Khinchin's 1929 paper on von Mises' frequency theory of probability (Q2075689)

In 1929, a few years prior to his younger colleague Kolmogorov's \textit{Grundbegriffe}, the leading Russian probabilist A. Khinchin published a paper in which he commented on the foundational ambitions of von Mises' frequency theory of probability from 1919. This brief introduction provides background and context for an English translation of Khinchin's historically revealing paper, published as an online supplement. Khinchin's paper is critical both of the logical mathematical part of von Mises' work, in particular his rudimentary notion of randomness, and of the philosophical implications. The author of the paper under review draws comparisons to a later criticism of von Mises' theory by Khinchin from about 1936. The latter paper, which is edited in an English version [\textit{B. V. Gnedenko}, Sci. Context 17, No. 3, 391--422 (2004; Zbl 1181.01046)], is even more critical of von Mises' adherence to the Austrian physicist and philosopher Ernst Mach who had been attacked by Lenin for his alleged idealism in his 1909 \textit{Materialism and empirio-criticism}. The author indicates that Khinchin drew also positive stimuli from von Mises' work particularly for ergodic theory and statistical mechanics. Lack of space may have prevented the discussion of the broader political and philosophical atmosphere in the Soviet Union at the time, with political watchdogs such as E. Kolman enforcing philosophical reflections also on the part of the mathematical practitioners. The paper is well documented with the exception of one source (Vere-Jones 2005) which cannot be traced.