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The mistaken belief that because complete induction (examining every case) is impossible, no inductive conclusion can be trusted. This fallacy rejects all generalizations on the grounds that we haven't examined every instance—ignoring that induction works by sampling, not census. It's the logic of "you haven't read every book, so you can't say books exist," of "you haven't met every French person, so you can't generalize about French culture." The fallacy of impossible induction is beloved of those who want to dismiss well-supported generalizations by demanding impossible standards of proof. It's a cousin of the perfect knowledge fallacy, and just as paralyzing.
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