In my free time, I’m reading the classic Dowty, Wall, and Peters 1981, Introduction to Montague Semantics, and came across this wonderful quote on the use of possible worlds in model-theoretic semantics, which I thought I’d post, both for others to read and as a bookmark for myself to have on hand in the future.
[I]t would seem that the value of any model-theoretic analysis involving possible worlds will depend on (1) how successfully it can be carried out technically, and (2) whether it results in definitions of validity and entailment among sentences of the formal language that reasonably match our intuitions about entailment and validity among the corresponding English sentences (taking into account the syntactic limits of the formal language). Any reasonably simple model-theoretic analysis of a semantic problem of natural language that satisfies these two requirements merits our serious attention (at least until a better model-theoretic analysis of the same problem is available), even if the primitive entities required in the model theory appear somewhat mysterious at first. If such an analysis meeting these requirements but involving some mysterious entity such as possible worlds is presented, then it behooves us to try to elaborate on the analysis and to try to further elucidate the mysterious entity involved. We are not entitled to reject such an analysis out of hand because we dislike the entities involved.
— Dowty, Wall, and Peters (1981, pp. 124–125)