If two worlds are B-indiscernible globally, then every object in one world has a B-indiscernible counterpart in the other, satisfying weak supervenience's individual-level condition.

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Key Terms

B-indiscernible(a in w and c in w* are B-indiscernible because B contains only P and Q, and they do not differ on P or Q): Two individuals are B-indiscernible if and only if they share all properties in the base set B
World (in philosophy)(metaphysics and logic): A complete possible scenario or reality—a fully detailed way that the universe could be, including all objects, facts, and relationships.
counterpart(Lewis's modal realism; used to ground de re modal claims without trans-world identity): An object y in world w2 is a counterpart of object x in world w1 if y resembles x and nothing else in w2 resembles x more than y.
individual-level condition(specifying that the rule works for each object separately): A requirement that applies to single objects or things, rather than to whole groups or systems.

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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.

If two worlds are B-indiscernible globally, then every object in one world has a B-indiscernible counterpart in the other, satisfying weak supervenience's individual-level condition.

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