On Sat, 10 Feb 2007 21:40:28 -0500, Benjamin Goertzel <[EMAIL PROTECTED]>
wrote:
Sorry it took me so long to get to this message...
About the Principle of Indifference and probability theory...
The question is what should an AGI system does when the data available
to it appears to support multiple contradictory conclusions.
It has to decide, somehow.
Yes, I understand.
The PI is one way to decide...
Yes, and there is nothing particularly wrong with the PI, I think,
provided that one understands it is not some kind of a priori 'logical
truth' handed down to us from the heavens. That is, I think there is no
logical sin in using some other method, just as subjective bayesians have
been telling the world since about 1926, much to the chagrin of objective
bayesians.
I note that the Occam prior connects more closely to neuroscience than
the PI, in that there are plausible arguments the brain uses an
"energy minimization" heuristic in some cases. Read Montague makes an
argument in this direction in:
I would need to learn more about Montague's idea to understand what he
means about the neuroscience connection, but it sounds reasonable.
However, when multiple choices seem to have roughly equivalent
complexity, then the Occam prior basically degenerates to the PI.
This goes back to my earlier idea that equivalent complexity (or
equivalent information) takes on a different practical meaning in the
special case in which there is no information at all, i.e., when one is in
a state of total ignorance, which is the case when the PI might be
invoked. Under such special circumstances I think one might say "All bets
are off. Think as thou wilt, within the bounds of reason." This at least
seems to me a reasonable position for humans to take here (and it is
consistent with Cox, I think). What this idea might mean for AGI is a
different question, of course, and I understand that is the question on
your mind.
I'll need also to read the paper by Zurek and others... thanks.
And, just as with the PI, these more sophisticated approaches must be
applied correctly and intelligently to be useful.
Yes.
-gts
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