Bibliography

RICHARD V. MISES. Wahrscheinlichkeit, Statistik und Wahrheit. Wien. Verlag von Julius Springer. 1928. Pp. VIII + 190.

R. Mises. Probability, statistics, and truth.

Prof. Mises, director of the Institute of Applied Mathematics of the University of Berlin, is known as one of the most energetic, consistent, and radical reformers of the theory of probability of our time. In this field he is responsible for a doctrine that provides new and highly distinctive foundations for mathematical statistics and its most important applications. The mathematical side of this doctrine was presented by the author with full thoroughness in 1919 in the fifth volume of Mathematische Zeitschrift; its fundamental and natural-philosophical aspects were treated in a series of short articles that appeared in Naturwissenschaften during 1919–1927. Finally, the author indicated the most important physical applications in two papers published in volume 21 of Physikalische Zeitschrift in 1920.

In the book under review the author sets himself the task of giving a generally accessible exposition of his doctrine together with its most important applications. The book presupposes no special knowledge on the reader’s part in mathematics or physics and, thanks to its clear, vivid, and sufficiently detailed exposition, can be understood without difficulty by anyone. Mises’ distinctive doctrine is developed here consistently and systematically against the background of a relentless criticism of traditional statistical conceptions.

Such a generally accessible and at the same time systematic exposition of one of the most important contemporary statistical theories, which has already exerted great influence, in particular on the statistical conceptions of the physical sciences, naturally cannot fail, in itself, to have very considerable value; and in this sense the appearance of the book under review, which makes intelligible to everyone what until now had been the possession of specialists alone, should be welcomed in every way.

To evaluate this book with respect to its content means, of course, to establish one’s attitude toward Mises’ doctrine itself. Within the limits of the present review, there is naturally no possibility of conveying, even in brief, the foundations of this doctrine. Let us note only that it may call forth serious objections from two different sides: with regard to the princi-

philosophically naturalistic point of view, cannot be satisfied by a definition of probability as the result of a known experiment—a definition which consciously tries to renounce knowledge of what truly exists and to accept as the ultimate truth the description of the connection between the results of various experiments; secondly, objections also arise from the formal-mathematical side; the reviewer believes that this aspect of the matter in Mises’s doctrine is not only unfinished, but, in the very formulation of the problem, offers no hope; already the fundamental concept of a collective, on which the whole doctrine is formally built, is, in the mathematical respect, not free from internal contradictions.

Undoubtedly a major historical merit of Mises is the “destructive,” critical part of his work; it seems that the scholastic traditions of the theory of probability, which for lack of fresh thought had retained their right to life even in modern textbooks, have never before been shattered with such ruthlessness and such scientific enthusiasm. We do not doubt that the initial principles of Mises’s doctrine will be revised many more times by science. But that stagnant and rotten material which has been smashed by his living and fresh scientific thought will never rise again from the ashes; and this alone is already sufficient to acknowledge significant value, complete freshness, and scientific temperament in the works of this outstanding German scholar.

A. Khinchin.