Inductive reasoning

Inference beyond what the premises deductively entail, often from observed cases to unobserved cases. This is distinct from mathematical induction.

The challenge of justifying inductive reasoning without either assuming the reliability being justified or demanding a deduction from premises that do not entail the conclusion.^[ref]

Nelson Goodman's challenge to explain why some predicates, rather than all predicates fitting the examined cases, are legitimate candidates for projection. It concerns projectibility, not a demonstration that every conceivable continuation is equally credible.^[ref]

The eligibility of a predicate or generalization for extending an inference beyond examined cases. Agreement with positive instances alone does not establish projectibility: grue and green can fit the same past examples while supporting incompatible predictions.

In Nelson Goodman's account, the standing a predicate acquires through a history of actual projections. It concerns the use of the predicate in inference, rather than merely the number of past objects satisfying it. Entrenchment is revisable and is not a proof of future reliability.^[ref]

For a fixed cutoff $t$, let $E_t(x)$ mean examined before $t$. Nelson Goodman's predicate is $G_t(x)⟺(E_t(x)\wedge \mathrm{green}(x))\vee (\neg E_t(x)\wedge \mathrm{blue}(x))$. An already examined green object remains grue after $t$ without a colour change. The conflicting projection concerns objects not examined before $t$.