Higher-Order Probabilities

At first sight, a hierarchical regress formed by probability statements about probability statements appears to be different from the probabilistic regress of the previous chapters. After all, the former involves higher and higherorder probabilities, whereas the latter is an epistemic chain in which one proposition or belief probabilistically supports another. Closer examination, however, teaches us that the two regresses are in fact isomorphic. A model based on coin-making machines demonstrates that the hierarchical regress is consistent.