The Reasonableness of Possibility From the Perspective of Cox

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 that appear in Cox's theorem. Linear possibilities are known to be related to the full range of possibility measures through a method for representing belief based on sets that is similar to a technique pioneered by Cox in the probabilistic domain. 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 his tolerance of partially ordered belief and his rejection of prior probabilities for inference which begins in ignorance.

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