  Although ‘possible world’ has been part of the  philosophical lexicon at least since Leibniz, the notion became  firmly entrenched in contemporary philosophy with the development of  possible world semantics for the languages of propositional and first-order modal logic. In addition to the usual sentence operators of  classical logic such as ‘and’ (‘∧’), ‘or’ (‘∨’), ‘not’ (‘¬’), ‘if...then’ (‘→’), and, in the first-order case, the quantifiers ‘all’ (‘∀’) and ‘some’ (‘∃’), these languages contain operators intended to represent the modal adverbs ‘necessarily’ (‘□’) and ‘possibly’ (‘◇’). Although a prominent aspect of logic in both Aristotle's work and the work of many medieval philosophers, modal logic was largely ignored from the modern period to the mid-20th century. And even though a variety of modal deductive systems had in fact been rigorously developed in the early 20th century, notably by Lewis and Langford (1932), there was for the languages of those systems nothing comparable to the elegant semantics that Tarski had provided for the languages of classical first-order logic. Consequently, there was no rigorous account of what it means for a sentence in those languages to be true and, hence, no account of the critical semantic notions of validity and logical consequence to underwrite the corresponding deductive notions of theoremhood and provability. A concomitant philosophical consequence of this void in modal logic was a deep skepticism, voiced most prominently by Quine, toward any appeal to modal notions in metaphysics generally, notably, the notion of an essential property. (See Quine 1953 and 1956, and the appendix to Plantinga 1974.) The purpose of the following two subsections is to provide a simple and largely ahistorical overview of how possible world semantics fills this void; the final subsection presents two important applications of the semantics. (Readers familiar with basic possible world semantics can skip to §2 with no significant loss of continuity.) 