possibleworlds

Possible worlds are a formal device used in philosophy and semantics to model modality—that is, what could have been, what must be, and what might be true. They represent complete, internally consistent ways the world could have been. In this framework, the truth of a proposition can vary across worlds: a statement is necessarily true if it is true in all accessible worlds, and merely possible if it is true in at least one accessible world. The accessibility relation specifies which worlds are relevant for a given context, often reflecting logical, physical, or metaphysical constraints.

In Kripke-style semantics, a model comprises a set of possible worlds, an accessibility relation between them, and a valuation that assigns truth values to propositions at each world. The actual world is the world that corresponds to our present facts. This setup underpins the interpretation of modal operators such as necessity and possibility and the evaluation of counterfactuals, where truth is often taken to hold in the closest possible worlds where the antecedent is true (as in the Stalnaker-Lewis theories).

Philosophical stances differ on what possible worlds are. Modal realism, notably advanced by David Lewis, treats possible worlds as concrete, causally isolated spaces just as real as the actual world. Actualism, by contrast, denies the existence of concrete possible worlds and instead uses abstract structures (such as properties, sets, or states of affairs) to model modality. Counterpart theory offers a way to handle transworld identity without reidentification of individuals across worlds. Possible worlds also inform philosophy of language, metaphysics, and formal semantics, though they face debates about ontological commitment and explanatory power.