Interpreting Probability: Controversies and Developments in the Early Twentieth Century (review)

The early twentieth century was rich in "controversies and developments" in probability. Perhaps the best-known development was Kolmogorov's axiomatization of probability that Jan von Plato (1994) presents as the product of a pure mathematics and theoretical physics culture. The present book analyzes a controversy with players from other cultures—statistics, philosophy, geophysics, and genetics.

Early in the century the foundations of statistics shifted. Karl Pearson, "Student" (William Sealy Gosset), and their contemporaries had run together Bayesian and classical arguments. The Bayesian argument rested on probability interpreted as a degree of reasonable belief (probability interpreted epistemically), while the classical argument rested on probability as a limiting frequency. However, from the 1920s R. A. Fisher (1890–1962), the most influential statistician of the century, rejected the Bayesian approach and based his work, including maximum likelihood, on frequentist foundations. (The labels Bayesian and classical, epistemic and frequentist are anachronisms, of course.)

Meanwhile, in Cambridge philosophy, epistemic probability prospered, advocated by W. E. Johnson, J. M. Keynes, and C. D. Broad. It reached Harold Jeffreys (1891–1989), physicist and applied mathematician, through Dorothy Wrinch, who had attended Johnson's lectures. The Wrinch and Jeffreys partnership used probability to explicate induction and to investigate the reasonableness of scientific theories, including the new theory of general relativity. For their purposes, probability as a limiting frequency was useless, but they considered it mathematically unsound as well.

Around 1930 Jeffreys, now involved in empirical geophysics, began devising methods for analyzing data, based—naturally—on epistemic probability. Fisher did not care much about philosophy or physics, but he knew about analyzing data and a dispute followed.

Interpreting Probability aims "to place the 1930s clash between the frequentist and epistemic interpretations of probability within a more general overview of the history of probability, and to provide . . . an account of the early work of R. A. Fisher and, especially, Harold Jeffreys. I have also tried to make the broader point that mathematical theories, like other products of science, can only be fully understood as products of their culture . . . . For Fisher and Jeffreys, the meaning of probability and the development of a theory of inference evolved in each case with a particular conception of scientific practice, characterized by the differing aims and method of genetics and geophysics respectively" (226).

A sketch of probability before the twentieth century, emphasizing the history of the two interpretations, follows a brief introduction. Chapters on Fisher and Jeffreys before the clash prepare for a chapter on the clash itself. The Fisher chapter is a useful synthesis of a fairly extensive literature. The Jeffreys chapter is very fresh with much new material and for me was the best in the book. The controversy has been discussed before, but this treatment is deeper; it makes good use of the correspondence between Fisher and Jeffreys and other unexploited sources. The business concludes with an interesting wide-ranging survey of probability in the 1930s, followed by a short epilogue.

"Culture" is so flexible it is easy to agree that theories "can only be fully understood as products of their culture," but the cultural explanations offered are not entirely convincing. The identification of Fisher's culture as genetics and Jeffreys's as geophysics is debatable. Fisher was always involved with genetics, but when he wrote about probability (for example, when reviewing Keynes's Treatise), he wrote as a statistician, using the same concept of probability as "Student" and other non-geneticist statisticians. Jeffreys's first probability publication predates his work in geophysics, and one could argue that his determining culture was one to which he never really belonged—Cambridge philosophy.

The author is drawn to the Fisher-Jeffreys dispute by the thought that "the deep assumptions and commitments of a research program, though usually tacit are often unveiled during periods of controversy" (9). In this case little is revealed, for each...