Extension (semantics)
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 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
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
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.
Mathematics
In mathematics, the 'extension' of a mathematical concept is the set that is specified by . (That set might be empty, currently.)
For example, the extension of a
This kind of extension is used so constantly in contemporary mathematics based on set theory that it can be called an implicit assumption. A typical effort in mathematics evolves out of an observed mathematical object requiring description, the challenge being to find a characterization for which the object becomes the extension.
Computer science
In computer science, some database textbooks use the term 'intension' to refer to the schema of a database, and 'extension' to refer to particular instances of a database.
Metaphysical implications
There is an ongoing controversy in
A similar problem arises for objects that no longer exist. The extension of the term "Socrates", for example, seems to be a (currently) non-existent object. Free logic is one attempt to avoid some of these problems.
General semantics
Some fundamental formulations in the field of general semantics rely heavily on a valuation of extension over intension. See for example extension, and the extensional devices.
See also
- Enumerative definition
- Extensional definition
- Extensional logic
- Generalization
- Sense and reference
- Semantic property
- Type–token distinction