 Paull and Sider pointed out that these argument strategies are no good (1992). The problem is that one cannot simply point to two worlds that do not themselves falsify a global supervenience thesis, and then claim that the case is compatible with that thesis. Those two worlds might entail the existence of other worlds that are not compatible with the global supervenience thesis. A global supervenience thesis is a claim about all worlds, not just two. The upshot is that although a global supervenience thesis fails to entail either a weak or strong supervenience thesis in virtue of logical form, it might nevertheless be the case that plausible metaphysical principles entail that whenever the former holds, so does the latter.