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An extensional definition gives meaning to a term by specifying its extension, that is, every object that falls under the definition of the term in question.. For example, an extensional definition of the term "nation of the world" might be given by listing all of the nations of the world, or by giving some other means of recognizing the members of the corresponding class.
A language is intensional if it contains intensional statements, and extensional otherwise. All natural languages are intensional. [4] The only extensional languages are artificially constructed languages used in mathematical logic or for other special purposes and small fragments of natural languages.
Any definition that attempts to set out the essence of something, such as that by genus and differentia, is an intensional definition. An extensional definition, also called a denotative definition, of a concept or term specifies its extension. It is a list naming every object that is a member of a specific set. [3]
It is typical (e.g., in university logic texts) to distinguish a number of different kinds and techniques of definition, including dictionary or lexical definition, intensional definition, extensional definition, ostensive definition, stipulative definition, operational definition, theoretical definition, persuasive definition, and definition ...
See also extensionality, and also intensional definition versus extensional definition; Intensional logic embraces the study of intensional languages: at least one of their functors is intensional. It can be contrasted to extensional logic; Intensional fallacy, committed when one makes an illicit use of Leibniz's law in an argument; See also ...
According to an extensional definition, they are abstract groups, sets, or collections of objects. According to an intensional definition, they are abstract objects that are defined by values of aspects that are constraints for being member of the class. The first definition of class results in ontologies in which a class is a subclass of ...
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 ...
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 — an extensional context (or transparent context) is a syntactic environment in which a sub-sentential expression e can be replaced by an expression with the same extension and without affecting the truth-value of the sentence as ...