 In any case, those who assert a weak or intermediate global supervenience thesis while denying the corresponding strong global supervenience thesis need to provide an explanation of why weak or intermediate global supervenience holds that does not entail that strong global supervenience holds. (Recall the discussion of weak and strong individual supervenience in  4.1).  That is, they need to explain what enforces the links between A- and B-preserving isomorphisms that are required by weak and intermediate global, without also enforcing the claim that every B-preserving isomorphism itself be A-preserving.