Extensional (from lat. Extentio - extension, space, distribution) is a term of semantics that denotes the volume of a concept , that is, a set of objects that can be called a given linguistic unit (category). For example, the extensional (category) of the concept of “man” includes all objects that have the property of “being a man” (Socrates is a man, a philosopher is a man, a thinking creature is a man, etc.).
Definition
The concept of extensional was introduced by the Austrian logician and philosopher R. Karnap to analyze the meaning of linguistic expressions. T. n. the method of intensions and extensions is a modification and further development of the semantic concept of the German mathematician and logician G. Frege .
The statement "Socrates is a man" can be interpreted in two ways. The statement can be considered as the fact that Socrates has some property of “being a man” (Socrates is a man). At the same time, the statement can be considered as the fact that the individual Socrates is included in the class of people (Socrates is a person).
An example shows that a predicate (in this case, “man”) can mean both possessing a property (Socrates is a man) and belonging to a class (Socrates is a man). The class denoted by the predicate expression is called the actual extension of this expression. That is, in this case, "Socrates" is included in the extension of the concept of "man."
Thus, the extensional is opposed to the intensional, which denotes the totality of the properties of a concept / term, which actually form the concept / term in the presentation. That is, more precisely, the extensional of a concept should be understood as a set of objects satisfying the intensional of a concept.
A special case of an extension is the extension of a proper name . The object designated by this name is considered to be such a single extensional.
Extensional and Intensional Contexts
The concepts of intensional and extensional are the basis for distinguishing the so-called. intensional and extensional contexts.
An intensional context is the set of statements in which the replacement of only intensionally equivalent expressions is permissible (that is, both intensional and extensional expressions are important to it). Extensional context refers to many statements in which only extensional equivalent language expressions are permissible (that is, only extensional expressions are important to it).
For example, the extension of the term “man” is a class of people. The predicates “creature capable of thinking” and “creature having limbs” will be extensional equivalent, since both can be denoted by the term “man”. The predicates “a creature capable of thinking” and “a creature capable of producing tools” are not only extensional, but also intensional equivalent, since both can be denoted by the term “man”, and both express the property that forms the term “man”.
Distinguishing between such contexts is important when defining a concept. For example, from the definition of “brothers in mind” as 1) “creatures capable of thinking” 2) “creatures with limbs” 3) “creatures capable of producing tools” - definition 2 should be deleted, since it is not necessary that the brothers reason can be humanoids.
Literature
- Linguistic Encyclopedic Dictionary. M .: Soviet Encyclopedia, 1989.
- Ivin A., Nikiforov A. Dictionary of logic. M., 1998.
- Kemerov V. Philosophical Encyclopedia. Publishing House "Panprint", 1998.