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In any of several studies that treat the use of signs, for example, 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 semiotics, a sign is generally defined as, ...something that stands for something else, to someone in some capacity. ...
Linguistics is the scientific study of human language. ...
Logic, from Classical Greek λόγος (logos), originally meaning the word, or what is spoken, (but coming to mean thought or reason) is most often said to be the study of criteria for the evaluation of arguments, although the exact definition of logic is a matter of controversy among philosophers. ...
Euclid, Greek mathematician, 3rd century BC, known today as the father of geometry; shown here in a detail of The School of Athens by Raphael. ...
In the main, semantics (from the Greek and in greek letters σημαντικός or in latin letters semantikós, or significant meaning, derived from sema, sign) is the study of meaning, in some sense of that term. ...
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In semiotics, a sign is generally defined as, ...something that stands for something else, to someone in some capacity. ...
In logic, the comprehension of an object is the totality of intensions, that is, attributes, characters, marks, properties, or qualities, that the object possesses, or else the totality of intensions that are pertinent to the context of a given discussion. ...
Intension refers to the meanings or characteristics encompassed by a given word. ...
Mathematics In mathematics, the extension of a mathematical concept is the set that is specified by that concept. Euclid, Greek mathematician, 3rd century BC, known today as the father of geometry; shown here in a detail of The School of Athens by Raphael. ...
This article is about sets in mathematics. ...
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, of course, 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. Partial plot of a function f. ...
In mathematics, an ordered pair is a collection of two objects such that one can be distinguished as the first element and the other as the second element (the first and second elements are also known as left and right projections). ...
Abstract algebra is the field of mathematics that studies algebraic structures, such as groups, rings, fields, modules, vector spaces, and algebras. ...
In mathematics, a group is a set, together with a binary operation, such as multiplication or addition, satisfying certain axioms, detailed below. ...
A forgetful functor is a type of functor in mathematics. ...
In axiomatic set theory and the branches of logic, mathematics, and computer science that use it, the axiom of extensionality, or axiom of extension, is one of the axioms of Zermelo-Fraenkel set theory. ...
This article or section is in need of attention from an expert on the subject. ...
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". Set theory is the mathematical theory of sets, which represent collections of abstract objects. ...
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. Computer science, or computing science, is the study of the theoretical foundations of information and computation and their implementation and application in computer systems. ...
The term database originated within the computer industry, though its meaning has been broadened by popular use,includes non-electronic databases within its definition. ...
The word schema comes from the Greek word σχήμα (skhēma) that means shape or more generally plan. ...
An object is fundamental concept in object-oriented programming. ...
Semantics In philosophical semantics or 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.) In the main, semantics (from the Greek and in greek letters σημαντικός or in latin letters semantikós, or significant meaning, derived from sema, sign) is the study of meaning, in some sense of that term. ...
Philosophy of language is the branch of philosophy that studies language. ...
The term monadic has multiple uses in mathematics: In category theory, an adjunction is monadic or tripleable if it is equivalent to the adjunction given by the Eilenberg-Moore algebras of its associated monad. ...
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 (by convention) as its logical value. So the extension of "Lassie is famous" is the logical value true, since Lassie is famous. In logic and mathematics, a logical value, also called a truth value, is a value indicating to what extent a proposition is true. ...
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.
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.) Plato and Aristotle, by Raphael (Stanza della Segnatura, Rome). ...
Possible Worlds is: Possible Worlds (play) a play by John Mighton Possible Worlds (poetry book) a book of poems by Peter Porter (poet) Possible Worlds (book) a book by J. B. S. Haldane This is a disambiguation page: a list of articles associated with the same title. ...
Sir Arthur Conan Doyle, DL (22 May 1859 – 7 July 1930) was a Scottish author most noted for his stories about the detective Sherlock Holmes, which are generally considered a major innovation in the field of crime fiction, and the adventures of Professor Challenger. ...
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. Free logic is a logic free of existential presuppositions. ...
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. General Semantics is a school of thought founded by Alfred Korzybski in about 1933 in response to his observations that most people had difficulty defining human and social discussions and problems and could almost never predictably resolve them into elements that were responsive to successful intervention or correction. ...
Intension refers to the meanings or characteristics encompassed by a given word. ...
In metaphysics, extension is the property of taking up space; see Extension (metaphysics). ...
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