Strike a match and it lights. Now consider the claim that it could have failed to light — that there is nothing about the world which made lighting inevitable.

That claim is obviously meaningful and surprisingly hard to state. It is not about the match, which lit. It is not about anyone's ignorance, because a perfectly informed observer could say it too. It is about how things might have gone, and nothing in the actual match is the truthmaker.

Possible worlds are the machinery built to handle exactly this. A proposition is possible if it is true in at least one world, necessary if it is true in all of them, and contingent if it is true in some and false in others. Modal claims, which resisted analysis for centuries, become ordinary quantification — some, all — over a domain.

Why it took over

Because it made a whole vocabulary tractable at once.

Counterfactuals. If the alert had fired, the outage would not have happened is true if, in the nearest worlds where the alert fires, there is no outage. Nearness does the work, and arguing about a counterfactual becomes arguing about which world is nearest — which is at least a well-formed disagreement.

Essence. A property is essential to a thing if the thing has it in every world where it exists at all. Socrates is a man in all of them; Socrates is snub-nosed in only some.

Necessity that is not analytic. Kripke's argument in Naming and Necessity (1980) that water is necessarily H₂O — true in every world, though discovered by experiment rather than by thinking — is stated in this vocabulary and is hard to state without it.

The term is Leibniz's, who used it to argue that God, surveying every world that could have been, actualised the best. That argument is now mostly read through the problem of evil, but the device outlived the theology by three centuries.

The price of taking it literally

David Lewis did take it literally. On his view the other worlds are as concrete as this one, spatiotemporally isolated from it, and actual is an indexical — it means this one, the way here means this place. Other worlds are no less real for being elsewhere.

Lewis held this position because he thought the semantics only works if the worlds are genuinely there. If they are stories, or maximal sets of sentences, or abstract states of affairs, then something has to explain what makes a story a consistent one — and consistency is a modal notion, so the analysis has gone in a circle.

Almost nobody follows him. The usual response is that the cost — an infinity of concrete universes, each as real as this one, to underwrite a semantics — is higher than any benefit. But the alternatives all face Lewis's question and mostly answer it by taking some modal notion as primitive, which is a concession rather than a refutation.

What survives the dispute

This is the useful thing to notice: the machinery works whether or not you believe the worlds exist.

You can reason with possible worlds, get correct results about entailment and counterfactuals, and hold no view whatever about their metaphysical status. That is why the device is everywhere in philosophy, linguistics and computer science while modal realism has almost no adherents.

It is worth holding onto as a general pattern. A formalism can earn its place by what it lets you calculate, and the question of what its terms refer to can stay open for a very long time without anything going wrong — which is roughly the situation of the principle of sufficient reason, and of most of mathematics.