Keynes vs. Kolmogorov: Two Axiomatics of Probability

Jakub Ryłow

No 2026-8, Working Papers from Faculty of Economic Sciences, University of Warsaw

Abstract: The paper examines the logical theory of probability formulated by John Maynard Keynes in A Treatise on Probability (1921) as an axiomatic project competing with the measure-theoretic approach codified by Andrei Kolmogorov in Grundbegriffe der Wahrscheinlichkeitsrechnung (1933). Beyond a synthetic comparison of both systems and their contemporary successors, the paper makes two original contributions. First, we identify and formally prove the Boolean presupposition of Ramsey's Dutch book argument: the argument establishes only a conditional result — if the event domain is a Boolean algebra, then coherence requires classical probability — whose antecedent is precisely what Keynes's partial order postulate denies. Ramsey therefore did not refute Keynesian logicism unconditionally; he refuted it within a domain whose universality Keynes contested. This formalises, using the Wroński–Godziszewski (2016) theorem, a gap in the standard history of the debate that has gone unnamed in the literature. Second, we propose the imprecision index of a credal set as the first candidate formal analogue of Keynes's weight of evidence within the established framework of imprecise probabilities.

Keywords: logical probability; measure theory; weight of evidence; imprecise probabilities; Bayesianism (search for similar items in EconPapers)
JEL-codes: B41 C10 C11 D81 G32 (search for similar items in EconPapers)
Pages: 21 pages
Date: 2026
New Economics Papers: this item is included in nep-his, nep-hme, nep-hpe and nep-pke
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https://www.wne.uw.edu.pl/download_file/7138/4282 First version, 2026 (application/pdf)

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Persistent link: https://EconPapers.repec.org/RePEc:war:wpaper:2026-8

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