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    Gödel demonstrated that semantic totalities can be cohere... — Carmelics
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    Challenges→Statements about 'all propositions' are meaningless.

    Gödel demonstrated that semantic totalities can be coherently quantified over without generating paradox, as in his completeness theorem.

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    1 reason for
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    Reasons For

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    Reason for
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    • 1.Gödel's completeness theorem successfully quantifies over all models of first-order logic without paradox, demonstrating semantic totality is coherent.
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    • 2.First-order logic permits unrestricted quantification over semantic domains while remaining consistent, proving some semantic totalities avoid paradox.
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    • 3.The completeness theorem shows syntax and semantics align systematically, enabling coherent reference to complete semantic structures without contradiction.
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    Reasons Against

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    • 1.Completeness theorem only applies to first-order logic; higher-order and set-theoretic semantics face incompleteness and non-categoricity problems.
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    • 2.Quantifying over 'all models' presupposes a fixed semantic domain; Gödel actually showed no single formal system captures all semantic truth.
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    • 3.The theorem addresses logical consequence, not whether semantic totalities themselves are coherent objects independent of formal frameworks.
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    Truth & Knowledge1 linkedPhilosophy of Language1 linked

    Related

    Completeness theorem only applies to first-order logic; higher-order and set-the...First-order logic permits unrestricted quantification over semantic domains whil...Gödel's completeness theorem successfully quantifies over all models of first-or...Quantifying over 'all models' presupposes a fixed semantic domain; Gödel actuall...
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    Statements about 'all propositions' are meaningless.The completeness theorem shows syntax and semantics align systematically, enabli...The theorem addresses logical consequence, not whether semantic totalities thems...

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