The Lowenheim-Skolem theorem
If a countable collection of sentences in a first order language describes a model (that is, some state of affairs in the world), then it describes more than one model.
Leopold Lowenheim (1915) & Thoralf Skolem (1922).

Note: Hilary Putnam's version (1981) of this argument employs a strengthened version of the Lowenheim-Skolem theorem and claims that the theorem shows that any statement in natural language has an unintended interpretation if it has any interpretation at all.
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The Lowenheim-Skolem theorem
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