Recently, Steve Minton circulated an announcement on this list
on the occasion of _JAIR_'s publication of Professor Halpern's article which
claims a counterexample to Cox's Theorem. Many readers will be familiar
with the controversy from Professor Halpern's AAAI 1996 paper.
Cox made the assumption which has been identified as sufficient to
defeat the counterexample. It appears on page 6, second column, immediately
after the introduction of the crucial equation (8) in Cox's 1946 paper. Some
further remarks on the subject, including the prominence of this assumption
in Cox's thought and the use he made of it in later work, can be found in
the other paper cited below.
I post because a colleague has run into some criticism from other
scholars for relying upon Cox's Theorem while its correctness appears to be
in dispute. I am also familiar with an earlier, similar situation. It is
unproductive that a true and competently demonstrated fact of mathematics
should any longer remain under an unwarranted cloud.
Paul
R.T. Cox, Probability, frequency, and reasonable expectation, _American
Journal of Physics_ 14(1), 1-13, January-February 1946.
P. Snow, On the correctness and reasonableness of Cox's Theorem for finite
domains, _Computational Intelligence_ 14(3), 452-459, August 1998.