ON THE CORRECTNESS AND REASONABLENESS OF COXS THEOREM FOR FINITE DOMAINS

Halpern has recently claimed a counterexample to Cox's Theorem, a well -known existence result for subjective probability distributions, but stated that the counterexample can be defeated by a specific assumptio n. Cox made this assumption, and so escapes the counterexample. Althou gh Halpern questioned whether the assumption is reasonable for finite sets of sentences, it supports features that distinguish Cox's work fr om other, more restrictive motivations of probabilism. Paris has recen tly offered a new proof of Cox's Theorem whose correctness is satisfac tory to Halpern, one that depends on a premise consistent with Cox's l ater work. As with any deductive argument, denial of a premise license s denial of the conclusion, but Cox's conclusion does follow from prem ises plainly acceptable to him.