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    LoyalLoyalJusticeJustice
    Made withinDC&Austin
    Statements
    321,452
    Perspectives
    108,905
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    42
    Home/Original/inverse
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    Inverse View

    It is not the case that Cut elimination is a metatheorem that must be proved for each Gentzen system, not a universal structural feature of all such systems.

    ?Set your confidence on the premises below to see your aggregate.

    Reasons For

    1 perspective
    Reason for
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    • 1.Cut elimination holds for all standard Gentzen sequent calculi precisely because the formalism is designed with this structural property in mind.
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    • 2.When cut elimination fails in some system, the failure indicates the system is non-standard or poorly designed, not that cut elimination is non-universal.
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    • 3.The proof strategy for cut elimination (proving by induction on cut rank) is fundamentally uniform across Gentzen systems, not fundamentally system-specific.
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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Different Gentzen systems (LK, LJ, modal logics) have distinct structural rules, so cut-elimination proofs vary significantly across them.
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    • 2.Cut elimination fails for some well-motivated Gentzen systems (e.g., relevant logics, paraconsistent systems), showing it's not universally guaranteed.
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    • 3.The cut-elimination proof depends on induction on formula complexity, which requires system-specific design of inference rules to ensure success.
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