> I think it's mathematically and conceptually clear that for a system with > unbounded > resources probability theory is the right way to reason. However if you > look > at Cox's axioms > > http://en.wikipedia.org/wiki/Cox%27s_theorem > > you'll see that the third one (consistency) cannot reasonably be expected > of > a system with severely bounded computational resources... > > So the question, conceptually, is: If a cognitive system can only > approximately > obey Cox's third axiom, then is it really sensible for the system to > explicitly > approximate probability theory ... or not? Because there is no way for the > system > to *exactly* follow probability theory.... >
I believe one could show that: For all epsilon, there exists a delta so that IF the deviation from Cox's axioms is less than delta THEN using probability theory will deviate from the optimal inference strategy by less than epsilon (not that this would be trivial to prove but it seems very likely to me, and I read Cox's proofs carefully with this in mind) But that doesn't help too much really (which is why I never worked out the details) ben g ------------------------------------------- agi Archives: https://www.listbox.com/member/archive/303/=now RSS Feed: https://www.listbox.com/member/archive/rss/303/ Modify Your Subscription: https://www.listbox.com/member/?member_id=8660244&id_secret=114414975-3c8e69 Powered by Listbox: http://www.listbox.com
