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GuySrinivasan comments on Bayesian Flame - Less Wrong
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I had another thought on the subject. Consider flipping a coin; a Bayesian says that the 50% estimate of getting tails is just your own inability to predict with sufficient accuracy; a frequentist says that the 50% is a property of the coin - or to be less straw-making about it, a property of large sets of indistinguishable coin-flips. So, ok, in principle you could build a coin-predictor and remove the uncertainty. But now consider an electron passing through a beam splitter. Here there is no method even in principle of predicting which Everett branch you find yourself in. (Given some reasonable assumptions about locality and such.) The coin has hidden variables like the precise location of your thumb and the exact force your muscles apply to it; if you were smart enough, you could tease a prediction out of them. But an electron has no such hidden properties. Is it not reasonable, then, to say that the 50% chance really is a property of the electron, and not the predictor?
I believe the answer to this question is currently "we don't know". But notice that "the electron" doesn't exist, it's a pattern ("just" a pattern? :)) in the wavefunction. A pattern which happens to occur in lots of places, so we call it an electron.
My intuition, IANAP, is that if anything it is more natural to say the 50% belongs somehow to which branch you find yourself in, not the pattern in the wavefunction we call an electron.
Ok, but I don't think that matters for the question of frequentist versus Bayesian. You're still saying that the 50% is a property of something other than your own uncertainty.
Moving the problem to lexical uncertainty seems to me to rely on moving the question in time; you can only do this after you've done the experiment but before you've looked at the measurement. This feels to me like asking a different question.