Problem of Induction

The problem it answers

Most of what counts as empirical knowledge depends on inference from observed cases to unobserved ones. We have seen bread nourish us in the past; we expect it to nourish us in the future. The sun has risen every morning of recorded experience; we expect it to rise tomorrow. Strikingly few of our beliefs about the world rest on what we have actually observed; almost all rest on inferential extensions of observation to cases we have not observed.

The question is what justifies these inferential extensions. The move from past observations to future predictions, or from observed cases to unobserved ones, is called induction. The problem of induction, raised most sharply by David Hume in the Treatise of Human Nature (1739) and the Enquiry Concerning Human Understanding (1748), is that induction cannot itself be justified by experience without circularity, and cannot be justified a priori. The most pervasive form of empirical inference therefore has no rational foundation.

The core claim

The Humean argument has three steps.

Induction is presupposed by most empirical knowledge. When you predict that fire will burn you, or that the sun will rise, or that this medicine will cure as it did before, you are inferring from observed regularities to unobserved cases.

The justification of induction cannot be a priori. It is not a logical truth that the future will resemble the past; we can coherently imagine a universe in which past regularities cease to hold. Therefore the principle that nature is uniform is not analytic, and cannot be established by pure reason.

The justification of induction cannot be empirical without circularity. To justify induction empirically, we would have to appeal to the fact that induction has worked in the past. But the inference from induction has worked in the past to induction will work in the future is itself an inductive inference. The justification therefore presupposes what it is meant to establish.

The conclusion: induction is not rationally justified. We continue to make inductive inferences (we have no alternative; we are creatures who form such expectations), but we do so on the basis of custom or habit, not on the basis of reason. The most basic procedure of empirical knowledge has no rational foundation.

History in one paragraph

The problem is raised most sharply by Hume in the Treatise of Human Nature I.iii (1739) and the Enquiry Concerning Human Understanding sections IV–V (1748). Earlier philosophers had noted versions of the difficulty (Sextus Empiricus's discussion of induction in Against the Logicians is the classical ancient anticipation), but the systematic Humean formulation is what shaped the subsequent debate. Kant reports that Hume interrupted his dogmatic slumber and provoked the Critical project; the Critique of Pure Reason's treatment of causation (the Second Analogy) is intended as a partial response. The nineteenth century saw various attempts at solution: John Stuart Mill's A System of Logic (1843) attempted to justify induction through the principle of the uniformity of nature; Charles Sanders Peirce developed pragmatist responses. Bertrand Russell's Problems of Philosophy (1912) presented the problem to a generation of analytic philosophers as canonical. The twentieth century produced several major responses: Hans Reichenbach (Experience and Prediction, 1938) offered a pragmatic vindication; Karl Popper (The Logic of Scientific Discovery, 1934/1959) attempted to dispense with induction altogether through falsificationism; Nelson Goodman (Fact, Fiction, and Forecast, 1955) introduced the new riddle of induction (the grue problem) showing that even the formal structure of induction is more problematic than the Humean argument had suggested. Bayesian responses (developed by Frank Ramsey, Bruno de Finetti, and the contemporary Bayesian epistemology literature) attempt to ground inductive reasoning in probability theory. Reliabilist responses (Alvin Goldman) treat induction as warranted insofar as it is in fact reliable, sidestepping the demand for a non-circular justification. The problem remains unresolved in the strict sense; the contemporary literature continues to develop responses and counter-responses.

Hume's positive account

Hume's response to the problem he raised is not to abandon induction (which would be unlivable) but to redescribe it. Inductive inference is not a product of reason; it is a product of custom or habit. Repeated observation of constant conjunction produces a felt expectation; this felt expectation is what we mistake for rational inference.

The naturalism is important. Hume is not a global skeptic counseling that we abandon inductive belief; he is an empiricist following his principles to their conclusion and accepting that what we call reasoning about matters of fact is in fact a feature of human nature rather than a rational process. The work of philosophy is to describe accurately what we actually do, not to provide a rational foundation it cannot in fact have.

