[extropy-chat] what is probability?

[gts]

I was inspired to start this thread when I saw some discussion of  
probability in the thread "Is Many Worlds testable?" In that thread Stuart  
writes, "Probability is a way of quantifying ignorance of the future."

Is that so? Is there not a better definition? What is the best definition  
of probability?

Actually this question of what is probability has occupied much of my free  
time since last July, when in a thread called "Popper and QT", Serafino  
wrote:

"I would say that I do not even remember
what... probability is. I vaguely remember
that von Weizsaecker wrote (in 'Zeit und Wissen')
that probability is 'the expectation value of
the relative frequency'. It seems a perfect
mix of subjectivism and frequentism."

Since that time I have familiarized myself with the subject such that I  
think I understand the basic philosophical issues at least enough to  
understand the question of what is probability. And it is a difficult one.

(As a probabilistic theory it's no wonder that QM's philosophical  
underpinnings are so inscrutable. Nevermind the mysterious results of  
atomic experiments; the best philosophers cannot agree even on the nature  
of probability in its own right!)

At least four theories of probability deserve attention:

1) The Logical Theory, in which probability is defined as a degree of  
rational belief (Keynes).

2) The Subjective Theory, in which probability is a degree of belief of a  
particular individual (Ramsey, De Finetti).

3) The Frequency Theory, in which probability of an outcome is the  
limiting frequency of that outcome in a long or infinite series of similar  
events (von Mises).

4) The Propensity Theory, in which probability is an objective property of  
an object or experimental arrangement (Popper).

Each of these theories come in several flavors. Generally they can be  
divided into two major camps: objectivist theories and epistemic theories.

Theories 3 and 4 are clearly objective, 2 is clearly epistemic, and 1 will  
be seen as either epistemic or objective depending on one's conviction  
concerning the alleged objective neo-platonic reality of logic.

In the interest of starting a discussion...

Consider a frequent event (E), such as 'Rain in the Amazon Rain Forest'.

Which statement is most true?

A) E is frequent because it is probable.
B) E is probable because it is frequent.

-gts