The Cox Theorem: Unknowns And Plausible Value

Abstract

We give a proof of Cox's Theorem on the product rule and sum rule for conditional plausibility without assuming continuity or differentiablity of plausibility. Instead, we extend the notion of plausibility to apply to unknowns giving them plausible values. Our proof is enormously simpler than others that have recently appeared in the literature, yet completely rigorous. For example, we do not need to investigate the 11 possibilities for conditional plausibilities as described on page 25 of Jaynes' recent book Probability Theory.