Extensional Definition

An Extensional Definition is a Definition of a Concept Class by means of presenting a set that contains some or all of the Member Concepts.

• AKA: Denotative Definition.
• Context:
  • It can be a complete set or a Partial Set of Examples (e.g. Training Examples).
  • It can make use of the Extension Of a Variable.
  • …
• Example(s):
  • The characters in the English Alphabet = {a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,t,u,v,w,x,y,z}.
  • The set of all positive integers less than 10 = {1,2,3,4,5,6,7,8,9}.
• See: Intensional Definition.

---

---

References

• (Wikipedia, 2009) ⇒ http://en.wikipedia.org/wiki/Definiendum#Intension_and_extension
  • An intensional definition, also called a connotative definition, specifies the necessary and sufficient conditions for a thing being a member of a specific set. 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.
• Misc
  • However, can’t we imagine some definition by enumeration of all instances? This is called the extension of a notion, and the corresponding definition is an extensional definition.
• Misc2
  • 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 called an 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.

2002

• (Cruse, 2002) ⇒ D. Alan Cruse. (2002). “Hyponymy and its Varieties.” In: (Green et al., 2002).
  • Taking a logical approach, we can define hyponymy either extensionally or intensionally.
  • One extensional definition is the following, after Cann (1994), but modified to exclude synonymy:
    • X is a hyponym of Y iff there exists a meaning postulate relation X' and Y' of the form:
    • ∀x[X'(x) → Y'(x)], but none of the form: ∀x[Y'(x) → X'(x)].
  • (Here, X' and Y' are the logical constants corresponding to the lexical items X and Y, and the definition states, effectively, that for X to be a hyponym of Y, the extension of X' must be included in the extension of Y'.)
  • An example of an intensional definition is the following:
    • X is a hyponym of Y iff F(X) entails, but is not entailed by F(Y).

---