THERE are many ways, none altogether satisfactory, of defining probability, but roughly speaking, these fall in two groups, namely, those based upon the 'equally-likely' concept of Laplace, and those based on the concept of frequency. In recent years the frequency method has been greatly developed by von Mises, who introduced the notion of a collective. This is defined as a mass phenomenon or an unlimited sequence of observations such that the relative frequency of a particular attribute tends to a fixed limit unaffected by any place selection or gambling system. The probability of the attribute in the given collective is then defined as this limit. It is claimed that this treatment avoids the logical difficulties inherent in Laplace's method.
Etude critique de la notion de collectif
Par Prof. Jean Ville. (Monographies des probabilites, Fascicule 3.) Pp. iv + 144. (Paris: Gauthier-Villars, 1939.) 75 francs.