  More generally, and a bit more exactly, put: As noted above, the  logical framework of basic possible world semantics is classical  predicate logic. The logical framework of abstractionism is modal  predicate logic. Hence, if possible world semantics is supplemented  with abstractionist definitions of possible worlds, then the logical  framework of possible world semantics becomes modal predicate logic  as well and, as a consequence, the extensionality of the semantics is lost once again. (This point is expressed somewhat more formally in  the supplemental document   The Intensionality of Abstractionist Possible World Semantics.)  Since, as noted above, the central motivation for possible world  semantics was to deliver an extensional semantics for modal  languages, any motivation for abstractionism as a semantic theory is  arguably undermined.[30]