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    The correct first-order translation of 'dragons exist' is... — Carmelics
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    The correct first-order translation of 'dragons exist' is '∃x (Exists(x) ∧ Dragon(x))', not '∃x Dragon(x)'.

    Philosophy of Language
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    1 reason for
    2 reasons against

    Reasons For

    1 perspective
    Reason for
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    • 1.The quantifier '∃x' is neutral with respect to existence on its own.
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    • 2.Existential import requires an explicit existence predicate in addition to the quantifier.
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    Reasons Against

    2 perspectives
    Reason against 1 of 2
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    • 1.In standard first-order logic, '∃x Dragon(x)' already carries existential import: the domain of quantification contains only existing objects.
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    • 2.Quine's canonical criterion of ontological commitment identifies what exists with what the bound variables of true sentences range over, making 'Exists(x)' a redundant predicate.
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    • 3.Adding 'Exists(x)' as a first-order predicate generates a vicious regress: we must then ask whether the extension of Exists itself exists, requiring a meta-level predicate.
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    Reason against 2 of 2
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    • 1.Free logic, not an enriched first-order predicate, is the proper formal tool for handling non-referring terms like 'dragon', preserving a neutral domain without inflating the predicate inventory.
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    • 2.The claim conflates a metalinguistic question about domain membership with an object-language predication, a confusion van Fraassen and Lambert's free logic literature explicitly diagnoses and resolves.
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    Philosophy of Language

    Related

    Adding 'Exists(x)' as a first-order predicate generates a vicious regress: we mu...Existential import requires an explicit existence predicate in addition to the q...Free logic, not an enriched first-order predicate, is the proper formal tool for...In standard first-order logic, '∃x Dragon(x)' already carries existential import...
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    Quine's canonical criterion of ontological commitment identifies what exists wit...The claim conflates a metalinguistic question about domain membership with an ob...The quantifier '∃x' is neutral with respect to existence on its own.

    Similar

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    SEP: ontological-commitment
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    According to the third objection to sufficiency, the quantifiers of first-order logic, properly understood, do not carry existential commitment; they are not “existentially loaded”. Indeed, calling ‘∃x’ the “existential quantifier” is a misnomer; it would be better to call it the “particular quantifier” in contrast with the “universal quantifier”. Ordinary language, on its face, supports the view that quantification need not be existentially loaded (see §4). For example, if we assert “some ficti
    Extraction notes

    Validity: Extracted via Max plan + API grounding/validity checks

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    claim
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