[extropy-chat] what is probability?

[gts]

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

> How does this help with the PI and so forth?  Not at all as far as I
> can tell, it's just the only work I know that formally addresses the
> issue of defining randomness ;-)

In 1928, Richard von Mises published _Probability, Statistics and Truth_,  
which pretty much started the frequentist revolution in probability.

In that book he developed two supposed 'empirical laws of probability':

The first law was not entirely original to him (he was following after  
Venn, famous for Venn diagrams, and after someone else whose name I don't  
recall). This first law is the law that relative frequencies converge as  
the number observations increase. As everyone knows, if you flip a fair  
coin enough times the % of heads will converge on 50% to any degree of  
precision.

Von Mises' second law was his own 'discovery': it is about the definition  
and meaning of randomness, what I have called here "The Law of Excluded  
Gambling Systems".

Principle of the Impossibility of a Gambling System
http://www.philosophyprofessor.com/philosophies/impossibility-of-a-gambling-system-principle.php

I don't think the frequency definition of "random" has changed very much  
since then, though Popper and some other people have attempted to improve  
on von Mises' theories.

-gts