The Problem of Induction
Bread has nourished you every time you have eaten it. You expect it to nourish you tomorrow. Hume's question is not whether this expectation is sensible, which he never doubted, but what supports it. His answer is that nothing does, and that the argument showing so is short enough to state in a paragraph and has resisted three centuries of attempts to answer it.
What induction is
Definition
Induction
Inference from premises that do not entail the conclusion but are taken to support it, typically from observed cases to unobserved ones or from a sample to a population.
Definition
Enumerative induction
The simplest inductive form: from the observation that all examined members of a class have a property, to the conclusion that all members do, or that the next one will.
The contrast with deduction is the whole of the problem. In a valid deduction the conclusion is already contained in the premises, and the price of that security is that nothing new is delivered. Induction delivers something new, and so cannot be valid, and the question is what its premises do for its conclusion if not entail it.
Almost everything anyone believes about the unobserved rests on induction. That the sun will rise, that the chair will hold, that the drug that worked in the trial will work in the clinic, that the laws of physics held before there were observers. Science is not an exception to this dependence but the most systematic instance of it.
Hume's argument
Definition
Uniformity of nature
The supposition that unobserved cases resemble observed ones, or that the future will resemble the past. Every inductive inference requires something of this kind as a suppressed premise.
Hume's move is to notice that the inference from observed to unobserved is not complete as it stands. That bread has nourished does not by itself entail anything about tomorrow's loaf. What licenses the step is an assumption that nature runs uniformly, and once that assumption is made explicit, it can be asked what supports it.
Hume's argument
- Every inductive inference requires the assumption that unobserved cases resemble observed ones.
- That assumption is not demonstrable, since there is no contradiction in supposing that nature changes its course.
- Nor can it be established from experience, since every argument from experience to it would itself be an inductive inference and would therefore assume it.
- Demonstration and experience exhaust the sources of justification available.
- ∴The assumption on which all inductive inference depends has no justification, and so no inductive inference is justified by reasoning.
Definition
Hume's problem of induction
The problem posed by the argument that inductive inference cannot be justified deductively, since its conclusions do not follow, nor inductively, since that would presuppose what is at issue.
Hume's own conclusion is not that we should stop. He holds that the expectation is produced by custom, a habit of the mind formed by repeated association, and that this is a fact about our constitution rather than a piece of reasoning. Nature has not left it to our judgement whether to expect the sun tomorrow. What he denies is that the expectation rests on any argument, and it is worth being precise that his target is the rational credentials of the practice and not the practice.
Check your understanding
Four responses
Deny that justification is needed. Peter Strawson argued that asking whether induction as a whole is justified is a confusion, because to call a belief justified just is to say it is supported by good inductive evidence. The demand for an external validation of inductive standards is like asking whether the law is legal. The reply is that the analogy may be less comforting than it looks, since legal systems can be assessed from outside by moral standards, and the question whether our inductive standards are the ones that lead to truth seems similarly askable.
Find a different justification. Hans Reichenbach's pragmatic vindication grants that induction cannot be shown to work and argues that it can be shown to be the best bet. If nature has any long-run stable frequencies, the straight rule of induction will eventually find them. If nature has none, no method will work. So induction succeeds if anything does, and adopting it costs nothing. The difficulty, pressed by Wesley Salmon, is that infinitely many rules share this property, including rules that predict wildly different things in the short run, and the argument gives no reason to prefer the straight one.
Reject induction altogether. Karl Popper's falsificationism holds that science never infers inductively. Theories are conjectures, observation can refute them but never confirm them, and what makes a theory acceptable is that it has survived severe attempts at refutation. Hume was right and it does not matter, because the practice he attacked is not the practice science uses. The standard objection is that surviving refutation is only a reason to rely on a theory if survival so far bears on performance in future, which is an inductive claim. Popper's notion of corroboration has struggled to be anything other than that.
Relocate the problem. Quine's naturalised epistemology takes the demand for a justification of induction from outside all empirical belief to be a relic of foundationalism. Epistemology becomes a chapter of psychology, describing how creatures who project as we do came to be, and the question why our innate similarity standards match nature's is answered by natural selection rather than by argument. The objection is that this explains why we induce, and why induction has worked so far, without addressing whether we are entitled to keep doing it.
Check your understanding
What survives
Three centuries have not produced a justification of induction that its critics accept, and the honest summary is that the argument has not been answered.
What has changed is the framing. The Bayesian machinery of the next article does not justify induction; it gives a precise account of how degrees of confidence should be updated on evidence, and shows that anyone updating that way is coherent. Whether the priors one starts from are reasonable, and whether coherence has anything to do with truth, are the same questions Hume asked in modern dress. Convergence theorems show that agents with different priors will come to agree given enough shared evidence, which is genuinely reassuring and which assumes that the world keeps behaving.
That is the pattern of the whole literature. Every proposal either presupposes something Hume's argument targets or changes the subject to one that can be settled. It is entirely possible that the argument is sound, that induction has no justification, and that this fact has no practical consequences whatever.
Objection
Induction is justified because it works. We use it, we build aircraft with it, the aircraft fly. A philosophical argument that ends by denying we have any reason to expect the next aircraft to fly is not a discovery about reasons; it is a demonstration that the notion of reason being used has come apart from anything recognisable. When a theory of justification says that no one has ever had a reason for any expectation about the future, the theory should be rejected, not the expectations.
Reply
The objection states Hume's own view of the practical situation and mistakes it for a refutation.
That induction works is the claim under examination. It has worked, which is a statement about the past, and the step from there to a conclusion about aircraft not yet built is the step whose credentials are at issue. The objection uses induction to defend induction, which is the third premise of the argument rather than a counter to it. This is not a debating point: the circularity is what makes the problem hard, and any response that does not notice it has not engaged.
The second half of the objection is stronger, and it is a version of Strawson's. If an account of reasons implies that nobody has ever had one, perhaps the account is too demanding. Fair enough. But then the work is to produce the more modest account and show that induction satisfies it, and the attempts to do so are the four responses above, none of which has commanded agreement.
Notice finally what Hume is not saying. He is not saying that believing the aircraft will fly is unreasonable, or that one should suspend judgement, or that the practice should change in any respect. He is saying that when we ask what argument underwrites the practice, there is none to be found. A person can accept that conclusion entirely and board the aircraft, which is what Hume did.
Check your understanding
Next
Belief as a matter of degree rather than an all-or-nothing state, and the rule for revising those degrees when evidence arrives.
Further reading
- David Hume, An Enquiry Concerning Human Understanding, sections IV and V.
- Nelson Goodman, Fact, Fiction, and Forecast (Harvard University Press, 1955), chapter 3.
- P. F. Strawson, Introduction to Logical Theory (Methuen, 1952), chapter 9.
- Wesley C. Salmon, "Should We Attempt to Justify Induction?", Philosophical Studies, volume 8, number 3 (1957), pages 33 to 48.
- Stanford Encyclopedia of Philosophy, "The Problem of Induction", by Leah Henderson.
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