Cox's Theorem Revisited

TL;DR

This paper critically examines the assumptions behind Cox's Theorem, exploring various strong and arguably unnatural sets of conditions under which the theorem can be proved.

Contribution

It provides a detailed analysis of the assumptions required for Cox's Theorem and presents alternative sets of assumptions for its proof.

Findings

Identifies the strength and unnaturalness of common assumptions

Proposes alternative assumption sets for Cox's Theorem

Highlights limitations of existing proofs

Abstract

The assumptions needed to prove Cox's Theorem are discussed and examined. Various sets of assumptions under which a Cox-style theorem can be proved are provided, although all are rather strong and, arguably, not natural.