Ben, To me, not only Assumption 3 is too strong, but also Assumption 1, which does assume that a real number is enough for the "plausibility of a statement". For this reason, these assumptions do not even "holds approximately" in the AGI context --- using one number or two numbers makes a huge difference, which I'm sure you know well.
The Halpern vs. Snow debate is largely irrelevant to this issue. I mentioned them just to show that Cox's work is well known to the UAI community. Pei On 2/2/07, Ben Goertzel <[EMAIL PROTECTED]> wrote:
The paper Pei forwarded claims that Cox's arguments don't work for the discrete case, but the attached paper from Snow in 2002 [which will come through if this listserver allows attachments...] presents a counterargument, suggesting that a variant of Cox's argument does in fact work for the discrete case. However, my contention is that Cox's assumptions, while reasonable, are too strong to be viably assumed for a finite-resources AI system (or a human brain). To see why, look at Assumption 3 in http://en.wikipedia.org/wiki/Cox's_theorem which states basically that " Suppose [A & B] is equivalent to [C & D]. If we acquire new information A and then acquire further new information B, and update all probabilities each time, the updated probabilities will be the same as if we had first acquired new information C and then acquired further new information D. " This is not exactly the case in Novamente, nor in the human brain. So one question is: If this assumption holds only to approximately in an AI system (or other mind), how inaccurate is the ensuing approximation of probabilistic correctness constituted by its judgments? I.e., how wide are the error bars on the conclusion of Cox's Theorem, when its assumptions are approximately varied? -- Ben On Feb 2, 2007, at 2:39 PM, Pei Wang wrote: >> > I don't know of any work explicitly addressing this sort of >> issue, do >> > you? >> >> No, none that address Cox and AI directly, but I suspect one is >> forthcoming perhaps from you. Yes? :) > > There is a literature on Cox and AI. For example, > http://www.cs.cornell.edu/home/halpern/papers/cox1.pdf > > Pei > > ----- > This list is sponsored by AGIRI: http://www.agiri.org/email > To unsubscribe or change your options, please go to: > http://v2.listbox.com/member/?list_id=303 ----- This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?list_id=303
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