 There is a view according to which propositions are sets of worlds. One might prefer to identify facts with sets of worlds (this is what is done in Restall 2004). On this view, for every fact \(x\), \(\ES(x) = x\), and for every world \(w, F_w = \{x : x\in F\) and \(w\in x\}\). Modal Criterion is then satisfied. Suppose that all non-empty sets of worlds are facts. This is a very natural option for the view under consideration, and is actually countenanced by Restall. Then the strong W4 is satisfied.