ABSTRACTThis book symposium onAccuracy and the Laws of Credenceconsists of an overview of the book’s argument by the author, Richard Pettigrew, together with four commentaries on different aspects of that argument. Ben Levinstein challenges the characterisation of the legitimate measures of inaccuracy that plays a central role in the arguments of the book. Julia Staffel asks whether the arguments of the book are compatible with an ontology of doxastic states that includes full beliefs as well as credences. Fabrizio Cariani raises (...) concerns about the argument offered in the book for various chance-credence principles. And Sophie Horowitz questions the assumptions at play in the book’s argument for the Principle of Indifference, as well as asking how the various laws of credence considered in the book relate to one another. (shrink)

Since Elga published his “Self-locating belief and the Sleeping Beauty problem,” there has been an intense debate about which credence between 1/2 and 1/3 Beauty should assign to (H) the coin’s landing heads, when she is awakened on Monday. The Halfers claim that she ought to assign 1/2 to H at that moment. The Thirders argue that she ought to assign 1/3 to H then. Meanwhile, Pettigrew defended a new chance-credence coordination principle, called the “Evidential Temporal Principle” (ETP), in a (...) recent edition of his book. In this paper, I provide a novel argument against the Halfer view and a partial defense of the Thirder view, respectively based on ETP. In addition, I generalize ETP to what I call the “Evidential Centered Principle,” which links one’s credences in centered propositions with their objective chances. (shrink)

Concerning the notorious Sleeping Beauty problem, philosophers have debated whether 1/2 or 1/3 is rational as Beauty’s credence in the coin’s landing heads. According to Kierland and Monton, the answer depends on whether her goal is to minimize average or total inaccuracy because, while the expected average inaccuracy of Halfing is smaller than that of Thirding, the expected total inaccuracy of Thirding is lower than that of Halfing. In this paper, I argue that Halfing is average accuracy dominated but Thirding (...) is not; and that each of the standard forms of Halfing and Thirding regards a different credence assignment as better than itself in terms of total accuracy. Therefore, Halfing is irrational, and Thirding is likely to be rational, for the goal of minimizing average inaccuracy; but both Halfing and Thirding, at least in their standard forms, are irrational for the goal of minimizing total inaccuracy. (shrink)

In his ‘A Subjectivist’s Guide to Objective Chance’, Lewis argued that a particular kinematical model for chances follows from his principal principle. According to this model, any later chance function is equal to an earlier chance function conditional on the complete intervening history of non-modal facts. This article first investigates the conditions that any kinematical model for chance needs to satisfy to count as Lewis’s kinematics of chance. Second, it presents Lewis’s justification for his kinematics of chance and explains why (...) it is bound to be problematic. Third, it gives an alternative justification for Lewis’s kinematics of chance that does not appeal to the principal principle. Instead, this justification appeals to a well-supported requirement for chance, according to which any prior chance function must be a convex combination of the possible posterior chance functions. It is shown that under a plausible assumption, Lewis’s kinematics of chance is equivalent to this requirement. Finally, by focusing on this requirement, it is explained why the so-called self-undermining chances fail to obey Lewis’s kinematics of chance. (shrink)