Probability, statistics, and the theory of errors

Abstract

A discussion of the logical basis of scientific method, replying to criticisms by R. A. Fisher. The process of generalizing from observational data is essential, but its use requires an a priori postulate incapable of proof; we must make such a hypothesis or reject scientific inference altogether. The theory of probability provides adequate primitive postulates for this purpose, but it is necessary to take probability as a fundamental idea and not to attempt to define it. The nature of the prior probability is discussed, and another argument is given showing that when there is no previous knowledge of the value of a standard error [sigma] its prior probability should be taken proportional to d[sigma]/[sigma].