[extropy-chat] what is probability?
gts_2000 at yahoo.com
Mon Jan 1 00:03:39 UTC 2007
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
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
"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.
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