[extropy-chat] what is probability?
gts_2000 at yahoo.com
Sun Jan 14 01:21:27 UTC 2007
On Sat, 13 Jan 2007 12:08:09 -0500, Benjamin Goertzel <ben at goertzel.org>
> All the Bertrand paradox shows is that the natural language concept
> "select at random" is ambiguous, and can be disambiguated to yield
> multiple meanings.
What then is the one true disambiguated meaning of "select at random"? Or
is there no such thing?
I mentioned Jaynes' proposed solution. Apparently Jaynes went to great
lengths to derive what he hoped would be the one true meaning of
"selecting a random chord". I've seen a summary of his argument and it
seems quite plausible, but even he stopped short of saying he had proved
his case in any formal logical sense.
And even assuming his argument is correct for the random chord paradox,
how is it in any way translatable to the other paradoxes?
If the Bertrand paradox is fundamentally unsolvable then it seems to me
the principle of indifference is toast as a logical principle, and if so
then it seems two rational agents would be free in certain cases to use
different bayesian priors.
I would guess that thought is probably anathema to AI researchers; we want
to know all robots of a kind will think and act identically under
identical circumstances, yes? Or do we? Real humans seem not to.
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