In Novamente, we use entities called "indefinite probabilities",
which are described in a paper to appear in the AGIRI Workshop
Proceedings later this year...
Roughly speaking an indefinite probability is a quadruple (L,U,b,N)
with interpretation
"The probability is b that after I make N more observations, my
estimated mean for the probability distribution attached to statement
S will be in the interval (L,U)"
So, these are probability intervals, but with a different semantics
than Walley's imprecise probabilities or Keyne's probability intervals.
We have computational algorithms for propagating these indefinite
probabilities through logical inferences.
-- Ben
On Feb 2, 2007, at 9:37 PM, gts wrote:
On Fri, 02 Feb 2007 15:57:24 -0500, Ben Goertzel <[EMAIL PROTECTED]>
wrote:
Interpretation-wise, Cox followed Keynes pretty closely. Keynes
had his own eccentric view of probability...
Although I don't yet know much about Cox, (Amazon is shipping his
book to me), I have studied a bit about Keynes and yes, eccentric
is my view an understatement!
I assume you are familiar with F.P. Ramsey? (If not, he was one of
the founders/discoverers of the subjective theory along with de
Finneti, but separately.) I read Ramsey's classic paper "Truth and
Probability" and found his arguments very convincing, including his
criticisms of Keynes. For example:
"But let us now return to a more fundamental criticism of Mr
Keynes' views, which is the obvious
one that there really do not seem to be any such things as the
probability relations he describes. He
supposes that, at any rate in certain cases, they can be perceived;
but speaking for myself I feel confident
that this is not true. I do not perceive them, and if I am to be
persuaded that they exist it must
be by argument; moreover I shrewdly suspect that others do not
perceive them either, because they
are able to come to so very little agreement as to which of them
relates any two given propositions." [1]
I agree with Ramsey that Keynes' supposed probability relations do
not seem to exist and that in any case they cannot be perceived in
the way Keynes claimed. I echo Ramsey here in saying, "I do not
perceive them, and if I am to be persuaded that they exist it must
be by argument."
I suspect that if Ramsey were alive today, he would shudder at the
thought of programming Keynesian-like probability relations in AGI.
Are you attempting something like this in Novamente? (Please
forgive my ignorance of your Novamente project. I'm still learning
about it.)
-gts
1. Truth and Probability by Frank P. Ramsey
cepa.newschool.edu/het/texts/ramsey/ramsess.pdf
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