Although it has become a common place to refer to the ׳sixth problem׳ of Hilbert׳s (1900) Paris lecture as the starting point for modern axiomatized probability theory, his own views on probability have received comparatively little explicit attention. The central aim of this paper is to provide a detailed account of this topic in light of the central observation that the development of Hilbert׳s project of the axiomatization of physics went hand-in-hand with a redefinition of the status of probability theory (...) and the meaning of probability. Where Hilbert first regarded the theory as a mathematizable physical discipline and later approached it as a ׳vague׳ mathematical application in physics, he eventually understood probability, first, as a feature of human thought and, then, as an implicitly defined concept without a fixed physical interpretation. It thus becomes possible to suggest that Hilbert came to question, from the early 1920s on, the very possibility of achieving the goal of the axiomatization of probability as described in the ׳sixth problem׳ of 1900. (shrink)

James Forbes' critical examination of the probabilistic reasoning, which led John Michell to infer a physical connection between optically double and multiple stars, is analysed. It is argued that despite the interpretations of its nineteenth-century defenders, Michell's reasoning has some force which does not depend upon questionable Bayesian principles. Attention is drawn to some of the ambiguities concerning the notion of randomness, and it is shown that these ambiguities render Forbes' objections less than conclusive.