Denotation

Denotation is a relation in linguistics and philosophy of language between an expression and the objects it refers to in the world. In this sense, denotation is often equated with extension: the set of all things that the expression designates. Denotation contrasts with connotation (the associations or evaluative content a word evokes) and with sense or intension (the mode of presentation or concept by which the referent is thought of).

For a given term, its denotation is its extension. For example, the denotation of "dog" is the set of all dogs; the denotation of "Socrates" is the individual Socrates; the denotation of the predicate "is a mammal" is the set of all things that are mammals. Proper names typically designate single objects; common nouns designate sets or properties. Denotation can be relativized to a context or to a possible world; the denotation of a term may change with the world state.

Philosophical theories distinguish sense and reference; Frege's distinction between Sinn (sense) and Bedeutung (denotation) is a foundational framework. In formal semantics and model theory, denotation is defined relative to a linguistic structure: a term denotes its extension within a model, and the denotation of a sentence is its truth value in a world (or model). In modal or indexical contexts, denotation can vary across possible worlds or contexts.

Several problems affect denotation. Some expressions have empty or nonexistent referents, such as "the present king of France." Fictional or hypothetical names can be assigned denotations in some theories but not in others. Indexicals like "here" or "now" require context to determine their denotation.

Beyond linguistics, "denotation" also appears in computer science in denotational semantics, where programming language constructs are mapped to mathematical objects such as functions, states, or domains.