 But appealing to weak supervenience while denying strong generates a certain explanatory burden. You will recall that we always want an explanation of why a supervenience relation holds (see  Section 3.7).  Thus someone who asserts a weak supervenience thesis but denies the corresponding strong supervenience thesis must provide an explanation of why the weak supervenience thesis is true that does not entail that the relevant strong supervenience thesis is true as well. And that can look mysterious: if there can be things in different worlds that are A-discernible but not B-discernible, why can’t there be two such things within a single world? If everything within each world that is B-indiscernible is A-indiscernible, how can different worlds enforce different B→A property pairings? (See Blackburn on the need to explain the “ban on mixed worlds,” 1973, 1985, and especially 1984, 184.)