One usually speaks of Hume's problem of induction in the singular, as if Hume had called our attention to only one problem which affects the justification of inductive inferences. But Hume shows that this justification depends on two assumptions which are not logically valid. In most studies about the justification of inductive inferences, Hume's approach to base the justification on two assumptions has not been discussed. This seems to have been a mistake, however. Not only do these assumptions play different (...) roles in the justification, but by distinguishing between them, one of them can be shown to be scientifically (though not logically) valid. (shrink)