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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 In standard first-order logic, '∃x Dragon(x)' already carries existential import: the domain of quantification contains only existing objects.

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

    Reasons For

    1 perspective
    Reason for
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    • 1.The domain of quantification is a formal construct independent of ontology; restricting it to 'existing' objects conflates semantics with metaphysics.
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    • 2.We can coherently quantify over fictional characters or abstract possible worlds without committing to their existence in reality.
      ?

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    • 3.Existential import belongs to the predicates and natural language, not to logical structure; first-order logic deliberately abstracts away this distinction.
      ?

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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Standard first-order logic requires domains to be non-empty sets; empty domains create logical pathologies and violate foundational axioms.
      ?

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    • 2.If quantifiers ranged over non-existent objects, true negations like '¬∃x Dragon(x)' would be ambiguous between absence and non-existence.
      ?

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    • 3.Mathematical practice treats domains as existing mathematical objects; restricting domains to existing things preserves this standard interpretation.
      ?

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