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Philosopher whose new riddle of induction concerns the selection of predicates for projection beyond examined cases.^[ref]

Nelson Goodman's new riddle of induction asks which descriptions of an observed regularity are fit for projection. David Hume's problem of induction asks how a projection beyond experience can be justified at all. The problems are related, but accepting that experience supports some expectations does not settle which predicates an acceptable inference may project.

Fix a future time $t$ and let $E_t(x)$ mean that $x$ was examined before $t$. Define grue bySuppose every emerald examined so far is green. Each is then also grue. The same positive instances fit both a green generalization and a grue generalization, although the latter assigns blue to an emerald first examined after the cutoff. This does not require an already examined green emerald to change colour at $t$: its classification uses whether it was examined before $t$, not whether the present time is before $t$. The problem concerns incompatible projections to unexamined objects.^[ref]

It does not resolve the difficulty to object that grue is artificially disjunctive. Introduce the converse predicate, bleen, for examined-before-$t$ blue objects and other green objects. Green can then be defined using grue, bleen and $E_t$. Syntactic simplicity depends on which predicates are primitive. Nor does calling green a genuine natural kind settle matters unless one explains how the relevant natural structure is identified without simply presupposing the preferred projection. Evidence about stable material composition can provide a scientific reason to project a colour response, but that reason goes beyond counting instances.

David Hume's argument exposes a different gap. The denial of an unobserved continuation is not a contradiction. An appeal to the past success of extrapolation already extrapolates from past cases, so cannot supply a noncircular demonstration of its general reliability. His discussion of necessary connection similarly distinguishes experienced successions from an independently perceived necessity binding events together. These claims concern the basis of causal and predictive inference, not merely the spelling of a predicate.^[ref]

Predicate entrenchment is Nelson Goodman's proposed way of distinguishing established projective practices. Green has a history of actual use in projections which its newly constructed rival lacks. This gives a practice-based account of projectibility, rather than an unconditional guarantee that familiar classifications are true. Its weakness is that an account must still permit scientifically successful innovations and correction of entrenched mistakes.^[ref]

Thus Nelson Goodman sharpens the problem facing scientific confirmation: a purely formal positive-instance rule is too permissive. A defensible response combines explicit background assumptions with revisable standards for selecting predicates. That explains why two syntactically parallel generalizations need not receive equal support; it does not provide the noncircular guarantee demanded by the strongest reading of David Hume's challenge.