Foundations I: The Frequentist Approach

A key feature of twentieth-century science is the clear understanding of the role played by mathematical models of real phenomena. One of the first to fully articulate this was the applied mathematician Richard von Mises, who constructed such models for a number of disciplines. One of these was his 1919 model for frequentist probability. An alternative subjective concept of probability was axiomatized slightly later by Bruno de Finetti and Frank Ramsey. An axiomatization of probability in purely mathematical terms without regard to its interpretation was provided by Kolmogorov in 1933. It has the advantage of being applicable to both the frequentist and the subjective concepts of probability and, unlike those interpretations, is accepted fairly generally and is noncontroversial.