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Inverse View
It is not the case that A claim of essential property possession that depends on an ill-defined domain of quantification fails to establish genuine modal necessity.
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Reasons For
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1.
Many legitimate essential properties (e.g., human rationality) rely on somewhat vague categories yet intuitively ground genuine modal facts.
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2.
Domain vagueness may reflect epistemic limitation rather than metaphysical failure; necessity can exist independently of our definitional precision.
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3.
The claim conflates a property's modal status with our ability to formalize it; essence and definability are conceptually distinct categories.
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Reasons Against
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Reason against
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1.
Modal claims require precise specification of possible worlds; vague domain boundaries make it unclear which worlds satisfy necessity conditions.
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2.
If we cannot specify what entities fall within the domain, we cannot definitively establish that a property holds across all relevant cases.
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3.
Essential properties must distinguish genuine necessities from contingent features; ill-defined domains conflate these by introducing ambiguity.
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