Possible worlds
Possible worlds are complete ways reality might have been, used to represent possibility, necessity, and related notions in philosophy and logic.
Modal logic: A formal system for reasoning about necessity, possibility, and other modes of truth. It formalizes claims about what holds in some or all possible worlds.
Modality: The status of being possible, necessary, or otherwise qualified rather than simply actual. Possible worlds provide a framework for analyzing modal notions.
Gottfried Wilhelm Leibniz: A German philosopher and mathematician who developed a metaphysics of possible worlds and divine choice. His account made possible worlds central to explaining contingency and creation.
Modal fictionalism: The view that discourse about possible worlds is useful fiction rather than literal ontology. It uses world-talk without committing to worlds as entities.
Conditional logic: A logic for representing conditionals, including claims about what would follow under hypothetical assumptions. World comparisons provide formal truth conditions for many conditional logics.
Kripke semantics: A semantics for modal logic using worlds, valuations, and accessibility relations. It gives possible worlds a precise role in evaluating modal formulas.
Necessity and sufficiency: Relations in which one condition must hold for, or guarantees, another. Necessity in modal logic concerns truth across the relevant worlds.
Rudolf Carnap: A twentieth-century philosopher who developed formal frameworks for analyzing meaning and modality. His state-descriptions offered an influential precursor to worlds in formal semantics.
ersatz possible world: An abstract representation, such as a set of propositions, used in place of a concrete possible world. Ersatz accounts preserve world-based analysis while rejecting Lewisian concrete worlds.
Epistemic logic: A logic for representing knowledge and belief, often using sets of worlds compatible with an agent's information. Worlds encode the alternatives an agent cannot rule out.