Accuracy, chance, and the principal principle

How should my degrees of credence in propositions about objective chances interact with my degrees of credence in other propositions? David Lewis (1980) formulated a precise answer. He called it the “Princi-pal Principle. ” And he took it to specify the role that a feature of the world must play if it is to count as chance. However, he also argued that the chances delivered by his best-system analysis of laws and chances could not possibly play the roles required of them by the Principal Principle: the Principal Principle is inconsistent with the best-system analysis. Later, Lewis (1994) came to accept a slightly different precise answer to the question. This is Michael Thau’s and Ned Hall’s amendment to the Prin-cipal Principle, which is known as the New Principle (Hall 1994; Thau 1994; Joyce 2007). The best-system analysis is consistent with the New Principle. Later still, Jenann Ismael (2008) proposed an alternative amendment to the Principal Principle, which she called the “Generalized Principal Principle. ” Ismael’s principle is also consistent with the best-system analysis. The large literature that has grown up around these proposals includes a number of different and illuminating arguments in their favor, as well as subtle improvements in their formulation. However, no attempt has been made to give them a formal justification. That is, there has been no attempt to deduce any chance-credence norm from more I would like to thank Rachael Briggs, Branden Fitelson, Ben Levinstein, Samir Okasha, Barry Loewer, Michael Strevens, Jim Pryor, Chris Hitchcock, and the referees and editors for this journal for very helpful comments on earlier versions of this article. This work for this article was carried out during my time as a British Academy Postdoctoral Fellow