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    In standard first-order logic, '∃x Dragon(x)' already car... — Carmelics
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    Challenges→The correct first-order translation of 'dragons exist' is '∃x (Exists(x) ∧ Dragon(x))', not '∃x Dragon(x)'.

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

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    Reasons For

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    • 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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    Reasons Against

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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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    Existential import belongs to the predicates and natural language, not to logica...If quantifiers ranged over non-existent objects, true negations like '¬∃x Dragon...Mathematical practice treats domains as existing mathematical objects; restricti...Standard first-order logic requires domains to be non-empty sets; empty domains ...
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    The correct first-order translation of 'dragons exist' is '∃x (Exists(x) ∧ Drago...The domain of quantification is a formal construct independent of ontology; rest...We can coherently quantify over fictional characters or abstract possible worlds...

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