 The Analysis of Intensions. As much a barrier to the  acceptance of modal logic as intensionality itself was the need to  appeal to intensions per se — properties, relations,  propositions, and the like — in semantical explanations.  Intensional entities have of course featured prominently in the  history of philosophy since Plato and, in particular, have played  natural explanatory roles in the analysis of   intentional attitudes  like   belief  and   mental content.  For all their prominence and importance, however, the nature of these entities has often been obscure and controversial and, indeed, as a  consequence, they were easily dismissed as ill-understood and  metaphysically suspect “creatures of darkness” (Quine  1956, 180) by the naturalistically oriented philosophers of the  early- to mid-20th century. It is a virtue of possible world  semantics that it yields rigorous definitions for  intensional entities. More specifically, as described above, possible world semantics assigns to each n-place predicate π a  certain function Iπ — π's intension  — that, for each possible world w, returns the extension Iπ(w) of π at w. We can define  an intension per se, independent of any language, to be any  such function on worlds. More specifically: 