Induction

Induction is the inference from observed particular cases to universal generalizations — from these swans are white to all swans are white. It is the apparent engine of empirical science: we observe, generalize, and form laws. Popper argued that induction is logically invalid and unnecessary: no finite number of confirming instances entails a universal law, but a single counterexample refutes it. The problem of induction, first articulated clearly by David Hume, is that our practice of inductive inference cannot be rationally justified without circularity (we would need to inductively justify induction). Hume concluded that induction is a habit, not a rational procedure; Popper concluded that science should be reformulated to eliminate induction in favor of conjecture and refutation. The debate between these positions remains open: Bayesian epistemology offers a probabilistic formalization of induction that treats it as rational belief updating rather than logical inference, but faces its own foundational problems in specifying rational priors. The question of whether any non-deductive inference can be genuinely rational — and what 'rational' means for an empirical agent with finite data — is one of the deepest unsolved problems in philosophy of science.