Ontic randomness, which may be better called physical indeterminism, is given as the best explanation for epistemic randomness for which no conditional variable exists (in the best theories of physics, etc.) to remove the epistemic randomness.
So, for a given epistemic-random Y, "0 < P(Y) < 1" => Y is ontic-random iff there is no such X st. P(Y|X) = 1 or P(Y|-X) = 1 where dim(X) is abitarily large
The existence of X is not epistemic, and is decided by the best interpretation of the best available science.
Bell's theorem limits the conditions on `X` so that either (X does not exist) or (X is non-local).
If you take the former branch then ontic-randomness falls out "for free" from highly specific cases of epistemic; if you take the latter, then there is no case in all of physics where one implies the other.
Personally, I lean more towards saying there is no case of ontic randomness, only "ontic vagueness" or measurement-indeterminacy -- which gives rise to a necessary kind of epistemic randomness due to measurement.
So that P(Y|X) = 1 if X were known, but X isn't in principle knowable. This is a bit of a hybrid position which allows you to have the benefits of both: reality isn't random, but it necessarily must appear so because P(X|measure(X)) is necessarily not 1. (However this does require X to be non-local still).
This arises, imv, because I think there are computability constraints on the epistemic P(Y|X, measure(X)), ie., there has to be some f: X -> measure(X) which is computable -- but reality isn't computable. ie., functions of the form f : Nat -> Nat do not describe reality.
This is not an issue for most macroscopic systems because they have part-whole reductions that make "effectively computable" descriptions fine. But in systems whether these part-whole reductions dont work, including QM, the non-computability of reality creates a necessary epistemic randomness to any possible description of it.
So, for a given epistemic-random Y, "0 < P(Y) < 1" => Y is ontic-random iff there is no such X st. P(Y|X) = 1 or P(Y|-X) = 1 where dim(X) is abitarily large
The existence of X is not epistemic, and is decided by the best interpretation of the best available science.
Bell's theorem limits the conditions on `X` so that either (X does not exist) or (X is non-local).
If you take the former branch then ontic-randomness falls out "for free" from highly specific cases of epistemic; if you take the latter, then there is no case in all of physics where one implies the other.
Personally, I lean more towards saying there is no case of ontic randomness, only "ontic vagueness" or measurement-indeterminacy -- which gives rise to a necessary kind of epistemic randomness due to measurement.
So that P(Y|X) = 1 if X were known, but X isn't in principle knowable. This is a bit of a hybrid position which allows you to have the benefits of both: reality isn't random, but it necessarily must appear so because P(X|measure(X)) is necessarily not 1. (However this does require X to be non-local still).
This arises, imv, because I think there are computability constraints on the epistemic P(Y|X, measure(X)), ie., there has to be some f: X -> measure(X) which is computable -- but reality isn't computable. ie., functions of the form f : Nat -> Nat do not describe reality.
This is not an issue for most macroscopic systems because they have part-whole reductions that make "effectively computable" descriptions fine. But in systems whether these part-whole reductions dont work, including QM, the non-computability of reality creates a necessary epistemic randomness to any possible description of it.