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    Henkin's completeness proof presupposes classical logic, ... — Carmelics
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    Challenges→Γ ⊢ φ (Γ proves φ)

    Henkin's completeness proof presupposes classical logic, including the law of excluded middle and double negation elimination.

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    1 reason for
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    Reasons For

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    Reason for
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    • 1.Henkin's proof constructs a maximal consistent set using the law of excluded middle to ensure completeness of witness sets.
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    • 2.Double negation elimination is used when collapsing negated formulas into the model, a central step in the proof.
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    • 3.The proof's reliance on classical bivalence is essential for the saturatedness property required for completeness.
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    Reasons Against

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    Reason against
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    • 1.Henkin's proof can be formalized in intuitionistic logic using constructive witnesses without invoking excluded middle.
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    • 2.The maximal consistent set construction uses only consistency and Lindenbaum's lemma, which hold in intuitionistic settings.
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    • 3.Completeness for intuitionistic logic has been proven via Kripke semantics without relying on classical logical principles.
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    Truth & Knowledge1 linkedPhilosophy of Language1 linked

    Related

    Completeness for intuitionistic logic has been proven via Kripke semantics witho...Double negation elimination is used when collapsing negated formulas into the mo...Henkin's proof can be formalized in intuitionistic logic using constructive witn...Henkin's proof constructs a maximal consistent set using the law of excluded mid...
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    The maximal consistent set construction uses only consistency and Lindenbaum's l...The proof's reliance on classical bivalence is essential for the saturatedness p...Γ ⊢ φ (Γ proves φ)

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