Induction

Reasoning from observed cases to a general claim - reliable, indispensable, and without any accepted justification.

Theme: Knowledge, truth and reason
Tradition: Cross-tradition
Term: ἐπαγωγή · epagōgē
Term fixed: c. 330 BC

In plain terms

Every swan anyone had seen was white, so all swans are white. That inference is exactly the kind everyone makes constantly, it was made carefully by careful people, and it was wrong.

Induction goes beyond what has been observed, which is its whole value and its whole problem. No number of confirming cases makes the general claim certain, because the next case is not covered by the ones already in.

And the obvious defence fails. Say induction works because it has always worked, and you have used induction to justify induction. Everyone uses it, nothing else would do the job, and there is no non-circular argument that it is sound. Two and a half centuries of very good philosophers have not fixed this.

As a philosopher would put it

Hume's argument is the centre of the subject. Any inference from observed to unobserved requires a principle that nature is uniform; that principle is not demonstrable, since its denial is not contradictory, and it is not established by experience, since that would be the inference in question. So the practice has no rational foundation, and Hume's own conclusion is that it rests on custom.

Goodman's new riddle sharpens it. Define grue as observed before some future time and green, or else blue. Every emerald observed confirms both green and grue equally, so the formal structure of confirmation cannot distinguish projectible predicates from unprojectible ones, and something outside the logic must be doing the work.

The responses divide. Popper accepts the argument and abandons induction, making science a matter of conjecture and falsification - which critics say cannot explain why we prefer well-tested theories for action. Bayesians reconstruct induction as probabilistic updating, which is coherent but requires priors that the argument was about. Strawson replies that asking whether induction is rational is like asking whether the law is legal, since induction is part of what rational means.

Where you meet it

In 1697 a Dutch expedition under Willem de Vlamingh sailed up a river on the western coast of New Holland and found black swans on it. They took two alive to Batavia. The river is still called the Swan.

Before that, the whiteness of swans had been a standing European example of a certainty. Juvenal used a black swan as his figure for something that does not exist, and the phrase had been in use as an idiom for an impossibility for sixteen hundred years.

The inference had been made from a very large number of observations, over a very long period, by people with no reason to doubt it. Nothing was wrong with the reasoning. The sample was simply confined to one hemisphere, and there was no way to know that from inside the sample - which is the position every inductive inference is in, and the reason the birds have become the standard name for the problem.

What is actually disputed

Whether induction needs a justification at all.

Sceptics take Hume's argument to stand and treat inductive practice as habit that happens to work. Popperians accept the argument and claim science does not use induction, a claim most philosophers of science reject as a description of what scientists actually do. Bayesians offer a formal reconstruction that is internally impeccable and does not answer the original question, since the priors have to come from somewhere.

The dissolving response - that demanding an external justification for induction misunderstands what justification means, because inductive support is part of the standard - is elegant and strikes opponents as changing the subject. What everyone agrees on is that the practice is indispensable and that no account of why it is entitled to our confidence has been generally accepted, which is an unusual situation for something used several thousand times a day by everyone alive.

Commonly confused with

mathematical induction A deductive proof technique with a guarantee attached. It shares the name and nothing else.
generalising carelessly Induction done badly is a fallacy. Induction done well has exactly the same logical structure, which is the point of the problem.

Defined against

Deduction Guaranteed conclusions against ampliative ones - the oldest division in the theory of reasoning

Philosophers

Aristotle Where the movement from particulars to universals is named
Francis Bacon The method of systematic observation and exclusion
David Hume The argument that it cannot be justified
John Stuart Mill The canons for identifying causes inductively
Karl Raimund Popper The proposal to do without it entirely
Charles Sanders Peirce Induction as one of three modes, with a self-correcting role

Works

Novum Organum The programme for systematic induction
A Treatise of Human Nature The problem, in its original statement
The Logic of Scientific Discovery Falsification in place of confirmation
How to Make Our Ideas Clear Induction's role in a self-correcting enquiry
Metaphysics Where the term is introduced

Schools

Peripatetic school (Aristotelianism) Where induction is named and placed
British Empiricism Where it is both central and undermined
Classical Utilitarianism Where Mill develops the methods
Vienna Circle Where confirmation is made the criterion of meaning
Classical Pragmatism Where enquiry is self-correcting rather than founded

Related concepts

Inference c. 330 BC · Deduction c. 330 BC · Abduction 1878 · Experience c. 330 BC · Fallibility 1878

Aristotle names epagōgē as the movement from particulars to universals; Hume's argument that it cannot be justified appears in 1739 and has never been answered to general satisfaction.