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It is not the case that Global supervenience entails strong supervenience when the B-properties include all relational and world-indexed properties, not just intrinsic ones.
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Reasons For
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Reason for
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1.
Strong supervenience requires counterfactual dependence in the same world. Relational and world-indexed properties are world-relative, making them unsuitable for grounding strong supervenience across modal space.
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2.
Including relational properties in B-base trivializes the claim—A-properties just become defined via B-relational facts, making supervenience analytic rather than substantive metaphysical insight.
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3.
World-indexing properties conflates levels of description. If B-properties include 'being in world W', this presupposes the very B-completeness needed to establish strong supervenience, risking circularity.
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Reasons Against
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Reason against
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1.
Strong supervenience requires that any A-difference necessitates a B-difference in the same world. Relational and world-indexed properties are part of B-facts, filling gaps intrinsic-only B-properties leave.
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2.
Global supervenience makes identical B-complete worlds metaphysically indistinguishable. Including relational facts ensures all difference-makers are captured, enabling strong supervenience to hold.
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3.
Intrinsic properties alone cannot determine relational facts. Only when B-properties encompass relations and world-indexing can global supervenience guarantee local supervenience necessary for strength.
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