F.Y. Edgeworth’s Treatise on Probabilities

Probability theory has a central role in Edgeworth's thought; this article examines the philosophical foundation of the theory. Starting from a frequentist position, Edgeworth introduced some innovations to the definition of primitive probabilities. He distinguished between primitive probabilities based on experience of statistical evidence, and primitive a priori probabilities based on a more general and less precise kind of experience, inherited by the human race through evolution. Given primitive probabilities, no other devices than the rules of calculus of probabilities are necessary for inferring complex probabilities, as the ones defined by Bayes's theorem—an enlargement of the frequentist tradition as defined by Venn. The notion of probability is objective; the passage from the objective sphere to the epistemic one requires rules external to the theory of probability. Edgeworth distinguishes between two notions: credibility, which is the direct translation of probability into the epistemic sphere and which obeys the same rules of the latter; and belief, which has a weak relation with probability, based as it is not only on experiential knowledge, but also on “instinct and sentiment.” According to a nineteenth-century tradition, belief is the base of human action; Edgeworth concludes therefore that probability is not useful for the theory of decision. We propose to classify Edgeworth's theory of probability as precursor of modern eclectic or pluralistic tradition on probability, and according to which probability has an irreducible dualistic nature.