The Problem of Induction

Every time you predict the sun will rise, expect a dropped ball to fall, or trust that a medicine that worked yesterday will work today, you are reasoning inductively: moving from a finite set of observed cases to a conclusion about unobserved ones. Induction is the engine of science, forecasting, and everyday life. Yet the Scottish philosopher David Hume (1711-1776) identified a problem at its core that has never been fully dissolved. In A Treatise of Human Nature (1739-40) and the more accessible An Enquiry Concerning Human Understanding (1748), Hume asked a deceptively simple question: what justifies our confidence that the future will resemble the past?

Hume's argument runs as follows. Our inductive inferences all rely on a hidden assumption he called the Uniformity of Nature — the premise that unobserved cases will resemble observed ones. How could we justify that premise? Only two routes are available. We might try to justify it deductively, by pure logic — but there is no contradiction in imagining a future that breaks with the past (bread that has always nourished us suddenly poisoning us), so logic alone cannot rule it out. Or we might justify it inductively, by pointing out that nature has been uniform up to now, so it will probably continue to be. But this argument assumes the very principle it is trying to prove — it uses induction to justify induction, and is therefore circular. Hume concluded that induction has no non-circular rational justification. His own resolution was psychological, not logical: we induce because of custom or habit. Repeated experience of constant conjunction produces an expectation in the mind, and it is this feeling, not reason, that carries us from past to future.

A thought experiment: Russell's inductivist turkey. Bertrand Russell, in The Problems of Philosophy (1912), gave a memorable illustration (later popularized as the 'turkey' by others). Imagine a turkey on a farm. On its first morning it is fed at 9 a.m. Being a careful empiricist, it does not jump to conclusions. It gathers data across many days: warm weather and cold, rainy days and dry, weekdays and weekends. Every single morning, without exception, food arrives at 9 a.m. Having amassed overwhelming inductive evidence, the turkey confidently infers a law: I am always fed at 9 a.m. Then comes the morning of Christmas Eve, when instead of being fed its throat is cut. The point is not that the turkey reasoned badly by the standards of induction — it reasoned impeccably. The point is that no amount of past confirmation logically guarantees the next instance. Every forecaster, poll aggregator, and backtested trading strategy is, in principle, a turkey.

It helps to contrast the two forms of inference directly:

Deduction is certain but non-ampliative (it tells you nothing new). Induction is ampliative (it extends knowledge) but never certain. Hume's problem is the price we pay for learning anything about the unobserved world at all.

Philosophers have offered several responses. Karl Popper (The Logic of Scientific Discovery, 1934/1959) argued we should abandon induction altogether: science does not confirm theories, it only falsifies them, so we keep bold conjectures that have survived rigorous testing without ever claiming they are proven. Nelson Goodman sharpened the puzzle with his 'new riddle of induction' (Fact, Fiction, and Forecast, 1955): the invented predicate grue (green if observed before some future time, blue otherwise) fits all our evidence for emeralds just as well as green, yet we project 'green' and not 'grue' — so the problem is not just justifying induction but explaining which regularities are projectible. Others adopt pragmatic vindications (Reichenbach): if any method works, induction will, so we lose nothing by using it. None of these fully answers Hume on his own terms, which is precisely why the problem endures. The practical lesson is humility: treat every forecast, backtest, and 'the data clearly shows' as an extrapolation that the world is under no obligation to honor.