Extensional
Encyclopedia
In philosophy of language
, a context in which a sub-sentential expression e appears is called extensional if and only if e can be replaced by an expression with the same extension and necessarily preserve truth-value. The extension
of a term is the set of objects that that term denotes.
Take the case of Clark Kent
, who is secretly Superman
. Suppose that Lois Lane
fell out of a window and Superman caught her. Thus the statement, "Clark Kent caught Lois Lane," is true because it has an extensional context. The names "Superman" and "Clark Kent" have the same extension, which is to say that they both refer to the same person, i.e., that superhero who is vulnerable to kryptonite
. Anybody that Superman caught, Clark Kent caught.
In opposition to extensional contexts are intensional contexts, where synonymous terms cannot be substituted in without potentially compromising the truth-value. Suppose that Lois Lane believes that Clark Kent will investigate a news story with her. The statement, "Lois Lane believes that Superman will investigate a news story with her," is false, even though Superman is Clark Kent. This is because 'believes' is typically an intensional context.
Philosophy of language
Philosophy of language is the reasoned inquiry into the nature, origins, and usage of language. As a topic, the philosophy of language for analytic philosophers is concerned with four central problems: the nature of meaning, language use, language cognition, and the relationship between language...
, a context in which a sub-sentential expression e appears is called extensional if and only if e can be replaced by an expression with the same extension and necessarily preserve truth-value. The extension
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...
of a term is the set of objects that that term denotes.
Take the case of Clark Kent
Clark Kent
Clark Kent is a fictional character created by Jerry Siegel and Joe Shuster. Appearing regularly in stories published by DC Comics, he debuted in Action Comics #1 and serves as the civilian and secret identity of the superhero Superman....
, who is secretly Superman
Superman
Superman is a fictional comic book superhero appearing in publications by DC Comics, widely considered to be an American cultural icon. Created by American writer Jerry Siegel and Canadian-born American artist Joe Shuster in 1932 while both were living in Cleveland, Ohio, and sold to Detective...
. Suppose that Lois Lane
Lois Lane
Lois Lane is a fictional character, the primary love interest of Superman in the comic books of DC Comics. Created by writer Jerry Siegel and artist Joe Shuster, she first appeared in Action Comics #1 ....
fell out of a window and Superman caught her. Thus the statement, "Clark Kent caught Lois Lane," is true because it has an extensional context. The names "Superman" and "Clark Kent" have the same extension, which is to say that they both refer to the same person, i.e., that superhero who is vulnerable to kryptonite
Kryptonite
Kryptonite is a fictional material from the Superman mythos —the ore form of a radioactive element from Superman's home planet of Krypton. It is famous for being the ultimate physical weakness of Superman, and the word kryptonite has since become synonymous with an Achilles' heel —the one weakness...
. Anybody that Superman caught, Clark Kent caught.
In opposition to extensional contexts are intensional contexts, where synonymous terms cannot be substituted in without potentially compromising the truth-value. Suppose that Lois Lane believes that Clark Kent will investigate a news story with her. The statement, "Lois Lane believes that Superman will investigate a news story with her," is false, even though Superman is Clark Kent. This is because 'believes' is typically an intensional context.
See also
- Extension (semantics)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...
- 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"...
- Extensional definitionExtensional definitionAn 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....