Keynes vs. Kolmogorov: Two Axiomatics of Probability

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 to probability codified by Andrei Kolmogorov in Grundbegriffe der Wahrscheinlichkeitsrechnung (1933). We present the structure of both approaches, identify the key divergences — the epistemological interpretation of the probabilistic relation, Keynes’s rejection of full numerability, the status of conditional probability, and the concept of the weight of evidence — and analyse the reasons for Kolmogorov’s triumph. We survey four contemporary interpretive traditions: subjective Bayesianism, frequentism, logical probability, and imprecise probabilities. Particular attention is paid to current applications — from Bayesian inference in machine learning and decision theory under uncertainty, to catastrophe risk pricing and uncertainty management in climate models. We argue that Keynes’s intuitions, long neglected, are gaining new significance in the face of the epistemic challenges of the twenty-first century.