3) It seems unlikely that subjective bayesian probability would work for this kind of uncertainty. In particular, I would expect the correct theory to violate Cox's assumption of consistency. To illustrate, we can normally calculate P(A,B|X) by either P(A|X)P(B|A,X) or P(B|X)P(A|B,X). But what if A is the proposition that we calculate the probability P(A,B|X) by using P(A|X)*P(B|A,X)? Then we will get different answers depending on how we do the calculation.