[extropy-chat] what is probability?

[gts]

On Sat, 13 Jan 2007 12:08:09 -0500, Benjamin Goertzel <ben at goertzel.org>  
wrote:

> 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.

-gts