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Journal Article
Higher Order Probabilities and Coherence
Soshichi Uchii
Philosophy of Science
Vol. 40, No. 3 (Sep., 1973), pp. 373-381
Published by: The University of Chicago Press on behalf of the Philosophy of Science Association
Stable URL: https://www.jstor.org/stable/186197
Page Count: 9
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Topics: Betting, Modal realism, Logical theorems, Real numbers, Mathematical theorems, Mathematical functions, Modal logic
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Abstract
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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Philosophy of Science © 1973 The University of Chicago Press