Nelson Goodman's grue paradox demonstrates that infinitely many past-consistent hypotheses project incompatible futures, so past information underdetermines which future-directed belief is warranted.

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Grue paradox(as the core philosophical problem being discussed): A thought experiment showing that the way we define and classify things (like colors) isn't as straightforward as we assume—it depends on choices we make about language.
Nelson Goodman(the philosopher whose theory is being discussed): A 20th-century American philosopher who developed theories about how symbols (like words, pictures, and artworks) work and mean things.
Past-consistent(describing hypotheses that fit what we already know): A hypothesis or idea that matches everything we've observed so far and doesn't contradict any past facts.
Project(describing how hypotheses make future predictions): To extend a pattern from past observations into predictions about the future; to assume what happened before will continue to happen.

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