Goodman's grue paradox demonstrates that without a privileged principle selecting natural over gerrymandered predicates, infinitely many incompatible generalizations fit any dataset equally well.

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Dataset(different rules can fit the same collection of observations equally well): A collection of information or observations you've gathered, like all the data points you've written down about something.
Generalization(Used in SQML proofs involving quantifiers): A proof rule in SQML by which a universally quantified formula is derived from an open formula, e.g. deriving ∀x(Fx → Fx) from the tautology Fx → Fx
Gerrymandered predicate(artificial or contrived groupings that don't reflect natural categories): A weirdly made-up property designed just to fit a particular situation, the way a politician might redraw voting districts to get a desired outcome—except for properties instead.
Goodman, Nelson(The statement refers to 'Goodman's third semantic condition,' which is a specific rule he created.): A 20th-century American philosopher who developed important theories about how symbols (like words, pictures, and musical notes) work and how we use them to represent reality.

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