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Transfuturist comments on Open thread, February 15-28, 2013 - Less Wrong Discussion
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I think there seems to be a mismatch of terms involved. Ontological probability, or propensity, and epistemological probability, or uncertainty, are being confused. Reading over this discussion, I have seen claims that something called "chaotic randomness" is at work, where uncertainty results from chaotic systems because the results are so sensitive to initial conditions, but that's not ontological probability at all.
The claim of the paper is that all actual randomness, and thus ontological probability, is a result of quantum decoherence and recoherence in both chaotic and simple systems. Uncertainty is uninvolved, though uncertainty in chaotic systems appears to be random.
That said, I believe the hypothesis is correct simply because it is the simplest explanation for randomness I've seen.
Their argument is that not only is quantum mechanics ontologically probabilistic, but that only ontologically probabilistic things can be successfully described by probabilities. This is obviously false (not to mention that nothing has actually been shown to be ontologically probabilistic in the first place).
They think they can get away with this claim because it can't even be tested in a quantum world. But you can still make classical simulations and see if probability works as it should, and it's obvious that it does. Their only argument is that it's simpler for probability to be entirely quantum, but they fail to consider situations where quantum effects do not actually affect the system (which we can simulate and test).
I don't think they refer to Bayesian probability as probability. The abstract is ill-defined (according to LessWrong's operational definitions), but their point about ontological probabilities originating in quantum mechanics remains. It, I think, remains intertwined with multiverse theories, as multiverse theories seem to explain probability in a very similar sense, but not in as many words or with such great claims.
Also, in a classical simulation, I would not see probability working as it should to be obvious at all. In fact, it's quite difficult to imagine an actually classical system that also contains randomness. It could be that the childhood explanations of physical systems in classical terms while seeing randomness as present is clouding the issue.
Whichever way. I don't think it's really worth much argument. Just as a basis in probability theory.