Ok here is some personal and speculative elaborations. I won't go into details, I only expand a little on the context and meaning of subjective probability in my view.
Fredrik said:
That sounds right on the surface, but in my opinion, the only interpretation that can have any value to a physicist is the frequency interpretation. Baez complains about how the limit of large n doesn't really exist in the real world, but so what? That only means that the "thing in the real world" that corresponds to an expectation value doesn't have an exact definition, but why should that matter when none of the "things in the real world" that a theory associates with a mathematical object or a mathematical structure has an exact definition? Those things are all defined operationally, so they can't possibly have an exact definition anyway.
IMO, Baez reflections is great but it doesn't expose the entire problem that I see.
But just like Baez writes the frequency interpretation and a subjective bayesian view is not necessarily in contradiction. On contrary in my personal endavours (which is formally speculative and under development so I will skip the details) does make use of a proper counting. The problem is not frequentism in itself, the problem is that the counting procedure and the representation itself is necesarily subjective. I envision a subjective counting system, in which the frequentist interpretation does play a role, but the fact that the counting procedure itself and the representation of the counts itself is constrained by an inside observer, gives rise to a subjective probability view.
So in this sense I am even more radical than just a bayesian view.
I consider a event counting over and event index, this builds up a discrete microstructure which is like a discretized probability concept over a discrete event space. But if the information capacity is bounded, what happens when new data arrives, and the memory is full?
Either you discard new data (which is not rational, right?), or you rearranges data into compressed form and randomly releases data.
So there are two ways to increase your information retention: evolve better compression and representation systems, and grow larger (this is in my idea also related to origin of mass)
One can apply transformations on these sets that effectively corresponds to lossy datacompression since no physical observer can represent the infinite amount of data, a straight time history is clearly a nonfit strategy. So the internal state of the obsevers is selected for optimum information retention under the constraint to limited memory capacity.
In such a view, "probability" is interpreted as a retained compressed form of a subjective timehistory of actual "frequences". The choice of compression makes this "probability" subjective. But the compression makes it different than regular frequences, and there I envision a natural selection for the optimal compression and representation systems. In these evolution, quantum logic is expcted to emerge as a form of information compression that is more fit that classical logic in the sense that it stabilises the observer complexes.
( On secret goal of mine is to show explictly how quantum logic emerges as a stable representation that has competitive advantages over classical logic, and that there is close to a one-2-one mapping onto the space of preferred representation systems including the compression algortighms and the particles and actions in nature. )
So I have a lot of things behind my view of "subjective probability". Baez gives a good initial point, but the rest of my "interpretations" is even more weird.
/Fredrik