OP seems like a good argument for the weak claim you apply to your own field, but then goes off the rails. For now I’ll note two points that seem definitely wrong.
1:
Bayesian accounts of epistemology seem to go haywire if we think one should have a credence in Bayesian epistemology itself,
On a practical level this just seems false. On an abstract level probability doesn’t deal with uncertainty about mathematical questions; but MIRI and others have made progress on this very issue. I think true modesty would lead you to see such issues as eminently solvable. (This is around the point where you seem to stop arguing for the standard you apply to yourself, on questions you care about, and start making more sweeping claims.)
I peripherally note that if you reject the notion of a degree of credence justified by your assumptions and evidence, you suddenly have a problem explaining what your thesis even means and why (by your lights) anyone should care. But I don’t think you actually do reject it (and you haven’t expressly questioned any other assumptions of Cox’s Theorem or the strengthened versions thereof).
2:
(e.g. the agreement of the U.S. and German governments with the implied view of the physicists). This is a lot more involved, but the expected ‘accuracy yield per unit time spent’ may still be greater than (for example) making a careful study of the relevant physics.
This is partly an artifact of the example, but I do not think a layman at the time could get any useful information at all by your method—not without getting shot. Also, you forgot to include a timeframe in the question. This makes theoretical arguments much more relevant then usual (see also: cryonics). It doesn’t take much study of physics to realize that a large positively-charged atomic nucleus could, in principle, fly apart. Knowing what that would mean takes more science, but Special Relativity was already decades old.
OP seems like a good argument for the weak claim you apply to your own field, but then goes off the rails. For now I’ll note two points that seem definitely wrong.
1:
On a practical level this just seems false. On an abstract level probability doesn’t deal with uncertainty about mathematical questions; but MIRI and others have made progress on this very issue. I think true modesty would lead you to see such issues as eminently solvable. (This is around the point where you seem to stop arguing for the standard you apply to yourself, on questions you care about, and start making more sweeping claims.)
I peripherally note that if you reject the notion of a degree of credence justified by your assumptions and evidence, you suddenly have a problem explaining what your thesis even means and why (by your lights) anyone should care. But I don’t think you actually do reject it (and you haven’t expressly questioned any other assumptions of Cox’s Theorem or the strengthened versions thereof).
2:
This is partly an artifact of the example, but I do not think a layman at the time could get any useful information at all by your method—not without getting shot. Also, you forgot to include a timeframe in the question. This makes theoretical arguments much more relevant then usual (see also: cryonics). It doesn’t take much study of physics to realize that a large positively-charged atomic nucleus could, in principle, fly apart. Knowing what that would mean takes more science, but Special Relativity was already decades old.