*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

**References**

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.