Experiment #88 · Thought experiment

Goodman's Grue

The new riddle of induction

Nelson Goodman · 1955 · Philosophy of science

First published: N. Goodman, *Fact, Fiction, and Forecast* (1955), ch. 3.

Define "grue" = green if observed before time t, blue otherwise. All emeralds so far are green; equivalently, all are grue. Which predicate is projectible into the future?

Goodman's "new riddle of induction" shows that purely formal accounts of inductive support cannot distinguish projectible predicates (like "green") from gerrymandered ones (like "grue"). All emeralds observed before time t are equally green and grue; inductive logic alone gives no reason to predict that the *next* emerald will be green rather than blue. The puzzle generalises: for any pattern of past evidence, infinitely many predicates fit it equally well but predict incompatible futures. Resolutions appeal to entrenchment (Goodman), natural properties (Lewis), or causal structure.

Formulation

Define grue(x) = green(x) if x examined before t, blue(x) otherwise. All examined emeralds are green ≡ all examined emeralds are grue. Future predictions diverge: green → next emerald green; grue → next emerald blue. Pure inductive logic cannot adjudicate.

Compare this experiment

Dimensions Engaged

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Information

A direct constraint on how information from past observation supports future prediction.

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Observer

Observer · Knowledge Extent: which predicates can rationally be projected onto the unobserved?

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Time

Bears on Time · Direction: the role of temporal indexing in defining projectible properties.

Responses — How Schools Engage

Affirms / takes the bait 2

Pragmatism

Goodman's own resolution — entrenchment — is pragmatist: projectibility tracks which predicates have proved useful in past inductions, not a metaphysical fact about properties.

Constructivism

Vindicates the constructivist insight: our "projectible" predicates are products of our cognitive and linguistic history, not direct readings of nature.

Denies / rejects the premise 1

Realism

Common-sense realism: emeralds are green, not grue, because greenness is a real property and grueness is gerrymandered. The puzzle is a logician's artifact.

Reframes the question 2

Naturalism

Naturalists appeal to natural kinds or natural properties (Quine, Lewis): "green" picks out a genuine similarity class, "grue" does not. The reply is partial — what makes a kind natural?

Structuralism

Projectibility is structural: predicates project well when they correspond to genuine structural features (natural kinds), not to arbitrary set-theoretic constructions.

Holds it inconclusive 1

Analytic Metaphysics / Logical Atomism

A canonical pressure-test for theories of natural properties, projectibility, and induction. Goodman's entrenchment, Lewis's natural properties, and causal-structural readings all leave residual issues.