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    The unprovability of the empty sequent is thus a feature ... — Carmelics
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    Challenges→The empty sequent is not provable

    The unprovability of the empty sequent is thus a feature of classical and intuitionistic systems, not a logical necessity across all coherent proof systems.

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    1 reason for
    1 reason against

    Reasons For

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    Reason for
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    • 1.Different proof systems encode logical consequence differently, so unprovability varies by formal architecture, not absolute truth.
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    • 2.Paraconsistent logics tolerate contradictions without explosion, showing unprovability depends on system-specific consistency assumptions.
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    • 3.Relevance logics reject weakening, making some sequents unprovable there but provable in classical logic due to structural rules.
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    Reasons Against

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    Reason against
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    • 1.The empty sequent's unprovability reflects a fundamental principle: no conclusion follows from no premises in any coherent system.
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    • 2.If some proof system proves the empty sequent, it's either inconsistent or redefines 'sequent' so fundamentally it's not comparable.
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    • 3.Logical necessity means unprovable in all sound systems for the same domain; the empty sequent meets this across foundational logics.
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    Proof of definition segments1 linkedTruth & Knowledge1 linked

    Related

    Different proof systems encode logical consequence differently, so unprovability...If some proof system proves the empty sequent, it's either inconsistent or redef...Logical necessity means unprovable in all sound systems for the same domain; the...Paraconsistent logics tolerate contradictions without explosion, showing unprova...
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    Relevance logics reject weakening, making some sequents unprovable there but pro...The empty sequent is not provableThe empty sequent's unprovability reflects a fundamental principle: no conclusio...

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