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What is David Hume's problem of induction?

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Marble bust of Aristotle with a beard and draped robe, showing detailed facial features and wavy hair, set against a dark background. — Philosophy of science Aristotle, marble portrait bust, Roman copy (2nd century bce) of a Greek original (c. 325 bce); in the Museo Nazionale Romano, Rome.

In the philosophy of science, the problem of induction is the challenge of justifying inferences from observed events to unobserved ones. Formulated by David Hume, it questions the rational basis for believing that the future will resemble the past.1

Hume argued that inductive inference relies on the assumption of nature's uniformity. However, any attempt to justify this assumption by appealing to past experience is circular, as it presupposes that the future will continue to behave like the past. Similarly, Hume challenged the notion of causation, or "necessary connection." He observed that we only experience a "constant conjunction" of events—such as fire and heat—rather than an observable necessity linking them.12

Hume did not deny that humans form beliefs through induction; rather, he maintained that these beliefs are products of "mental habit" rather than rational justification. Consequently, he concluded that we lack a logical foundation to know that such beliefs are true.12