A.J. AYER, HUME'S FORMULATION OF THE PROBLEM OF INDUCTION
FROM THE LEGACY OF HUME, IN PROBABILITY AND EVIDENCE 3-6 (1972)
A rational man is one who makes a proper use of reason: and this implies, among other things, that he correctly estimates the strength of evidence. In many instances, the result will be that he is able to vindicate his assertions by adducing other propositions which support them. But what is it for one proposition to support another? In the most favourable case, the premisses of an argument entail its conclusion, so that if they are true the conclusion also must be true. It would seem, however, that not all our reasoning takes the form of deductive inference. In many cases, and most conspicuously when we base an unrestricted generalisation on a limited set of data, we appear to run beyond our evidence: that is, we appear not to have a logical guarantee that even if our premisses are true, they convey their truth to the conclusion. But then what sort of inference are we making, and how can it be justified? These questions have not proved easy to answer, and their difficulty creates what philosophers call the problem of induction.
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