The problem of induction: did Hume's problem need to be solved, or is it dissolved?

Karl Popper, answered from the texts and cited to the page.

The position in brief

Hume's problem of induction is dissolved, not solved.¹ Science does not use induction; therefore Hume's question of how induction could be justified does not arise.² We start with bold conjectures (which need not be derived from observation at all), deduce testable consequences, and submit those consequences to severe tests. Refutation, when it occurs, is deductive; the survival of a theory under severe testing is corroboration, which is not a measure of probability and not a smuggled-in induction.

The choice between competing conjectures is settled by which has survived more severe tests with higher content (verisimilitude), not by which is more probable on the evidence.³

Sources

1. Hume showed that it is not possible to infer a theory from observation statements; but this does not affect the possibility of refuting a theory by observation statements. The full appreciation of this possibility makes the relation between theories and observations perfectly clear. This solves the problem of the alleged clash between the principles (a), (b), and (c), and with it Hume's problem of induction.

   Conjectures and Refutations, p. 56

2. I take it as an important task to make clear, even at the cost of some repetition, where I agree and where I disagree with Hume. T agree with Hume's opinion that induction is invalid and in no sense justified.

   Popper Selections, pp. 103–105

3. Appendix ':·ix to L.Sc.D.). Nor do I believe that it makes a positive contribution to methodology or to philosophy-except in the sense that it may help (or so I hope) to clear up the great confusions which have sprung from the prejudice of induction, and from the prejudice that we aim in science at high probabilities-in the sense of the probability calculus-rather than at high content, and at severe tests. 33.

   Realism and the Aim of Science, pp. 255–256

Where the argument is made

• The Logic of Scientific Discovery, Chapter 1 (the rejection of induction)
• Objective Knowledge (1972), Chapter 1 ('Conjectural Knowledge: My Solution of the Problem of Induction')
• Conjectures and Refutations, especially the title essay and 'Truth, Rationality, and the Growth of Scientific Knowledge'
• Realism and the Aim of Science (Postscript I, 1983)

How the argument was received

The signature methodological claim and the most contested. Wesley Salmon argued throughout his career that even after Hume is dissolved, the residual problem of theory-choice requires something inductive; Hilary Putnam pressed the same line. Colin Howson (Hume's Problem, 2000) develops a Bayesian alternative. The Bayesian tradition broadly treats Popper's corroboration as a notational variant of likelihood- based confirmation. Popperians (Watkins, Miller, Notturno) defend the deductivist dissolution.