[extropy-chat] what is probability?

[gts]

On Tue, 16 Jan 2007 12:23:35 -0500, Benjamin Goertzel <ben at goertzel.org>  
wrote:

> It seems that the notion of randomness is definable objectively only
> for infinite entities.

Yes, at least under the frequentist interpretation no doubt assumed by  
these researchers. And this infinity issue exists as a philosophical  
problem not only for the definition of "random" but also for the  
definition of "probability".

As you probably already know, probability on the frequentist view is  
calculated as the relative frequency of an outcome in the limit as the  
number of observations goes to infinity. (This is how most of us where  
taught to believe. Certainly I was.)

Von Mises, who developed the frequency theory, defended his use of  
mathematical infinities by arguing that he was merely 'abstracting' or  
'idealizing' the objective laws of nature from empirical observations, in  
the same way as it is thought all scientists do.

-gts