Wittgenstein and Ramsey on Probability, Frequency and Belief

Although both Wittgenstein and Ramsey were supporters of an epistemic notion of probability, they embraced different interpretations. On the one hand, Wittgenstein defined probability as a logical relation between propositions; on the other hand, Ramsey regarded probability as a subjective degree of belief. Wittgenstein’s conception influenced Waismann and, through the latter’s work, Carnap, but it has attracted little attention in the literature. By contrast, Ramsey has inspired an ongoing debate about subjective probability and decision theory. In this paper, Wittgenstein’s conception of probability is reconstructed from a number of observations found in his writings and is compared with that of Ramsey. Particular attention is paid to the link between epistemic probability and frequencies, an issue addressed by both. The paper also briefly focuses on Waismann’s work.