[extropy-chat] what is probability?

[gts]

On Mon, 08 Jan 2007 17:58:12 -0500, John K Clark <jonkc at att.net> wrote:

> But I'm not just picking on you, I think that is largely the case for all
> philosophers of science. The thing is, if they were really onto  
> something, if they really did have a better understanding of the 
> scientific method  then mere scientists you'd think they wouldhave made  
> major contributions to our understanding of how theuniverse works just  
> like those silly scientists have. But I can't thinkof a single  
> philosopher of science that has done that. Isn't that strange?

Ernst Mach comes to mind as a philosopher of science who made major  
contributions to our understanding of how the universe works. As one  
biographer put it: "[Mach was] an Austrian physicist and philosopher who  
established important principles of optics, mechanics, and wave dynamics  
and who supported the view that all knowledge is a conceptual organization  
of the data of sensory experience (or observation)."  
http://www.erraticimpact.com/~analytic/mach.htm

Mach's influence as a philosopher is also very relevant to this subject of  
probability.  Richard von Mises, famous for developing the frequency  
theory of probability, considered himself a "devoted disciple of Mach"  
(his own words) and according to Gillies (2000), "Von Mises in his  
development of probability theory follows exactly the pattern of Mach's  
development of mechanics."

As a philosopher Mach was a empirical positivist, meaning that he  
considered it meaningless to speak of things that cannot be verified  
empirically. Mach's positivist attitude was so strong that he even refused  
to acknowledge the existence of atoms on the grounds that no one had ever  
seen one!

The frequency theory of von Mises is true to that same philosophy of  
science; according to frequentists it is meaningless to speak of the  
probability of an outcome except in terms of the empirical frequency of  
that outcome in a collection of observations.

-gts