[extropy-chat] Coin Flip Paradox

[gts]

On Mon, 29 Jan 2007 21:02:56 -0500, Jef Allbright <jef at jefallbright.net>  
wrote:

> ON the contrary, I think the subject of probability is very interesting  
> and relevant to the extropy list.  It's about how we make certain  
> decisions under uncertain circumstances

Exactly!

Probability theory has relevance to almost area of life, to say nothing of  
its extreme relevance to extropian topics like AI, decision theory, the  
philosophy of science, epistemology, and QM.

My interest in this subject stems from my reading of Karl Popper  
(_Conjectures and Refutations_ in the Spring of last year and, more  
recently, _The Logic of Scientific Discovery_). These two dense tomes  
inspired me to study this subject more intensively.

I highly recommend Donald Gillies book _Philosophical Theories of  
Probability_.  Gillies is a Professor of Philosophy of Science and  
Mathematics at King's College, London. He earned his Phd under the  
supervision of Popper's student Imre Lakatos. His book was a turning point  
for me; many of the ideas and arguments I've presented here come from  
Gillies' excellent survey of the subject. Professor Gillies also wrote a  
book about AI and the scientific method, currently on my must-read list.

Currently I am reading _Subjective Probability: The Real Thing_ by the  
late professor Richard Jeffrey of Princeton. Professor Jeffery spent his  
entire life studying probability and decision theory. In the end he was an  
enthusiastic supporter of the radical subjectivist philosophy of Bruno de  
Finneti, or so I gather so far from reading his book.

I think it's important that people realize this field of knowledge is  
essentially brand new, in its modern form newer even than quantum  
mechanics (the classical probability theory of Laplace is essentially  
dead). Andrei Kolmogorov formalized the axioms of probability theory in  
1933, barely 70 years ago, and since around that time we've seen a  
proliferation of competing interpretations, each purporting to explain the  
meanings behind the symbols. Much work still needs to be done.

-gts