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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.

  1. How would a purely objective account of probability, broadly speaking, make sense of this distinction?

  2. How would a purely epistemic account of probability, broadly speaking, make sense of this distinction?

  3. 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?

  • "Objective" is a wrong opposite, many epistemic accounts constrain probability by available evidence in a way that makes it perfectly objective. The distinction is really between epistemic (lack of knowledge) and physical (inherent in nature) probability. Few would assert physical randomness in coin flips, no matter how objective the bias is. It is typically reserved for quantum physics, but a monist can claim that quantum randomness comes from lack of knowledge as well, Einstein did. See SEP, Interpretations of Probability. – Conifold Sep 7 at 21:33
  • And if we flip a coin only 5 times then what we get is not the probability distribution, but what is called empirical distribution of a sample in statistics. Both that and the objective distribution determined by the unknown bias are epistemic. The difference lies elsewhere, in what knowledge is available or lacking. – Conifold Sep 7 at 21:41
  • @Conifold I guess different sources use different terminology. I chose "objective" rather than "physical" so as not to exclude the immaterial by fiat. For example, if Platonism is true, then there may be probability propensities among abstract objects, or if mind-body dualism is correct, then we might consider the probability that one thought leads to another, even if not supervenient on anything physical (which would seem to be non-epistemic despite being related to a mind, since it's not a probability implicitly qualified with "for all that mind knows"). – user48231 Sep 7 at 22:14
  • I also do not want whatever terminology I choose to target the question around fundamental indeterminacy, present in some interpretations of quantum mechanics. Rather, I would want the category opposite of epistemic probability to include coin tosses and die rolls, since, roughly speaking, if coins and dice existed but not any species intelligent enough to analyze their probabilities, the probabilities of each outcome would still hold. – user48231 Sep 7 at 22:16
  • I think the "fundamental indeterminacy" is simply the natural relativity of epistemic probabilities, subjective or objective they are always relative to the background knowledge. As for probabilities holding without intelligent species, they will not hold for Laplace's demon, he knows the outcomes with probability 1. This does not make them subjective, but it does make them relative, many objective things are relative. Even Laplace's demon can calculate what the probability is supposed to be assuming that the bias is unknown, indeed he is uniquely qualified. – Conifold Sep 7 at 22:50

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