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    Without bivalence, a false antecedent cannot be establish... — Carmelics
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    Challenges→The formula (p → q) ∨ p is classically valid because if p is false, conditionals with false antecedents are vacuously true

    Without bivalence, a false antecedent cannot be established merely from the absence of proof of p, blocking the vacuous truth inference in constructive settings.

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    1 reason for
    1 reason against

    Reasons For

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    Reason for
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    • 1.Constructive logic requires explicit proof of propositions; absence of proof cannot establish negation without violating constructive principles.
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    • 2.Vacuous truth relies on classical bivalence where ¬p is automatically true when p lacks proof, conflating unprovability with falsity.
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    • 3.In constructive settings, false antecedents must be actively demonstrated constructible, not merely assumed from proof-theoretic silence.
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    Reasons Against

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    Reason against
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    • 1.Constructive logic still validates ex falso quodlibet; any consistent falsehood blocks vacuous truth regardless of bivalence assumptions.
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    • 2.The claim conflates proof availability with semantic falsity; antecedent falsity remains determinate independent of constructive methodology.
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    • 3.Intuitionistic systems reject bivalence yet still require explicit refutation for falsity; the inference problem precedes bivalence debate.
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    Connections

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    Modality & Possibility1 linkedPhilosophy of Language1 linked

    Related

    Constructive logic requires explicit proof of propositions; absence of proof can...Constructive logic still validates ex falso quodlibet; any consistent falsehood ...In constructive settings, false antecedents must be actively demonstrated constr...Intuitionistic systems reject bivalence yet still require explicit refutation fo...
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    The claim conflates proof availability with semantic falsity; antecedent falsity...The formula (p → q) ∨ p is classically valid because if p is false, conditionals...Vacuous truth relies on classical bivalence where ¬p is automatically true when ...

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    2 (1 for, 1 against)
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