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    Soundness entails that if an argument is deducible (proof... — Carmelics
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    Supports→An argument is deducible if and only if it is valid

    Soundness entails that if an argument is deducible (proof-theoretically), then it is valid (model-theoretically)

    Philosophy of Language
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    An argument is deducible if and only if it is validCompleteness entails that if an argument is valid (model-theoretically), then it...

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    Completeness entails that if an argument is valid (model-theoretically...

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    An argument is deducible if and only if it is valid89%
    An argument is valid in a model only when in any point at which the pr...83%
    A deductively valid argument is also semantically valid81%

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    Soundness and completeness together entail that an argument is deducible if and only if it is valid, and a set of sentences is consistent if and only if it is satisfiable. So we can go back and forth between model-theoretic and proof-theoretic notions, transferring properties of one to the other. Compactness holds in the model theory because all derivations use only a finite number of premises.

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