= Solution
<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> by
$$
G_t(x)\iff\bigl(E_t(x)\land\operatorname{green}(x)\bigr)\lor\bigl(\neg E_t(x)\land\operatorname{blue}(x)\bigr).
$$
Suppose 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 \b[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.<Fact, Fiction, and Forecast by Nelson Goodman>[Chapter III, section 4, especially pp. 72–80 in the fourth edition; original examined-before-cutoff definition]{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.<An Enquiry Concerning Human Understanding by David Hume>[Section IV, parts I–II; section VII, part II, on customary inference and necessary connexion: https://davidhume.org/texts/e/7]{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.<Fact, Fiction, and Forecast by Nelson Goodman>[Chapter IV, sections 2–4: actual projections, entrenchment and presumptive projectibility]{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.
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