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Perplexed comments on Book Club Update, Chapter 3 of Probability Theory - Less Wrong
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Comments (19)
Are you suggesting that Jaynes is only finitely additive? I have to admit that I don't know exactly how Jaynes's methodological preachments about taking the limit of finite set solutions translates into real math.
I'm not sure I understand your second paragraph either (I am only an amateur at math and less than amateur at analysis.) But my inclination is to say, "Yes, of course there is always a possible isomorphism in the reasonings upward from a shared collection of axioms. But no, there is not an isomorphism in the reasonings or justifications advanced in choosing that set of axioms. But I suspect I missed your point.
Incidentally, Appendix A-1 of the book includes much discussion, quite a bit of it over my head, of the relationship between Jaynes and Kolmogorov.
(Heh, I'm pretty sure being a college sophomore makes me an amateur too.)
Yep. Cox's theorem implies only finite additivity. Jaynes makes a big point of this in many places.
I'm not asking for an isomorphism in the reasoning of choosing a set of axioms. I'm asking for an isomorphism in the reasoning in using them.
For large classes (all?) of problems with discrete probability spaces, this is trivial -- just map a basis (in the topological sense) for the space onto mutually exclusive propositions. The combinatorics will be identical.