The Reasonableness of Possibility From the Perspective of Cox

of the full paper The possibility calculus is shown to be a reasonable belief representation in Cox's sense, even though possibility is formally different from probability. So-called "linear" possibility measures satisfy the equations which appear in Cox's Theorem. General possibility measures encode sets of linear measures, consistent with a method of belief representation based on sets which Cox pioneered. Exploring the relationship between possibility and Cox's belief measures provides an opportunity to discuss some of the ways in which Cox dissented from Bayesian orthodoxy, especially in his tolerance of partially ordered belief and his rejection of prior probabilities for evidentiary inference which begins in ignorance.