Does possible-worlds semantics require believing in other worlds?

No. The semantics is a formal tool, and most philosophers who use it deny that other concrete worlds exist. They interpret 'worlds' as abstract objects — ways things could have been — so that quantifying over worlds is a perspicuous way of talking about possibilities without ontological extravagance.

Possible-Worlds Semantics

Possible-worlds semantics interprets necessity as truth in all accessible worlds and possibility as truth in some, turning modal logic into a tractable model theory.

Definition

Possible-worlds semantics evaluates modal sentences at points called worlds linked by an accessibility relation, with 'necessarily A' true at a world iff A holds at every world accessible from it.

Scope

This topic covers the relational (Kripke) model theory for modal logic: frames consisting of a set of worlds and an accessibility relation, valuations, and the truth clauses for the modal operators. It treats the technical role of frames and the philosophical question of what possible worlds are — concrete universes, abstract states of affairs, sets of propositions, or mere formal indices — and how that bears on the explanatory value of the semantics.

Core questions

What exactly is a possible world, and do worlds exist?
What is the accessibility relation, and what does it represent?
Does the formal semantics explain modal truth or merely model it?
How do worlds help analyze counterfactuals, propositions, and content?

Key concepts

possible world
accessibility relation
frame and model
valuation
actualism vs. possibilism
ersatz worlds

Key theories

Kripke relational models: A model is a set of worlds with an accessibility relation and a valuation; modal operators quantify over accessible worlds, so logical features of modality reduce to structural properties of the relation.
Worlds as abstract objects: Stalnaker treats possible worlds as ways things could have been — abstract maximal possibilities — rejecting Lewis's concrete worlds while retaining the explanatory benefits of worlds for modality and content.

History

Carnap's state-descriptions and Leibniz's talk of possible worlds anticipated the idea, but the rigorous semantics emerged with Kripke's 1963 relational models. Philosophers then divided over the metaphysics: Lewis's 1986 modal realism treats worlds as concrete, while Stalnaker and others defend abstract 'ersatz' worlds.

Debates

Concrete vs. abstract worlds: Whether the worlds the semantics quantifies over are concrete spatiotemporal universes or abstract surrogates such as maximal consistent sets of propositions, and which reading makes the semantics genuinely explanatory.

Key figures

Saul Kripke
David Lewis
Robert Stalnaker
Jaakko Hintikka
Rudolf Carnap

Seminal works

kripke1963
lewis1986plurality

Frequently asked questions

Does possible-worlds semantics require believing in other worlds?: No. The semantics is a formal tool, and most philosophers who use it deny that other concrete worlds exist. They interpret 'worlds' as abstract objects — ways things could have been — so that quantifying over worlds is a perspicuous way of talking about possibilities without ontological extravagance.