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It is not the case that Kim's own formulation of strong supervenience already accommodates relational properties, collapsing the alleged gap when the base is properly specified.
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Reasons For
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1.
Specifying 'all relevant relations' already smuggles in the relational properties we're trying to explain, making the account circular rather than reductive.
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2.
Even with relational base properties included, mental properties may possess intrinsic qualities (qualia, intentionality) that don't supervene on any physical facts.
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3.
Kim's formulation preserves causal exclusion worries: if mental properties just are complex relational facts, they lack independent causal powers.
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Reasons Against
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1.
Relational properties like 'being married to' supervene on physical facts about individuals and their spatiotemporal connections when base is fully specified.
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2.
Kim's formulation requires complete physical specification of all relevant entities and their relations, which naturally includes relational base facts.
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3.
The apparent gap between mental and physical dissolves once we recognize that mental content itself is relationally constituted by organism-world interactions.
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