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    Logical characterizations like SO∃ are themselves artifac... — Carmelics
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    Challenges→The availability of machine-independent logical characterizations provides additional evidence for the mathematical robustness of complexity classes like NP.

    Logical characterizations like SO∃ are themselves artifacts of specific metatheoretical choices about syntax, semantics, and expressive power.

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    1 reason for
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    Reasons For

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    Reason for
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    • 1.Different formal systems (first-order, second-order, infinitary logic) capture different classes of properties depending on their syntactic rules.
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    • 2.What counts as 'definable' or 'expressible' varies with semantic choices (Tarskian models vs. alternative model classes).
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    • 3.SO∃ boundaries reflect prior commitments about quantifier scope and variable domains, not mind-independent logical facts.
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    Reasons Against

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    Reason against
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    • 1.SO∃'s logical properties (incompleteness, capturing NP on finite structures) hold across multiple formal frameworks and metatheories.
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    • 2.If characterizations were mere artifacts of choices, isomorphic logical systems would yield different core results—but they don't.
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    • 3.The claim conflates epistemological dependence on frameworks with metaphysical dependence, risking collapsing all logic into pure convention.
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    Truth & Knowledge1 linkedModality & Possibility1 linked

    Related

    Different formal systems (first-order, second-order, infinitary logic) capture d...If characterizations were mere artifacts of choices, isomorphic logical systems ...SO∃ boundaries reflect prior commitments about quantifier scope and variable dom...SO∃'s logical properties (incompleteness, capturing NP on finite structures) hol...
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    The availability of machine-independent logical characterizations provides addit...The claim conflates epistemological dependence on frameworks with metaphysical d...What counts as 'definable' or 'expressible' varies with semantic choices (Tarski...

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    claim
    Perspectives
    2 (1 for, 1 against)
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