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Inverse View
It is not the case that Plantinga's modal ontological argument shows that S5-based necessity and conceptual necessity collapse into the same inferential structure.
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Reasons For
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Reason for
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1.
S5's accessibility relation assumes logical possibility, but conceptual coherence and metaphysical possibility are distinct epistemic categories.
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2.
Plantinga's argument requires that conceivability entails possibility, but this premise itself needs independent justification beyond S5 axioms.
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3.
Critics (Oppy, Sobel) show the argument's success depends on prior theological assumptions, not on S5 semantics demonstrating their equivalence.
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Reasons Against
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Reason against
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1.
S5 modal semantics treats possible worlds as equally accessible, making metaphysical necessity identical to conceivability across all models.
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2.
Plantinga's maximal greatness concept requires logical equivalence between 'possibly necessary' and 'necessarily necessary' in S5 semantics.
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3.
If a property is conceptually coherent (God's omnipotence), S5 guarantees it holds in some possible world, collapsing conceptual into modal necessity.
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