On the Correctness and Reasonableness of Cox's Theorem for Finite Domains

Abstract

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 assumption. Cox made this assumption, and so escapes the counterexample. Although Halpern questioned whether the assumption is reasonable for finite sets of sentences, it supports features that distinguish Cox's work from other, more restrictive motivations of probabilism. Paris has recently offered a new proof of Cox's Theorem whose correctness is satisfactory to Halpern, one that depends on a premise consistent with Cox's later work. As with any deductive argument, denial of a premise licenses denial of the conclusion, but Cox's conclusion does follow from premises plainly acceptable to him.