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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global supervenience(Modal supervenience relations in philosophy of mind and metaphysics)
A globally supervenes on B if and only if no two possible worlds share the same global pattern of distribution of B-properties while differing in their global pattern of distribution of A-properties.
strong supervenience(Conceded by Kim to not be entailed by global supervenience)
A supervenience relation where, across all possible worlds, any individual that shares B-properties with another individual also shares A-properties with that individual
supervenience(Philosophy of mind and reduction; contrasted with full reduction)
A relation in which mental (or higher-level) states are dependent on physiological (or lower-level) states such that any two cases with identical lower-level bases are identical in their higher-level states; a necessary but not sufficient condition for reduction.