Abstract
Russell's The Problems of Philosophy tries to establish a new theory of induction, at the same time that Hume is there accused of an irrational/ scepticism about induction". But a careful analysis of the theory of knowledge explicitly acknowledged by Hume reveals that, contrary to the standard interpretation in the XXth century, possibly influenced by Russell, Hume deals exclusively with causal inference (which he never classifies as "causal induction", although now we are entitled to do so), never with inductive inference in general, mainly generalizations about sensible qualities of objects ( whether, e.g., "all crows are black" or not is not among Hume's concerns). Russell's theories are thus only false alternatives to Hume's, in (1912) or in his (1948).