Janina Hosiasson’s logic of rational degrees of belief: subjective probability before and after Ramsey

Abstract:

In 1931, Janina Hosiasson-Lindenbaum proposed a proto-decision-theoretic answer to the value of evidence problem, originally posed by C. D. Broad and eventually solved by I. J. Good in the context of Savage’s decision theory. As an influence on her paper she credited Frank Ramsey, whose then unpublished “Truth and Probability” she had read shortly after Ramsey’s death in 1930. But Hosiasson also insisted that she had “previously thought independently on similar lines”.

This raises two questions. First, what is it exactly that Hosiasson-Lindenbaum took herself to be in agreement on with Ramsey, or what part of her approach has been inspired by his paper? And second: what did she “previously [think] independently”? In the talk, I will try to answer the two questions, drawing on Hosiasson-Lindenbaum’s work published before her contact with Ramsey’s work, as well as shortly after (and which has not received any attention to date).

This reconstruction of Hosiasson’s early philosophical views contributes to our understanding of how the different philosophical interpretations of probability that took shape in the first half of the 20th century developed in their early stages. Hosiasson  eventually saw herself as working on the logic of rational degrees of belief, and was not invested in any external justifications of the rules of such logic, especially ones which would ground it through pragmatic arguments. At the same time, while she built on Keynes’s formal results about a posteriori probabilities, Hosiasson does not appear to have taken on board his interpretation of probability as an objective, semantic relation the access to which is direct, but not always possible. Hosiasson turns out to be much closer in her approach to what we have come to think of the late stages of Rudolf Carnap’s inductive logic project—which is an interesting footnote to the history of the field, given the influence that late Hosiassson’s work had on the early inductive logic of Carnap.