re: "the right order of definition"
De Finetti's (and Ramsey's) main contribution was in showing that the
formal axioms of probability can be derived entirely from considerations
about people betting on their subjective beliefs under the relatively
simple constraint of coherency. No other rational/logical constraints are
needed, which is contrary to the suppositions of for example Keynes. This
was I think a pretty remarkable discovery!
I'm not yet sure what it means to derive the 'axioms of Novamente' in the
same way, but I think it's pretty cool that Ben is attempting it. :)
-gts
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