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    Carmelics

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    LoyalLoyalJusticeJustice
    Made withinDC&Austin
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    It is not the case that Sharing a variable 'x' across two existential quantifiers in separate conjuncts creates a misleading syntactic appearance of a linked ranging, which Prior warned distorts logical form.

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    Reasons For

    1 perspective
    Reason for
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    • 1.Standard logical notation uses variable renaming conventions that trivially resolve ambiguity; the issue is notational carelessness, not logical distortion.
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    • 2.Experienced logicians automatically parse ∃x(P(x)) ∧ ∃x(Q(x)) correctly as independent; the 'distortion' exists only for novices lacking competence.
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    • 3.Prior's warning conflates cognitive psychology with logical form; syntax perfectly captures the truth conditions regardless of how readers interpret appearance.
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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Prior demonstrated that ∃x(P(x)) ∧ ∃x(Q(x)) syntactically suggests a single domain of x, misleading readers about actual logical independence.
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    • 2.Formal semantics requires separate variable instantiations across conjuncts; shared notation obscures this by implying coordinated quantification.
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    • 3.Pedagogically, students routinely misinterpret such formulas as expressing constraints between the two existential domains, requiring explicit clarification.
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