How many possible worlds are there? (Q2701943)

An argument is presented that is meant to raise doubts about the existence of possible worlds and hence to show that the equivalenceNEWLINENEWLINE\hskip 17mm (1) It is possible that \(p\) iff there is a possible world \(w\) such that,NEWLINENEWLINE\hskip 17mm at \(w\), \(p\).NEWLINENEWLINENEWLINEmay fail. The author holds that the equivalence leaves room for being doubted, because the right side makes an ontological commitment, whereas it is not clear that the left side does. A number of assumptions is made about entities being named or not in order to present a Cantor-style proof of the absurd claim that there are more possible worlds than entities. As the author remarks, the possible worlds semantics of modal logics is not challenged by the argument.