 Supervenience is a direct consequence of No Twins, but one may wish to leave open the possibility of distinct worlds containing the same facts. (On the view that to be a fact is to be a true proposition, Supervenience trivially holds if it is assumed that no proposition can be true if it does not exist. If that assumption is dropped, then there is room for Supervenience to fail. That might be taken to be an argument for keeping the assumption on the view under consideration.)