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]
An Enquiry Concerning Human Understanding by David Hume. section IV, part II
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]
Fact, Fiction, and Forecast by Nelson Goodman. Chapter III, section 4
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.
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The problem of induction is a philosophical question regarding the justification of inductive reasoning, which is the process of deriving general principles from specific observations. Inductive reasoning involves making generalizations based on a finite set of observations, such as concluding that "All swans are white" after observing many white swans. The problem arises from the challenge of providing a rational justification for this type of reasoning.