Interpretations of probability, 1919-1939: Harold Jeffreys, R. A. Fisher, and the Bayesian controversy

A probability can be interpreted in one of two distinct ways. On a ‘frequentist’ definition, it is a limiting ratio of samples from some physical ensemble; on a Bayesian definition, it is a degree of rational belief in a proposition or hypothesis. This dissertation is a historical study of the two interpretations of probability during the 1920s and 1930s. It focuses on two British scientists, Sir Harold Jeffreys (1891–1989) and Sir Ronald Aylmer Fisher (1890–1962). Jeffreys was a theoretical physicist who used sophisticated mathematical models to study the Earth and solar system. Since his hypotheses were always uncertain, needing revision or even abandonment in the face of incoming results, Jeffreys tried to construct a formal theory of scientific reasoning based on Bayesian probability. Fisher was a biological and agricultural statistician specializing in problems of genetic inheritance. Chiefly concerned with the reduction of experimental data, he regarded Bayesian methods as unfounded in principle and misleading in practice, and worked to replace them with a theory of statistical inference based on frequencies. A direct confrontation between the two men during the early 1930s proved inconclusive: though the two theories were incompatible, each was coherent and defensible. Yet they were not generally regarded as equally persuasive. The Bayesian interpretation, though implicitly adopted by many scientists and statisticians during the eighteenth and nineteenth centuries, was gradually abandoned during the 1920s and largely discredited by 1939. This was not solely due to conceptual difficulties with Bayesianism. I argue instead that not even a mathematical theory of probabilistic reasoning is a disembodied product of logical deduction. The specific meaning given to Bayesian methods, their evaluation as tools for scientific research, and ultimately the reasons why they lost out to the frequentist school—at least until their post-War revival—depended on local contexts of disciplinary practice