extension (semantics)
please note:
- the text and code below is from The Pseudopedia
- it has been imported raw for GetWiki
In any of several studies that treat the use of
signs, for example in
linguistics,
logic,
mathematics,
semantics, and
semiotics, 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
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
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
Frege 1892) 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.
Mathematics
{{Mergefrom|Extension (predicate logic)|date=May 2008}}In
mathematics, the 'extension' of a mathematical concept is the
set that is specified by that concept. For example, the extension of a
function is a set of
ordered pairs that pair up the arguments and values of the function; in other words, the function's graph. The extension of an object in
abstract algebra, such as a
group, is the
underlying set of the object. The extension of a set is the set itself. That a set can capture the notion of the extension of anything is the idea behind the
axiom of extensionality in
axiomatic set theory.This kind of extension is used so constantly in contemporary mathematics based on
set theory that it can be called an implicit assumption. It can mean different things in different cases, and there is no universal definition of the term "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
metaphysics about whether or not there are, in addition to actual, existing things, non-actual or nonexistent things. If there are--if, for instance, there are possible but non-actual dogs (dogs of some non-actual but possible species, perhaps) or nonexistent beings (like Sherlock Holmes, perhaps), then these things might also figure in the extensions of various concepts and expressions. If not, only existing, actual things can be in the extension of a concept or expression. Note that "actual" may not mean the same as "existing". Perhaps there exist things that are merely possible, but not actual. (Maybe they exist in other universes, and these universes are other "
possible worlds"--possible alternatives to the actual world.) Perhaps some actual things are nonexistent. (Sherlock Holmes seems to be an 'actual' example of a fictional character; one might think there are many other characters
Arthur Conan Doyle 'might' have invented, though he actually invented Holmes.)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
External links
Extenze a intenzeExtension und Intensionمصادیق (معناشناسی)外延ЭкстенсионалEkstensionaalinenРозширення (філософія)外延
- content above as imported from The Pseudopedia
- "extension (semantics)" does not exist on GetWiki
- time: 12:45pm EDT - Sun, Mar 14 2010
