Category: epistemology
Type: paradox
Associated thinker(s): Nelson Goodman
Original publication or approximate period: Goodman, Fact, Fiction, and Forecast (1955)
Difficulty: Intermediate
Themes: induction, projectibility, language
Related experiments: Hempel’s Paradox of the Ravens; Bertrand’s Random Chord Paradox
Fix a future time t later than all the observations under discussion. Goodman defines grue so that an object examined before t is grue if it is green, while an object not examined before t is grue if it is blue. Every emerald examined so far is green and was examined before t, so it is also grue by definition.
Under simple instance-confirmation reasoning, the same evidence appears to support both “all emeralds are green” and “all emeralds are grue.” Their predictions conflict for emeralds first examined after t: the first generalization predicts green, while the second predicts blue. Goodman introduces this case in Fact, Fiction, and Forecast, Chapter III, §4, pp. 73–75; see also the SEP account.
What makes a generalization projectible—appropriate to extend beyond the observations—when rival descriptions fit the same evidence but lead to incompatible predictions?
Hume’s traditional problem asks how induction can be justified. Goodman’s new riddle raises a further question: which predicates and regularities should we project? A rule that simply extends every observed pattern can support incompatible forecasts when the evidence is described in different ways. This is the problem of projectibility, not a proof that science is irrational. See Goodman’s entry in the Stanford Encyclopedia of Philosophy and the SEP’s overview of the problem of induction.
Goodman’s proposed account appeals to entrenchment: predicates, including predicates coextensive with them, gain standing through past actual projections. Better-entrenched hypotheses can override equally supported rivals. This is an account of how projection works in practice, not an independent proof that the practice is normatively correct.
One alternative family of approaches appeals to naturalness or similarity to explain why green-like predicates may be better suited to projection than grue-like ones. Scholz (2024) discusses Gärdenfors’s conceptual-spaces proposal and argues that its current cognitive form offers descriptive progress but does not provide a normative justification. This is a specific proposal and critique, not a finding about scholarly consensus (Scholz, 2024).
A positionality reply objects that grue’s definition depends on a time, unlike green. Goodman’s symmetry response is that a language taking grue and bleen as basic predicates can make green and blue positional instead. Positionality alone therefore is not a language-invariant test of projectibility (SEP, §5.3).
Some Bayesian analyses formalize confirmation in grue cases, but results depend on background assumptions and the confirmation measure. As an editorial takeaway, assigning priors does not automatically settle which predicates or model classes should be projected; see Fitelson (2008) for the measure-sensitive confirmation analysis.
The riddle does not claim that emeralds will change colour. It shows that the same past observations can be described by predicates that imply conflicting future predictions. The choice of representation matters to the projection problem.
As a teaching analogy, the riddle resembles model-selection problems in which a feature set or hypothesis class constrains extrapolation. That modern machine-learning comparison is an editorial extension, not a claim established by Goodman’s original argument.
Goodman introduces other constructed predicates, including “emerose.” Place-dependent variants can also be constructed by analogy, but the cited primary passage does not present that substitution as a specific version of grue. Treat it as an extension of the example, not as a variant attributed to Goodman.
Goodman’s Fact, Fiction, and Forecast was consulted through a full-text scan of the fourth edition (1983; first published 1955), including Chapter III, §4, pp. 73–81, and Chapter IV on projection and entrenchment. The definition here is simplified for teaching. The SEP entries, Fitelson’s published-paper manuscript, and Scholz’s open-access article were also consulted. The place-dependent construction and machine-learning comparison are explicitly presented as extensions, not claims established by Goodman’s text.
Research check: 2026-11-01. This is an educational explanation, not expert review or a substitute for the primary text. Additional comparisons are teaching prompts, not established historical variations.