Synthese 198 (12):11713-11724 (2020)

Michael Nielsen
University of Sydney
I show that de Finetti’s coherence theorem is equivalent to the Hahn-Banach theorem and discuss some consequences of this result. First, the result unites two aspects of de Finetti’s thought in a nice way: a corollary of the result is that the coherence theorem implies the existence of a fair countable lottery, which de Finetti appealed to in his arguments against countable additivity. Another corollary of the result is the existence of sets that are not Lebesgue measurable. I offer a subjectivist interpretation of this corollary that is concordant with de Finetti’s views. I conclude by pointing out that my result shows that there is a sense in which de Finetti’s theory of subjective probability is necessarily nonconstructive. This raises questions about whether the coherence theorem can underwrite a legitimate theory of rational belief.
Keywords De Finetti  Coherence  Foundations of Probability  Hahn-Banach
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DOI 10.1007/s11229-020-02825-7
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References found in this work BETA

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