Belief and deductive inference

That a deductive inference can be useful depends upon, even though it is not quite the same as, its being possibly informative. This in turn amounts to it being possible to believe its premisses without believing its conclusion. Belief is involved also in the notion of legitimate inference: if recognition of the truth of its premisses, which is the same as believing in them, is to suffice for believing its conclusion then, and only then, some a priori links must exist between beliefs, which we ought to be able to spell out. The very existence of deductive inference raises therefore a problem or, rather, a pair of symmetric problems, which any theory of belief, and more generally of propositional attitudes, must grapple with. I shall claim that the beginning of a solution can be found by re-examining the ordinary notion of belief and other propositional attitudes.