Ben, this is also why I was wondering why your hypothesis is framed in terms of both Cox and De Finetti. Unless I misunderstand Cox, their interpretations are in some ways diametrically opposed. De Finetti was a radical subjectivist while Cox is (epistemically) an ardent logical/objectivist (or so I gather). Apparently you see their ideas as complementary rather than mutually exclusive, which is interesting... is it because De Finetti's subjective interpretation gives a theoretical foundation to your use of [U,L] ranges in your quadruples?
I know that those two men had different philosophical ideas, but the math they developed is quite interoperable. for instance in Snow's 2002 paper he freely mixes ideas from Cox and de Finetti, being fairly careful not to step on anyone's philosophical toes..
Another question on my mind is if and how it might be possible to design an AGI based entirely on the subjectivist ideas of De Finetti, an idea that I find very attractive. However I am at the moment stumped on that question; it may be true that no matter the philosophy of the programmer, he must for practical reasons implement something like a logical/objective interpretation of bayes' rule. Comments?
My comment is that in novamente we use probabilistic **mathematics**, and what the system does can probably be interpreted in many different philosophical ways by different people...
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