Extensional definition
Encyclopedia
An extensional definition of a concept or term formulates its meaning by specifying its extension
, that is, every object
that falls under the definition
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 a type of enumerative definition
.
Extensional definitions are used when listing examples would give more applicable information than other types of definition
, and where listing the members of a set tells the questioner enough about the nature of that set.
This is similar to an ostensive definition
, 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
, which defines by listing properties that a thing must have in order to be part of the set captured by the definition.
Extension (semantics)
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...
, that is, every object
Object (philosophy)
An object in philosophy is a technical term often used in contrast to the term subject. Consciousness is a state of cognition that includes the subject, which can never be doubted as only it can be the one who doubts, and some object or objects that may or may not have real existence without...
that falls under the definition
Definition
A definition is a passage that explains the meaning of a term , or a type of thing. The term to be defined is the definiendum. A term may have many different senses or meanings...
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 a type of 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 objects 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 passage that explains the meaning of a term , or a type of thing. The term to be defined is the definiendum. A term may have many different senses or meanings...
, and where listing the members of a set 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 predicatea truth-valued functionis the set of tuples of values that, used as arguments, satisfy the predicate. Such a set of tuples is a relation.For example the statement "d2 is the weekday following d1"...
- Intensional definitionIntensional definitionIn 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....