The problem of induction concerns the justification of inductive reasoning: drawing conclusions about unobserved cases or general regularities from observed instances. Repeated observations may support a prediction without logically guaranteeing it. The philosophical question is whether such inferences have a rational foundation that does not already presuppose their reliability. Closely associated with David Hume, the problem is central to epistemology and the philosophy of science. It concerns the grounds of inference, not whether people actually make predictions or acquire expectations through experience. (plato.stanford.edu)
Induction and deduction
In deductive reasoning, a valid argument cannot have true premises and a false conclusion. Inductive arguments are different: their conclusions extend beyond what their premises logically entail. Observing many green emeralds, for example, does not exclude the possibility of an unobserved emerald of another color. Inductive support is therefore commonly understood in terms of strength or probability, rather than deductive validity. The problem is not simply that predictions sometimes fail, but why observations should support conclusions extending beyond them at all. (plato.stanford.edu)
Induction includes more than predicting the future. It also encompasses generalizing from samples to populations and assessing explanatory hypotheses. Its philosophical use should be distinguished from mathematical induction, a deductive proof procedure that establishes a base case and an implication from each case to its successor. Sharing a name does not make the two procedures epistemically equivalent. (plato.stanford.edu)
Hume’s argument
Hume presented the argument in A Treatise of Human Nature in 1739 and reformulated it in An Enquiry concerning Human Understanding in 1748. His discussion begins with causation: experience teaches us that certain kinds of events occur together, but what warrants extending these associations beyond the instances already observed? (plato.stanford.edu)
Hume distinguishes relations of ideas from matters of fact. The denial of an established relation of ideas involves a contradiction; the denial of a factual prediction need not. That the sun will not rise tomorrow is conceivable without logical contradiction. Consequently, no demonstrative argument establishes that future events must resemble past events. This remains so however familiar or psychologically compelling the expectation becomes. (davidhume.org)
An appeal to experience appears equally problematic. Arguing that observed regularities will continue because they have continued previously already assumes that past experience is a reliable guide to unobserved cases. This is circular reasoning: the proposed justification employs the very kind of inference whose authority is being questioned. A frequently used reconstruction describes the missing premise as a principle of the uniformity of nature, although the relevant similarity need not mean that everything remains unchanged. (davidhume.org)
The difficulty thus concerns epistemic justification, not merely certainty. Replacing “will occur” with “will probably occur” does not automatically explain why past evidence warrants that probability judgment. (davidhume.org)
Habit and skeptical interpretation
Hume explains ordinary expectations through custom or habit. Repeated conjunctions generate a propensity to expect one event when another appears. This supplies an account of how expectations arise, rather than a demonstrative proof that they track unobserved reality. He treats this disposition as fundamental to practical life and reasoning from experience. (davidhume.org)
The relationship between this explanation and philosophical skepticism remains disputed. Interpretations differ over whether Hume excludes all rational justification or challenges a particular conception of reasoning. Accordingly, his argument should not simply be equated with the claim that every empirical belief is worthless. (plato.stanford.edu)
Major responses
Pragmatic vindication. Hans Reichenbach proposed evaluating induction as a method for approaching limiting relative frequencies. If an observed sequence has a limiting frequency, estimates based on its accumulating relative frequencies will eventually approximate that limit. This offers a conditional vindication of the method, not a guarantee of accurate short-term predictions or proof that the required limits exist. (plato.stanford.edu)
Conjectures and refutations. Karl Popper argued that science need not justify theories inductively. Scientists propose conjectures and deductively test their consequences. A universal claim cannot be conclusively verified by finitely many positive instances, whereas a genuine counterexample contradicts it. His account emphasizes falsifiability and corroboration through severe tests, rather than establishing a theory’s probability through repetition. Critics question whether selecting previously successful theories for practical use nevertheless requires expectations resembling induction. (plato.stanford.edu)
Bayesian approaches. Bayesian inference represents uncertainty through degrees of belief and updates them using Bayes’ theorem. This gives a precise framework for relating evidence to competing hypotheses. However, results depend on the prior probabilities and likelihoods supplied to the model. Updating rules alone do not determine why one initial distribution, or one family of hypotheses, should be preferred. Bayesian methods therefore clarify inductive support without constituting an uncontested solution to its foundational problem. (plato.stanford.edu)
Goodman’s new riddle
Nelson Goodman shifted attention from whether induction is justified to which generalizations observations support. Define an object as grue if it is examined before a specified time and is green, or is not examined before that time and is blue. Every green emerald examined before the cutoff is also grue. The observations therefore fit both “all emeralds are green” and “all emeralds are grue,” although these hypotheses predict different colors for subsequently examined emeralds. (plato.stanford.edu)
This new riddle of induction concerns projectibility: why some predicates support extrapolation while others do not. It does not suppose that emeralds suddenly change color. Goodman’s proposed account emphasizes the entrenchment of predicates in previous successful and accepted projections. The dispute consequently extends beyond the amount of evidence to the conceptual vocabulary through which evidence and predictions are formulated. (plato.stanford.edu)