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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 formalization ∃x[L(x,j)] ∧ ∃x[L(r,x)] uses 'x' in scopes where it is semantically unrelated, violating the Quinean criterion that canonical notation must eliminate such ambiguity.

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    Reasons For

    1 perspective
    Reason for
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    • 1.Variable reuse across independent quantifiers is standard practice in first-order logic and causes no actual semantic confusion or formal error.
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    • 2.The Quinean criterion targets material ambiguity in reference, not notational economy; using 'x' twice in separate scopes violates neither principle.
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    • 3.Requiring distinct variables for all independent quantifications would unnecessarily burden notation without improving logical validity or semantic content.
      ?

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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Quine's canonical notation demands that variables with distinct semantic roles should have distinct notational markers to preserve logical clarity.
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    • 2.Using 'x' in both ∃x[L(x,j)] and ∃x[L(r,x)] obscures that these quantifiers bind semantically independent existential claims.
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    • 3.Ambiguity in notation risks scope confusion and makes logical structure less transparent than using distinct variables like ∃x[L(x,j)] ∧ ∃y[L(r,y)].
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