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    Carmelics

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

    It is not the case that Frege and Russell established that universal affirmatives like 'all S are P' carry existential import only under interpretations that presuppose non-empty domains.

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

    Reasons For

    1 perspective
    Reason for
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    • 1.Medieval logicians successfully reasoned about universals without explicit non-empty domain presuppositions, suggesting these aren't necessary for the claim's meaning.
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    • 2.Some modern formal systems (like free logic) handle empty domains without presupposing existential import, undermining the claim's universality.
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    • 3.The presupposition approach may conflate semantics with pragmatics—existential import might be a contextual implicature rather than a logical requirement.
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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Classical Aristotelian logic treated 'all S are P' as false when S is empty, but modern logic requires explicit domain assumptions for consistency.
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    • 2.Frege and Russell's quantificational analysis shows existential import depends on whether ∃x(S(x)) is presupposed, not inherent to the proposition.
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    • 3.Non-empty domain presuppositions allow universal statements to avoid truth-value gaps and maintain logical coherence across systems.
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