LEADING TO THE ONLY THING REALLY INTERESTING ABOUT THIS DISCUSSION:
What interests me is that the Principle of Indifference is taken for granted by so many people as a "logical truth" when in reality it is fraught with logical difficulties.
Gillies (2000) makes an analogy between the situation in probability theory concerning the Principle of Indifference and the situation that once existed in set theory concerning the Axiom of Comprehension.
Like the Principle of Indifference, the Axiom of Comprehension seemed logical and intuitively obvious. That axiom states that all things which share a property form a set. What could be more logical and intuitively obvious? But the Axiom of Comprehension led to the Russell Paradox, and a crisis in set theory.
Similarly the Principle of Indifference (and its predecessor the Principle of Insufficient Reason) led to numerous difficulties, (e.g., the Bertrand Paradoxes, and arguments such as Cox's). Subsequently we saw a schism in probability theory. The classical theory was discredited, including the classical interpretation of Bayes' Theorem, and replaced with at least four different alternative interpretations.
Among bayesians, one might say De Finetti and Ramsey and the subjectivists helped rescue bayesianism from the jaws of (philosophical) death, by separating bayesianism from that albatross around its neck which is the Principle of Indifference.
-gts ----- This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?list_id=303
