[extropy-chat] what is probability?

[gts]

> Methinks the problem is that there is no such thing as "two identically
> rational agents"

That is almost certainly true for now and may remain true into the  
indefinite future, but here we are discussing theories and principles. In  
the argument I presented, the two rational agents are in principle  
absolutely identical with respect to their rationality and background  
knowledge/inputs, including in this important respect: they each have an  
identical ability to make totally arbitrary decisions between equally  
rational alternatives.

In machine terms this would mean they each have the ability to output a  
random number (real or pseudo-random, it makes no difference here) to  
facilitate their arbitrary decisions.

Is it rational for the agents to make arbitrary decisions between rational  
alternatives? I think so. The alternative leads to paradox.

But a consequence is that rational agents with the same background  
knowledge may be permitted to have different judgemental probabilities on  
the same outcome, as in the subjective theory of probability.

(The only way to escape this conclusion short of abandoning the principle  
of indifference even as a heuristic tool, would be, at least that I can  
see, to prove somehow that one of the three alternative physical  
parameters are preferable to the other two for setting a prior probability  
on the dimensions of the unseen cube.)

-gts