On Sun, 04 Feb 2007 12:46:06 -0500, Richard Loosemore <[EMAIL PROTECTED]>
wrote:
If we knew for sure that the human mind was using something like a
formalized system (and not the messy nonlinear stuff I described), then
we could quite comfortably say "Hey, let's do the same, but simpler and
maybe even better." My problem is, of course, that the human mind may
well not be doing it that way...
I'm somewhat sympathetic to that point of view, Richard, in case it's any
consolation to you. :)
Your words remind me of the criticism that the subjectivist theorist F.P.
Ramsey had of the logical theories of J.M. Keynes, which I mentioned here
yesterday or the day before and which I find very persuasive.
Keynes argued for the existence of something he called probability
relations. These relationships were supposed to be perceivable by the
human mind in the same manner in which it sees logical relationships. For
Keynes, probability theory was in fact a sort of extension of deductive
logic in which probable conclusions were partially entailed by their
premises. The degree of partial entailment was supposed to be equal to the
probability.
So for example on Keynes' view the statement "Ten black ravens exist"
partially entails the statement "All ravens are black" and the degree of
entailment = P("All ravens are black").
On this view all rational minds should assign exactly the same value to:
P(All ravens are black|Ten black ravens exist)
Keynes was influenced heavily by Bertrand Russell and Alfred North
Whitehead who had together attempted to do something similar with their
*Principia Mathematica*. It's doubtful that Russell and Whitehead
succeeded, and I think the same can be said of Keynes.
Ramsey's most pointed criticism was that these Keynesian probability
relationships, if they exist, certainly are not perceived by the mind as
Keynes claimed. And who here can argue with Ramsey's criticism? If these
probability relationships were perceivable in the same way as ordinary
logical relations then there would be hardly any question about the
correct way to do probabilistic reasoning in AGI -- we'd all immediately
recognize the correct algorithms and agree.
-gts
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