Direct Inference and the Problem of Induction

Abstract

It would be difficult to overestimate influence Hume's problem of induction exercises on contemporary epistemology. At same time, problem of induction has not perceptibly slowed progress of mathe matics and science. This ironic state of affairs, immortalized by C. D. Broad's description of induction as the glory of science and the scandal of philosophy,1 ought in all fairness to give both sides some pause. And on occasion, it does: mathematicians stop to concede that Hume has not yet been answered,2 scientists worry about randomization of ex periments,3 and inductive skeptics stir uneasily in their chairs at mention of certain mathematical theorems that seem palpably to have bearing on problem.4 But even when there is some cross-pollination between fields, there is depressingly little sign of consensus on underlying problem. Part of difficulty lies in babble of conflicting interpretations of probability, which has grown markedly worse since Broad's time.5 Part of it lies in structure of Hume's original argument, which scarcely makes direct contact with mathematically sophisticated approach of contemporary statisti cians and probabilists.6 And no small part of it lies in conviction of a considerable number of philosophers that Hume's problem, or at any rate a refurbished modern version thereof, is quite simply and clearly insoluble.7 I aim to show that this pessimism is unfounded. To this end I will ar ticulate and defend epistemic legitimacy of a very simple form of direct inference; a version so minimal, indeed, that celebrated questions of confirmational conditionalization do not arise.8 This is tantamount to side stepping delicate issue of competing reference classes, surely one of most difficult problems facing any comprehensive theory of inductive