 When we let the propositional quantifier range over sets of worlds in \(W\), we find that Kaplan’s sentence can only be satisfied in such a model if there is a map from the set of sets of worlds in \(W\) into \(W\), which is not possible on account of Cantor’s theorem. Kaplan thought this is a problem because the model theory for quantified propositional model should not unduly constrain the space of intuitive possibilities. If we interpret \(Qp\) to mean that \(p\) is Queried, i.e., it is asked whether it is the case that \(p\), then (K) states that for every proposition, \(p\), it is possible that \(p\) and only \(p\) is Queried.