[extropy-chat] what is probability?

[gts]

On Wed, 17 Jan 2007 21:02:46 -0500, Jef Allbright <jef at jefallbright.net>  
wrote:

> Gordon, this is the same as the problem of the boxes.

No question about that! It is yet another version of the bertrand paradox.

> The Principle of Indifference is correct and beautiful in its elegance.

So it would seem, but these problem situations demonstrate that the PI  
fails to guide us under certain conditions of high uncertainty; that is,  
it fails when it is most needed.

> Maybe it would help you to remember that there's only a single TRUE
> speed of the train.

Of course, but the point here is that the PI fails to give us a logically  
consistent epistemic probability of that one true objective speed.

The bertrand paradoxes are a problem and a source of embarrassment for  
those who advocate a logic-driven epistemic interpretation of probability  
theory, as opposed to a purely subjective or objective frequentist theory  
(neither of which make use of the PI as a logical principle).

-gts