In Chapter 6 of Objects of Credence, Anna Mahtani argues that the opacity of credence raises difficulties for the Principal Principle and proposes a revised principle relating credence and chance that avoids it. In this comment on her book, I both defend Mahtani’s proposed principle against a charge of triviality and argue that the opacity of belief does not threaten the role of chance in guiding credence.

It is widely thought that chance should be understood in reductionist terms: claims about chance should be understood as claims that certain patterns of events are instantiated. There are many possible reductionist theories of chance, differing as to which possible pattern of events they take to be chance-making. It is also widely taken to be a norm of rationality that credence should defer to chance: special cases aside, rationality requires that one’s credence function, when conditionalized on the chance-making facts, should coincide with the objective chance function. It is a shortcoming of a theory of chance if it implies that this norm of rationality is unsatisfiable. The primary goal of this paper is to show, on the basis of considerations concerning computability and inductive learning, that this shortcoming is more common than one would have hoped.

An indifference principle says that your credences should be distributed uniformly over each of the possibilities you recognise. A chance deference principle says that your credences should be aligned with the chances. My thesis is that if we are anti-Humeans about chance, then these two principles are incompatible. Anti-Humeans think that it is possible for the actual frequencies to depart from the chances. As long as you recognise possibilities like this, you cannot both spread your credences evenly and defer to the chances. I discuss some weaker forms of indifference which will allow anti-Humeans to defer to the chances.