Full Idea
The main benefit of the possible worlds move is to permit one to paraphrase modal claims in an extensional language that has quantifiers, but no modal auxiliaries, so the semantic stucture of modal discourse can be discussed without the controversies.
Gist of Idea
Possible worlds allow discussion of modality without controversial modal auxiliaries
Source
Robert C. Stalnaker (Reference and Necessity [1997], 2)
Book Reference
Stalnaker,Robert C.: 'Ways a World Might Be' [OUP 2003], p.171
A Reaction
The strategy introduces the controversy of possible worlds instead, but since they just boil down to collections of objects with properties, classical logic can reign. Possible worlds are one strategy alongside many others.
Related Idea
Idea 16397 If it might be true, it might be true in particular ways, and possible worlds describe such ways [Stalnaker]