Interpreting Probability: Controversies and Developments in the Early Twentieth Century. By David Howie. New York: Cambridge University Press. 2002. xi; 262 pp. $60.00.
The early twentieth century was rich in “controversies and developments” in probability. Perhaps the best known development was Kolmogorov’s axiomatisation of probability which von Plato (1994) presents as the product of a pure mathematics and theoretical physics culture. The present book analyses a controversy with players from other cultures—statistics, philosophy, geophysics and genetics.
Early in the century the foundations of statistics shifted. In the 20s R. A. Fisher (1890-1962), probably the most influential twentieth century statistician, rejected the Bayesian approach founded on probability as a degree of reasonable belief (probability interpreted epistemically) and based his work, including maximum likelihood, on frequentist foundations. Karl Pearson, ‘Student’ and their contemporaries had run together Bayesian and non-Bayesian (classical) arguments.(The labels Bayesian and classical, epistemic and frequentist are anachronisms, of course.)
In Cambridge philosophy, however, 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 his collaborator Dorothy Wrinch who had attended Johnson's lectures. Wrinch and Jeffreys used probability to explicate induction and investigate the reasonableness of scientific theories, including general relativity. For such purposes, probability as a limiting frequency was useless but they considered it mathematically unsound as well.
Around 1930 Jeffreys, now working in empirical geophysics, started devising methods for analysing data based—naturally—on epistemic probability. Fisher did not care much about philosophy or physics but he knew about analysing data and a dispute ensued.
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, specially, 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.”
A sketch of probability before the twentieth century, emphasising 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 was for me the best in the book for it is very fresh with much new material. 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 debateable. Fisher was always involved with genetics but when he wrote about probability, e.g. 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.” In this case little is revealed for each man set out doing things his way and then, when challenged, justified himself with a summary of his past writings. There was a genuine clash between rival interpretations but the parties spoke for themselves, not for Bayesians or frequentists in general.
Neither protagonist conceded a thing but the debate affected the work of both. Jeffreys reacted to the dose of statistics Fisher administered by reconstructing the subject on Bayesian lines in the Theory of Probability. The reviews were not appreciative but for Jeffreys there was the sweetest of endings when modern Bayesians, especially Zellner and Lindley, canonised him for carrying on regardless. Fisher also got something—arguments from Jeffreys to use against other frequentists! The book mentions these consequences without treating them in detail. A detailed account of any of them would have sustained the narrative drive of the earlier chapters. As it is, the Jeffreys-Fisher controversy was too esoteric, too personal to be any more than a detail in the big probability picture with which the book closes.
Overall the book is interesting and well written. It is particularly good to see historians of science entering a field dominated by memorialists.
John Aldrich, University of Southampton
Fisher, R. A. 1922/3. Review of J. M. Keynes's Treatise on Probability, Eugenics Review, 14, 46-50.
Jeffreys, Harold. 1939. Theory of Probability. Oxford: Oxford University Press.
von Plato, Jan. 1994. Creating Modern Probability. Cambridge: Cambridge University Press.