ALBERTO MURA HUME’S INDUCTIVE LOGIC ∗ ABSTRACT. This paper presents a new account of Hume’s “probability of causes”. There are two main results attained in this investigation. The first, and perhaps the most significant, is that Hume developed – albeit informally – an essentially sound system of probabilistic inductive logic that turns out to be a powerful forerunner of Carnap’s systems. The Humean set of principles include, along with rules that turn out to be new for us, well known Carnapian principles, such as the axioms of semiregularity, symmetry with respect to individuals (exchangeability), predictive irrelevance and positive instantial relevance. The second result is that Hume developed an original conception of probability, which is subjective in character, although it differs from contemporary personalistic views because it includes constraints that are additional to simple consistency and do not vary between different persons. The final section is a response to Gower’s thesis, by which Hume’s probability of causes is essentially non-Bayesian in character. It is argued that, on closer examination, Gower’s reading of the relevant passages is untenable and that, on the contrary, they are in accordance with the Bayesian reconstruction presented in this paper. 1. INTRODUCTION According to Humean scepticism, probabilistic inductive reasoning has no rational foundation. This tenet is at the core of the traditional interpretation of Hume’s standpoint by which probabilistic inferences are nothing but the result of a psychological process devoid of any interest from a logical or philosophical viewpoint. This interpretation explains the little attention paid in the past to those parts of the Treatise (section xii of Book I, part III) and of the first Enquiry (section 6) devoted to the study of the probabilistic inductive process. David Stove so summarised the general attitude up to the time he was writing (1973): [S]ections xi–xiii [part III, Book I of the Treatise] are not only an unessential part of Hume’s philosophy of induction. They are, philosophically considered, altogether unre- warding intrinsically. Commentators on Hume have without exceptions failed to extract from them anything of philosophical interest. Their best aids, in dealing with these sec- tions, have been brevity or even silence, and mere paraphrase or (still more not committal) quotation. And there are ample reasons for this state of affairs. The most important single reason is that, in sections xi–xiii, the kind of interest which Hume displays, in the inferences he is discussing, is an empirical, psychological interest, rather than a logico-philosophical and evaluative one (1973, 120). Synthese 115: 303–331, 1998. © 1998 Kluwer Academic Publishers. Printed in the Netherlands.