Problem of induction

Why can no number of past observations guarantee that the next one will match?

The sun has risen on every morning anyone has recorded. Bread has nourished every person who has eaten it. On that basis you expect tomorrow's sunrise and eat tomorrow's bread without a flicker of doubt, and the expectation keeps being met. So here is a question that sounds pedantic and turns out not to be: what justifies the step from "every observed case was like this" to "the next one will be too"?

Not "what causes us to take it" — habit obviously does. The question is whether there is an argument for it. Hume asked exactly that, and the answer he arrived at has never been comfortably improved on.

Lay out the two kinds of argument available. Either the conclusion follows with necessity, so that denying it is a contradiction — Hume called this demonstrative reasoning — or it rests on experience.

Take the first. Is there a contradiction in supposing that bread nourishes today and poisons tomorrow? Try to find one. We can describe such a world without incoherence: the description is strange, but it does not stumble the way "a square circle" stumbles. If no contradiction is involved, no demonstration is available.

So the second. We argue that inference from experience has worked — overwhelmingly, for as long as anyone has tried it. But look at the shape of that argument. It says: induction succeeded in the observed past, therefore it will succeed in the unobserved future. That is an inductive inference. To accept it as support, you must already accept that past regularities license future expectations, which is exactly what was in question. The argument does not fail because it is weak. It fails because it assumes its own conclusion.

Notice how narrow the escape routes are. You cannot appeal to a principle that nature is uniform, because that principle is either a necessary truth — and we have just seen it is not — or a claim supported by experience, in which case the same circle closes. Nor does probability help: its arithmetic tells you what follows from your assumptions about the sample, and the assumption that the future resembles the past is one of them, not a result.

What have people done with this? Karl Popper denied that science needs induction at all. Theories are conjectures; we never confirm them, only fail to refute them; the logic of science is deductive falsification, which is perfectly valid. That is clever, and it does not settle the matter. Wesley Salmon's objection is the natural one: if a theory has survived every test and its rival has not, and we must act tomorrow, on what ground do we prefer the survivor? Popper says it is better corroborated — but corroboration is a record of past performance, and treating a past record as a guide to future performance is the very step in dispute.

Hans Reichenbach tried a pragmatic vindication instead: we need not show that induction works, only that if any method works, induction will, so a gambler with nothing to lose should use it. But two rules can agree on everything observed so far and diverge afterwards, and the argument licenses a family of methods rather than the one we use.

Then Nelson Goodman turned the problem inward. Define grue: applying to things examined before some future time t and found green, and to other things just in case they are blue. Every emerald ever examined is green — and every one is also grue. Our evidence supports "all emeralds are grue" exactly as well as "all emeralds are green", by the same counting, yet the two predict opposite things about the emerald dug up after t. So the trouble is not only that we cannot justify projecting the past; we cannot say, without helping ourselves to something, which pattern we are projecting. Goodman proposed that some predicates are better entrenched — have a longer history of successful projection — which describes our practice more than it vindicates it, and he knew it.

The result is easy to over-read in two directions.

It is not a claim that induction is unreliable, or that tomorrow will probably be different. Hume was emphatic that we cannot help reasoning inductively and should not try; he described the absence of a justification, and did not recommend a change of practice. Scepticism here is about grounds, not behaviour.

Nor is it a puzzle that better science dissolves. Adding data, refining instruments, or moving to statistics changes nothing structural, because each of those methods embeds the assumption in question. That is why the problem stays alive in modern philosophy of science rather than sitting in a history chapter.

What the responses share is that each relocates the difficulty rather than removing it: Popper into the choice of which corroborated theory to act on, Reichenbach into which of many equivalent rules to adopt, Goodman into which predicates are projectible. This is a genuinely open problem, and saying so is not modesty.

• Whether Bayesian confirmation theory answers Hume or merely relocates the assumption into the choice of priors.
• Why "projectible" predicates cluster in the vocabulary of established science.

Every term the collection defines is gathered in the glossary.