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    Carmelics

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    LoyalLoyalJusticeJustice
    Made withinDC&Austin
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    Home/Original/inverse
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    Inverse View

    It is not the case that The relational generalization of CL is second-order in nature, unlike CL itself

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    Reasons For

    2 perspectives
    Reason for 1 of 2
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    • 1.Relational generalizations can be expressed via higher-order typed lambda calculi where relations are first-class objects at the base type level.
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    • 2.Church's own type theory (STT) encodes relations as functions to truth values, collapsing the first/second-order distinction within a typed framework.
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    Reason for 2 of 2
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    • 1.Quine argued that second-order logic is 'set theory in sheep's clothing,' meaning purportedly second-order quantification over relations reduces to first-order quantification over sets.
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    • 2.If relational quantification is reinterpreted as first-order quantification over set-theoretic proxies, the generalization of CL need not be genuinely second-order in logical kind.
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    Reasons Against

    1 perspective
    Reason against
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    • 1.CL applies to functions and is a principle of first-order logic
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    • 2.The generalization of CL to arbitrary relations requires quantification over relations, which is second-order
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