The Problem of Induction

We constantly infer from observed cases to unobserved ones — the sun has always risen, so it will rise tomorrow — yet Hume argued that no reasoning can justify this leap without already assuming that nature is uniform, the very thing in question.

Definition

The problem of induction is the question, raised by Hume, of how, if at all, inferences from observed instances to unobserved or future ones can be rationally justified, given that such inferences appear to presuppose without argument that the future will resemble the past.

Scope

This topic covers Hume's classical problem of induction and its modern descendants: Goodman's new riddle, which shows that the very notion of confirming evidence presupposes a choice of projectible predicates; Popper's falsificationist attempt to dispense with induction; and probabilistic and pragmatic responses. It connects to confirmation theory and Bayesianism, treated in companion topics, while focusing on the justification of inductive inference itself.

Core questions

• Can inductive inference be justified without circularity?
• Does inductive reasoning presuppose an unprovable principle of the uniformity of nature?
• Which predicates are legitimately projectible, and why?
• Can science proceed by falsification rather than confirmation?

Key theories

Hume's skeptical argument

Hume argues that inductive inferences cannot be justified deductively, since their conclusions can be false while premises are true, nor inductively without circularity, since that would assume the reliability of induction; we project the past onto the future from habit, not reason.

Goodman's new riddle

Goodman shows with the predicate 'grue' that the same evidence equally confirms incompatible generalisations unless we restrict confirmation to projectible predicates, shifting the problem from justifying induction to explaining which predicates are projectible.

Falsificationism

Popper denies that science relies on induction at all, holding that theories are never confirmed but only tested by attempts at refutation, so the growth of knowledge proceeds through bold conjectures and their falsification.

History

Hume posed the problem in the eighteenth century, arguing that the foundation of all reasoning about matters of fact is custom rather than reason. In 1955 Goodman recast it as the new riddle of induction with his grue example, redirecting attention to projectibility, and Popper's falsificationism offered an influential, if contested, way of denying that science needs induction at all.

Debates

Whether induction can be justified or must be dissolved

Some seek a justification of induction through pragmatic vindication, reliabilism, or probabilistic frameworks, while others, following Popper, deny that genuine induction occurs, and still others treat the demand for justification as confused; Goodman's riddle shows any answer must also explain projectibility.

Key figures

• David Hume
• Nelson Goodman
• Karl Popper

Seminal works

• hume-enquiry
• goodman1955

Frequently asked questions

What exactly is Hume's problem of induction?

It is the challenge of justifying inferences from observed to unobserved cases. Hume argued that such inferences are not deductively valid and that trying to justify them by their past success is circular, since that very move is inductive, so induction rests on habit rather than reason.

What is the 'grue' paradox?

Goodman defines 'grue' to apply to things examined before some future time and found green, or else not so examined and blue. All emeralds observed so far are both green and grue, so the same evidence confirms both 'all emeralds are green' and 'all emeralds are grue', which make opposite predictions. This shows confirmation depends on which predicates are projectible.