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Extensional definition
 
 
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An extensional definition of a concept or term formulates its meaning by specifying its extension
Extension (semantics)

In any of several studies that treat the use of sign s, 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 is, every object
Object (philosophy)

In philosophy, an object is a thing, an entity, or a being. This may be taken in several senses.In its weakest sense, the word object is the most all-purpose of nouns, and can replace a noun in any sentence at all....
 that falls under the definition
Definition

A definition is a statement of the Meaning of a word or phrase. The term to be defined is known as the definiendum . The words which define it are known as the definiens ....
 of the concept or 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.






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An extensional definition of a concept or term formulates its meaning by specifying its extension
Extension (semantics)

In any of several studies that treat the use of sign s, 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 is, every object
Object (philosophy)

In philosophy, an object is a thing, an entity, or a being. This may be taken in several senses.In its weakest sense, the word object is the most all-purpose of nouns, and can replace a noun in any sentence at all....
 that falls under the definition
Definition

A definition is a statement of the Meaning of a word or phrase. The term to be defined is known as the definiendum . The words which define it are known as the definiens ....
 of the concept or 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. An explicit listing of the extension, which is only possible for finite sets and only practical for relatively small sets, is called an enumerative definition
Enumerative definition

An enumerative definition of a concept or term is a special type of extensional definition that gives an explicit and exhaustive listing of all the object s that fall under the concept or term in question....
.

Extensional definitions are used when listing examples would give more applicable information than other types of definition
Definition

A definition is a statement of the Meaning of a word or phrase. The term to be defined is known as the definiendum . The words which define it are known as the definiens ....
, and where listing the members of a set
Set

A set is a collection of distinct objects, considered as an object in its own right. Sets are one of the most fundamental concepts in mathematics....
 tells the questioner enough about the nature of that set.

This is similar to an ostensive definition
Ostensive definition

An ostensive definition conveys the Meaning of a term by pointing out examples. This type of definition is often used where the term is difficult to define verbally, either because the words will not be understood or because of the nature of the term ....
, in which one or more members of a set (but not necessarily all) are pointed out as examples. The opposite approach is the intensional definition
Intensional definition

In logic and mathematics, an intensional definition gives the Meaning of a term by specifying all the properties required to come to that definition, that is, the necessary and sufficient conditions for belonging to the set being defined....
, which defines by listing properties that a thing must have in order to be part of the set captured by the definition.

See also

  • Extensional context
  • Extension (predicate logic)
    Extension (predicate logic)

    The extension of a predicate a truth-valued function is the Set of tuples of values that, used as arguments, satisfy the predicate. Such a set of tuples is a relation ....