Problem of Induction
The problem of induction is Hume’s challenge that inductive inferences (from observed instances to unobserved ones) cannot be given a non-circular rational justification, as set out in the SEP entry. Saying “the sun will rise tomorrow because it always has” leans on a Uniformity Principle (the future resembles the past) that itself can only be supported inductively.
Why does this matter?
If induction can’t be justified non-circularly, then most of what we call empirical knowledge is psychological habit dressed up as reason.
Hume’s dilemma: there are only two kinds of argument, and neither grounds induction.
- Demonstrative: conclusions whose negation is inconceivable. The sun failing to rise is perfectly conceivable, so no demonstrative argument gets us there
- Probable (inductive): extrapolates from past cases, but presupposes the Uniformity Principle it’s trying to justify. Circular
Hume’s diagnosis is that induction is grounded in custom or habit, a psychological propensity to project past regularities forward. Imagination does the work, not reason. This is the same cut as Hume on Causation: we never observe necessity, only constant conjunction.
The main attempted escapes (per SEP):
- Kant, synthetic a priori: causation and uniformity are preconditions of any possible experience. Flips the problem; still contested whether the transcendental move is legitimate
- Popper, deductivism: we never justify theories by induction, only falsify them deductively. Survives a test ≠ confirmed
- Reichenbach, pragmatic vindication: if any method converges on the true limiting frequency, induction does. Doesn’t tell you you’re right, only that nothing systematic does better
- Bayesianism: update priors by Bayes’ rule. But the prior is itself an empirical assumption; circularity moved, not removed
- Goodman, the new riddle (“grue”): “grue” = green before time t, blue after. Both “all emeralds are green” and “all emeralds are grue” are equally supported by past observations. Induction doesn’t pick one; projectibility has to come from somewhere else
- Strawson, dissolution: asking whether induction is justified is like asking whether the legal system is legal. “Justified” just means “following inductive standards”
SEP's verdict
None of these fully closes the gap. Each either smuggles in an empirical assumption or redefines “justification” to duck the original question.
My take
The problem doesn’t bother me much in practice, which is a Humean position in itself. I’ve called myself an empiricist my whole life, and empiricism without induction is paralysis. What I actually buy:
- Hume is right that there’s no non-circular justification, and pretending otherwise (Kant, Bayes with “objective” priors) is hand-waving
- Popper is the most honest working attitude: I don’t confirm, I fail to falsify. This matches how I already think about engineering and research; IBE gets you moving, but the conclusion is always provisional
- Goodman’s grue is the part that should scare you more. It says even if you grant induction, you don’t get a unique answer; you get whatever the background concepts project. The real action is in which predicates we carve the world with, not in the logic of generalization
Induction is load-bearing and unjustified. That’s fine, I just want to stop pretending the load-bearing part is doing logical work it isn’t.