Formal consistency of the Principal Principle revisited

Abstract

We rigorously describe the relation in which a credence function should stand to a set of chance functions in order for these to be compatible in the way mandated by the Principal Principle. This resolves an apparent contradiction in the literature, by means of providing a formal way of combining credences with modest chance functions so that the latter indeed serve as guides for the former. Along the way we note some problematic consequences of taking admissibility to imply requirements involving probabilistic independence. We also argue, contra (Hawthorne et al., The British Journal for the Philosophy of Science, 68(1), 123–131 2017), that the Principal Principle does not imply the Principle of Indifference.