Problem of Induction
justification of induction
Hume's argument that inductive inference — from observed cases to unobserved ones — cannot be rationally justified without circularity, and yet underlies most of what counts as empirical knowledge.
In practice
A metric has risen for six straight quarters. That is equally consistent with 'this rises' and with 'this rises until t'. Nothing in the six quarters distinguishes them, and you are about to budget against one of them.
The common mistake
Filing Hume under skepticism. He is not recommending that you doubt induction or stop using it — he thought stopping was not available. His claim is narrower and stranger: the expectation is habit rather than reasoning, and it is reliable enough to live by regardless.
Past performance is no guarantee of future results. It is printed on every financial product sold, by law, and it is the only piece of philosophy most people encounter in writing.
Hume's argument is that the disclaimer describes everything, cannot be fixed, and underwrites almost everything you believe.
The argument, in full
It takes three steps and it is airtight, which is the problem.
Almost nothing you believe rests on what you have observed. You have watched the sun rise some thousands of times. You believe it will rise tomorrow. You have never observed tomorrow. Nearly every belief you hold about the world is an extension of a finite set of observations to cases outside it.
That extension cannot be justified by pure reason. There is no contradiction in a universe where the regularities stop. You can imagine it without difficulty, which means "the future will resemble the past" is not a logical truth and reason alone will not deliver it.
And it cannot be justified by experience without arguing in a circle. The obvious move is to say induction has an excellent track record. But going from induction has worked to induction will work is itself an induction. You have used the method to certify the method.
There is no fourth option. Induction is not a form of reasoning that can be grounded, and yet it is the one you use for everything.
What Hume actually concluded
Not that you should stop. He thought stopping was not available — you are the kind of animal that forms expectations, and no argument will talk you out of it.
His conclusion was about what the expectation is. Habit: repeated exposure to one thing following another produces a felt anticipation, and we mistake the feeling for a piece of reasoning.
This is the part people miss when they file Hume under skepticism. He is not recommending doubt. He is describing accurately what humans do, having found that the rational reconstruction is unavailable. The expectation is real, it is reliable enough to live by, and it is not reason.
The deeper cut: which pattern are you even seeing?
Two hundred years later Nelson Goodman made it worse, and his version is the one with teeth for anyone who works with data.
Define grue: a thing is grue if it is observed before some future time t and is green, or observed after t and is blue.
Every emerald ever examined has been green. Every emerald ever examined has also been grue — the definition is satisfied by all of them. So the evidence supports "all emeralds are green" and "all emeralds are grue" exactly equally. The two predict different things about emeralds dug up after t, and nothing in the data prefers either.
The original problem was whether induction can be justified. Goodman's is worse: the observations never tell you which rule you are looking at. Any finite run of data is compatible with indefinitely many rules that agree on everything seen so far and diverge afterwards.
If that sounds familiar it is because it is overfitting, stated in 1955 without a computer. Every metric that has gone up for six quarters is consistent with "this goes up" and with "this goes up until t". The data is the same either way.
The escapes, and what each gives up
Kant took it as the provocation for his whole critical project — he said Hume woke him from dogmatic slumber. His answer: causation is not something we extract from experience, it is a condition the mind imposes on anything that could count as experience at all. This does not license any particular prediction. It relocates the necessity rather than supplying it.
Popper tried to make induction unnecessary. Science does not generalize from observations; it conjectures boldly and tries to refute. Theories that survive serious attempts at falsification are held tentatively and never established. Elegant — but it struggles to explain why anyone is entitled to act on a well-tested theory, which is the entire practical point.
Bayesians formalize the updating: hold degrees of belief, revise them by the evidence. It is the most usable answer and probably the one you already operate on. It also requires priors, and where a prior comes from is the original question wearing different clothes.
Reliabilists grant the circle and deny it matters. A belief is warranted if the process producing it is in fact reliable, whether or not you can prove it from outside. Critics say this answers a different question than the one Hume asked. They are right, and it may still be the answer to live by.
Nobody has closed it. Three centuries of first-rate people have tried.
Why it is worth your time
Because you will make a forecast this week, and the honest form of it is narrower than the form you will be tempted to use.
The practical residue of Hume is a specific discipline: knowing that it has worked so far is a report about the past wearing the grammar of a claim about the future. The grue problem sharpens it further — before extending a pattern, ask what other rule fits every observation you have and breaks later.
That question has no general answer. Asking it anyway is most of what separates a forecast from a hope.
Further reading
- David Hume — who found it
- An Enquiry Concerning Human Understanding — sections IV and V, the full text
- Immanuel Kant — woken by it
- Empiricism — the tradition it runs aground
- Episteme — the kind of knowing it puts out of reach
- Skepticism — the position Hume is usually mis-filed under
Concept web
Open the full webQuestions
What is the problem of induction?
Hume's argument that reasoning from observed cases to unobserved ones cannot be justified without assuming the future resembles the past — which is the very thing the reasoning is meant to establish.
Why can't induction be justified by its success?
Because arguing that induction has worked before, so it will work again, is itself an inductive argument. The justification assumes what it is trying to prove.
Does the problem undermine science?
Hume did not think so in practice; he held that nature compels us to reason inductively whatever philosophy concludes. Popper responded by recasting science as falsification rather than confirmation.