Higher order probabilities and coherence

Philosophy of Science 40 (3):373-381 (1973)
It is well known that a degree-of-belief function P is coherent if and only if it satisfies the probability calculus. In this paper, we show that the notion of coherence can be extended to higher order probabilities such as P(P(h)=p)=q, and that a higher order degree-of-belief function P is coherent if and only if it satisfies the probability calculus plus the following axiom: P(h)=p iff P(P(h)=p)=1. Also, a number of lemmata which extend an incomplete probability function to a complete one are established
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DOI 10.1086/288538
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Zoltan Domotor (1981). Higher Order Probabilities. Philosophical Studies 40 (1):31 - 46.

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