The Problem of Induction

Inductive reasoning moves from observed instances to general laws: from "all observed ravens have been black" to "all ravens are black". But no matter how many black ravens we observe, we cannot rule out the possibility that the next raven we encounter will be white. The number of past observations, however large, does not entail anything about the future by deductive logic alone. There is always a logical gap between what has been observed and what has not. This gap cannot be closed by simply observing more instances — each additional observation is just another past event, and the gap between past and future remains.

We might try to justify induction by pointing out that it has worked well in the past — but this is precisely the kind of inductive argument whose validity is in question. To say "induction has succeeded before, so it will succeed again" is to reason inductively about induction itself. The justification goes in a circle. Russell finds no non-circular way to establish the reliability of inductive inference, and argues that the "principle of induction" — that the future will resemble the past in the relevant respects — cannot be proved by logic or by experience. It is, if anything, a primitive a priori probability judgment that we cannot but make.

Russell does not resolve the problem of induction but insists on its importance. Science rests on induction; so does every practical expectation about the world. The problem reveals that the foundations of our most reliable knowledge are not as secure as we assume. For Russell, this is not an occasion for despair but for philosophical honesty: the appropriate response to genuine uncertainty is to acknowledge it clearly rather than paper over it with false confidence. The philosopher who has faced the problem of induction sees science differently — not as a collection of certainties, but as a systematic and highly successful way of betting on the future.

Russell's treatment of induction appears in The Problems of Philosophy, Chapters 6–7. Hume posed the classical formulation of the problem; Russell's version remains one of the clearest in the literature. Karl Popper later proposed falsificationism as an alternative to inductive reasoning.