On 2/4/07, gts <[EMAIL PROTECTED]> wrote:
On Sun, 04 Feb 2007 07:52:02 -0500, Pei Wang <[EMAIL PROTECTED]> wrote:
> However, the axioms of probability theory and interpretations of
> probability (frequentist, logical, subjective) all take a consistent
> probability distribution as precondition.
Also I think the meaning of 'probabilistic consistency' might change
according to the interpretation of probability. For example two
subjectivist-like AGI's might arrive at different conclusions, at least
early in the learning process, without probabilistic inconsistency. Such
apparent inconsistencies are however prohibited under the logical
interpretation.
I'm talking about the consistency within a single system, which is
required by all interpretations. Cross-system consistency is required
by the logical and frequentist interpretations, but is usually called
"objectiveness".
This I think may also go to the question of resources. I'm thinking a
subjectivist (De Finetti-Ramsey inspired) AGI should require a different
amount of resources than a logical (Keynes-Jaynes-Cox inspired) AGI. At
the moment my conjecture is that implementations of the logical
interpretation would require the greater resources in that it imposes more
restraints, but I can also see some possible rationale for the converse.
The interpretation of probability is a different matter --- we have
been talking about consistency, which is largely independent to which
interpretation you subscribe to.
In my opinion, in the AGI context, each of the three traditional
interpretation is partly applicable but partly not. The subjectivist
is not better in general.
Pei
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?
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?
-gts
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