 Plantinga’s haecceitist account illustrates an important point about most forms of actualism that is sometimes a source of confusion, namely, that most actualists are also modalists. That is, most actualists take the English modal operators “necessarily”, “possibly”, and the like, collectively, to be primitive and, hence, not to be definable in terms of non-modal notions. On the face of it, however, insofar as the formal operators \(\Box\) and \(\Diamond\) are taken to symbolize their English counterparts, defining the modal operators would appear to be exactly what possible world semantics purports to do. For, unlike  the classical connectives and quantifiers,  in basic possible world semantics the modal operators are not interpreted homophonically. That is, they are not interpreted with the very natural language operators they are intended to represent—a necessitation \(\Box\psi,\) in particular, is not defined to be true in an interpretation just in case \(\psi\) is necessarily true in it. Rather, in basic possible world semantics, the necessity operator is interpreted as a restricted universal quantifier: a necessitation \(\Box\psi\) is true in an interpretation \(\calM\) just in case \(\psi\) is true at every possible world of \(\calM\). However, whether or not that proves to be a definition of the necessity operator depends on what one takes a possible world to be.  David Lewis  famously  defined possible worlds  to be (typically) large, scattered concrete objects similar in kind but spatio-temporally unconnected to our own physical universe. Under such an understanding of possible worlds, possible world semantics arguably provides a genuine definition of the modal operators on which the truth conditions assigned to modal formulas do not themselves involve any modal  notions.[69]  As it is sometimes put, such a definition is “eliminative” or “reductive”—modal notions are eliminated in the semantics in favor of quantification over (non-modal) worlds.