Donald Gillies, in his book "Philosophical Theories of Probability," draws a distinction between monistic views and dualistic views of probability, the latter of which, at least in his formulation, involves both objective and epistemic probabilities. He draws finer distinctions toward the end of the book, but I take this high level distinction to be independent of the distinctions between physical determinism, fundamental (quantum?) randomness, libertarian free will, etc., instead referring to something like the distinction between probabilities that would hold with or without human minds (objective), and probabilities "for all we know," or "for all some particular person knows" (epistemic).
What I don't understand is how a monistic perspective, whether purely objective or purely epistemic, could make sense of certain examples of probability. For example, I would say that flipping a coin with an unknown bias has an objective probability of producing heads VS tails. The number might be a function of the strength of gravity around the coin, etc., or we might prefer to ascribe the objective probability to a series of flips instead of an individual flip, but the main idea is that this probability distribution points to the world, not the mind. On the other hand, if we flip the coin 5 times, what we obtain is an epistemic probability distribution of the aforementioned objective probability distribution. There clearly seems to be a valid distinction here.
How would a purely objective account of probability, broadly speaking, make sense of this distinction?
How would a purely epistemic account of probability, broadly speaking, make sense of this distinction?
Given that these two views are tenable, and thus both probabilities can be explained as either objective or epistemic, could one adopt the reverse of the account I described above, where the "inner" probability of the coin flip is treated as epistemic, and the "outer" probability of the probability of the coin flip is treated as objective?
