What was Kolmogorov's attitude regarding the frequentist versus Bayesian statistics controversies? Did he ever write or speak about his own views on Fisher or de Finetti, Jeffreys, etc.? Or were those times so politically charged that it was wiser for him not to get involved with words/concepts such as "subjective" or "objective", etc?

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    $\begingroup$ Kolmogorov was a committed frequentist:"In laying out the assumptions needed to make probability theory applicable to the world of real events, the author has followed in large measure the model provided by Mr. von Mises". See Shafer, The origins and legacy of Kolmogorov's Grundbegriffe for commentary, which concludes:"Whereas Kolmogorov's axiomatization became standard, his philosophy of probability showed little staying power... aside from Cramer's imitation, we find hardly any mention of Kolmogorov's philosophy in the subsequent literature". $\endgroup$
    – Conifold
    Sep 12, 2022 at 5:31
  • $\begingroup$ @Conifold Are you also implying that Kolmogorov never changed his mind between the "Grundbegriffe (1933) and his death (1987)? Do you know if he ever wrote explicitly against "Bayesianism" or he kept this to himself? $\endgroup$
    – hyportnex
    Sep 13, 2022 at 1:04
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    $\begingroup$ This is what Shafer says (p. 51):"Kolmogorov’s high regard for von Mises’s theory of Kollektivs was sincere. It emerged again in the 1960s, as a motivation for Kolmogorov’s thinking about the relation between algorithmic complexity and probability. The evident sincerity of Kolmogorov’s frequentism, and his persistence in it throughout his career, gives us reason..." $\endgroup$
    – Conifold
    Sep 13, 2022 at 3:33


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