Interpretation-wise, Cox followed Keynes pretty closely. Keynes had
his own eccentric view of probability, which held among other things
that a single number was not enough information to capture a judgment
of uncertainty (and I agree with this). However, even so, Cox's
Theorem does pertain to single-number representations (but does not
state that a single number is a sufficient quantification of a mind's
uncertainty about a statement)
ben
On Feb 2, 2007, at 1:52 PM, gts wrote:
On Thu, 01 Feb 2007 14:00:06 -0500, Ben Goertzel <[EMAIL PROTECTED]>
wrote:
Discussing Cox's work is on-topic for this list...
Okay, I'll get a copy and read it.
Let me tell you one research project that interests me re Cox and
subjective probability:
****
Justifying Probability Theory as a Foundation for Cognition.
Cox's axioms and de Finetti's subjective probability approach,
developed in the first part of the last century, give mathematical
arguments as to why probability theory is the optimal way to
reason under conditions of uncertainty.
What are you quoting here, if I may ask? I'm surprised to see Cox
mentioned this way in the same sentence with de Finetti, because
it's my impression that Cox's views are similar to those of Jaynes,
who was a pretty sharp critic of de Finetti.
I was under the impression that Cox, like Jaynes, rejected the
extreme subjectivist views of de Finetti in favor of a more
objective/logical interpretation. But this is admittedly based only
on my very scant knowledge of Cox.
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? :)
The only work I know of that addresses both AI and probability
theory is one currently on my reading list by Professor Donald
Gillies of King's College, London (not to be confused with some
Canadian character named Donald B. Gillies, whose name comes up in
a google search). Gillies earned his Phd under your own favorite
Lakatos, with a dissertation in probability theory (I think) and
wrote a book about AI and the scientific method which I believe
also deals with at least tangentially with probability theory.
Maybe you've already read it. It was published a while ago and you
probably stay on the leading of edge of AI.
Artificial Intelligence and Scientific Method (Paperback)
http://www.amazon.com/Artificial-Intelligence-Scientific-Method-
Gillies/dp/0198751591/sr=8-2/qid=1170441700/
ref=sr_1_2/103-6974055-7831844?ie=UTF8&s=books
I should mention here that although I am certified with Microsoft
as a C++ application developer, I clam no special knowledge of AI
programming techniques. I expect this may change soon, however.
-gts
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