The Kantian response

Kant's response in the Critique of Pure Reason takes the problem seriously and proposes a structural solution. The principle that every event has a cause (the Second Analogy of Experience) is not an inductive generalization from observation; it is a synthetic a priori principle that the understanding necessarily applies to any object of experience. Causal connection is not discovered in nature; it is contributed by the mind to the structure of experience.

This is not a vindication of induction in the form Hume challenged; specific inductive generalizations (this kind of event will produce that kind) still require empirical support. But it is a response to the deeper Humean problem: causation in general is a presupposition of any unified experience, not something we infer from observation.

Whether Kant's response succeeds depends on whether transcendental arguments of his sort can in fact establish substantive a priori principles. The contemporary literature on transcendental arguments (Strawson, Stroud, McDowell) continues to engage this question.

The Popperian response

Karl Popper's response in The Logic of Scientific Discovery (1934/1959) is to dispense with induction altogether. Science, on Popper's account, does not proceed by inductive generalization from observation; it proceeds by conjecture and refutation. Scientists propose bold hypotheses; observations test the hypotheses by potentially refuting them; hypotheses that survive serious attempts at falsification are tentatively accepted, but never proven true.

The position has the elegance of avoiding the inductive problem entirely. Its difficulty is that scientific practice (the actual acceptance of well-tested theories, the use of accepted theories to predict and intervene) seems to require more than tentative non-refutation. The contemporary literature on Popper and on falsificationism is divided about whether the program succeeds.

The new riddle of induction

Nelson Goodman's Fact, Fiction, and Forecast (1955) deepened the problem with the new riddle of induction. Goodman introduced the predicate grue: an object is grue if it is examined before time t and is green, or is examined after time t and is blue. All emeralds examined before now have been green; they are also all grue. The inductive generalization all emeralds are green and the inductive generalization all emeralds are grue are equally supported by the same evidence; yet they make incompatible predictions about emeralds examined after time t.

Goodman's puzzle shows that the problem of induction is not merely about whether induction is justified; it is about which inductions are even projectible (legitimately extendable to new cases). The contemporary literature on the grue problem (Israel Scheffler, Joseph Ullian, the projectibility tradition) is extensive.

Common confusions

Induction is not the same as inductive logic in the formal sense. Inductive logic in the contemporary technical sense names the formal study of degrees of confirmation (Bayesian and related frameworks); induction in the Humean sense names a more general kind of inference from observed to unobserved cases. The two are related but not identical.

The problem of induction is not the problem of unreliable inductive inferences. The Humean problem is not that some inductions are unreliable (which is obvious); it is that even reliable inductions cannot be given a non-circular rational justification.

Hume's conclusion is not that induction is irrational in the sense of crazy. Hume's claim is the more specific one that induction is not a process of reason in the strict philosophical sense. It is a natural process, integral to human life; what it is not is a process whose conclusions are rationally guaranteed by their premises.

Live debates

Bayesian responses. Contemporary Bayesian epistemology treats inductive inference probabilistically: given evidence, beliefs should be updated according to Bayes's theorem. Whether this dissolves the problem of induction or merely relocates it (the priors required for Bayesian updating require their own justification) is contested.

Reliabilism. Alvin Goldman and other reliabilists treat inductive beliefs as warranted insofar as they are in fact reliable, sidestepping the demand for a non-circular rational justification. Critics argue that this misses the original force of the Humean problem.

The pragmatic vindication. Reichenbach's argument that we are pragmatically justified in using induction (because if any method of prediction works, induction will work; therefore using induction is no worse than using any alternative) continues to be engaged.

Contemporary engagement

Major recent scholarly work includes John Norton's A Material Theory of Induction (2021), the contributions to the Stanford Encyclopedia of Philosophy entries on the problem of induction and on Hume's epistemology, and the continuing literature on Bayesian epistemology (especially the work of Branden Fitelson, James Joyce, and Brian Weatherson). The problem remains one of the central topics in contemporary epistemology and philosophy of science.

Further reading

• Hume — the author of the problem
• Empiricism — the tradition
• Kant — the philosopher whose Critical philosophy is in part a response
• Episteme — the cognitive achievement the problem challenges
• Essay Concerning Human Understanding — the broader empiricist context

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