditional if nesting of arrows is not allowed; for nested arrows I have weaker results. For ease of reading, I have limited the body of this paper to an exposition of the philosophical disputes, while the technical results are collected in a many- sectioned appendix.1