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    Classical tautologies like double negation elimination ha... — Carmelics
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    Challenges→The Curry-Howard correspondence holds not only between provable formulae and type ascriptions, but also between proof terms and proofs of corresponding formulae

    Classical tautologies like double negation elimination have no canonical computational term, undermining the claim's scope beyond intuitionistic systems.

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    Reasons For

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    Reason for
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    • 1.The Curry-Howard correspondence shows classical tautologies lack direct computational witnesses that intuitionistic proofs possess.
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    • 2.Double negation elimination requires excluded middle, which needs non-constructive choice principles absent from intuitionistic logic.
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    • 3.If a principle has no canonical term, its truth cannot be computationally verified, limiting its scope to formal systems only.
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    Reasons Against

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    Reason against
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    • 1.Classical tautologies have well-defined computational content via continuation-passing style and call-cc operators in typed languages.
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    • 2.Lack of canonical intuitionistic proof doesn't undermine classical validity—classical and intuitionistic systems have different proof standards.
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    • 3.Many classical results (excluded middle, choice) are computationally meaningful in classical type theories like cubical or observational type theory.
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    Truth & Knowledge1 linkedPhilosophy of Language1 linked

    Related

    Classical tautologies have well-defined computational content via continuation-p...Double negation elimination requires excluded middle, which needs non-constructi...If a principle has no canonical term, its truth cannot be computationally verifi...Lack of canonical intuitionistic proof doesn't undermine classical validity—clas...
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    Many classical results (excluded middle, choice) are computationally meaningful ...The Curry-Howard correspondence holds not only between provable formulae and typ...The Curry-Howard correspondence shows classical tautologies lack direct computat...

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