If the antecedent of strong global supervenience is vacuously satisfied due to domain mismatch, intermediate global supervenience can still fail for worlds with non-overlapping individuals.
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A condition that is technically true but only because the requirement it's supposed to check never actually gets tested—like saying 'all unicorns are blue' being true simply because unicorns don't exist.
strong global supervenience(Metaphysics of supervenience; distinguished from strong individual supervenience)
A supervenience relation spelled out in terms of world-wide patterns of distribution of properties, as opposed to individual-level supervenience
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.