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    Non-standard models don't undermine first-order logic's p... — Carmelics
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    Challenges→Non-standard models of Peano arithmetic, as demonstrated by Thoralf Skolem in 1933, contain 'natural numbers' with no standard correlates, making first-order provability insufficient to exclude pathological interpretations.

    Non-standard models don't undermine first-order logic's purpose: they show what FOL can express, not that it fails at intended use.

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