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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.
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]
The extensional definition of function equality, discussed above, is commonly used in mathematics. A similar extensional definition is usually employed for relations : two relations are said to be equal if they have the same extensions .
Extensional definition, a definition that enumerates every individual a term applies to; Extensionality; Other uses. Extension of a function, defined on a larger domain;
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 ...
Extensionalism, in the philosophy of language, in logic and semantics, is the view that all languages or at least all scientific languages should be extensional.It has been described as the default option for the scientism in the nineteenth century and the result of the application of empiricistic inductive methodology to the problem of semantics.
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In mathematical logic, more specifically in the proof theory of first-order theories, extensions by definitions formalize the introduction of new symbols by means of a definition. For example, it is common in naive set theory to introduce a symbol ∅ {\displaystyle \emptyset } for the set that has no member.