Editing Extension (semantics) (section)

{{short description|In the context of semantics the extension of a concept, idea, or sign}}
{{redirects here|Extension (logic)|another use in mathematical logic|Conservative extension}}
In any of several fields of study that treat the use of signs — for example, in [[linguistics]], [[logic]], [[mathematics]], [[semantics]], [[semiotics]], and [[philosophy of language]] — the '''extension''' of a concept, idea, or sign consists of the things to which it applies, in contrast with its [[comprehension (logic)|comprehension]] or [[intension]], which consists very roughly of the ideas, properties, or corresponding signs that are implied or suggested by the concept in question.

In philosophical [[semantics]] or the [[philosophy of language]], the 'extension' of a concept or expression is the set of things it extends to, or applies to, if it is the sort of concept or expression that a single object by itself can satisfy.  Concepts and expressions of this sort are [[monad (Greek philosophy)|monadic]] or "one-place" concepts and expressions.

So the extension of the word "dog" is the set of all (past, present and future) dogs in the world: the set includes Fido, Rover, [[Lassie]], Rex, and so on.  The extension of the phrase "Wikipedia reader" includes each person who has ever read Wikipedia, including ''you''.

The extension of a whole statement, as opposed to a word or phrase, is defined (since [[Gottlob Frege]]'s "[[On Sense and Reference]]") as its [[truth value]]. So the extension of "Lassie is famous" is the logical value 'true', since Lassie is famous.

Some concepts and expressions are such that they don't apply to objects individually, but rather serve to relate objects to objects.  For example, the words "before" and "after" do not apply to objects individually—it makes no sense to say "Jim is before" or "Jim is after"—but to one thing in relation to another, as in "The wedding is before the reception" and "The reception is after the wedding".  Such "relational" or "polyadic" ("many-place") concepts and expressions have, for their extension, the set of all sequences of objects that satisfy the concept or expression in question.  So the extension of "before" is the set of all (ordered) pairs of objects such that the first one is before the second one.