What does extensional context mean?
Definitions for extensional context
ex·ten·sional con·text
This dictionary definitions page includes all the possible meanings, example usage and translations of the word extensional context.
Wikipedia
Extensional context
In any of several fields of study that treat the use of signs — for example, in linguistics, logic, mathematics, semantics, semiotics, and philosophy of language — an extensional context (or transparent context) is a syntactic environment in which a sub-sentential expression e can be replaced by an expression with the same extension and without affecting the truth-value of the sentence as a whole. Extensional contexts are contrasted with opaque contexts where truth-preserving substitutions are not possible. 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 sentence "Superman caught Lois Lane" is true. Because this sentence is an extensional context, the sentence "Clark Kent caught Lois Lane" is also true. Anybody that Superman caught, Clark Kent caught. In opposition to extensional contexts are intensional contexts (which can involve modal operators and modal logic), where terms cannot be substituted without potentially compromising the truth-value. Suppose that Lois Lane believes that Clark Kent will investigate a news story with her. Thus, the sentence "Lois Lane believes that Clark Kent will investigate a news story with her" is true. However, the statement, "Lois Lane believes that Superman will investigate a news story with her," is false. This is because 'believes' typically induces an intensional context. Lois Lane doesn't believe that Superman is Clark Kent and the propositional attitude "believe" induces an intensional context, so the substitution alters the meaning of the original sentence.
Wikidata
Extensional context
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.
Numerology
Chaldean Numerology
The numerical value of extensional context in Chaldean Numerology is: 5
Pythagorean Numerology
The numerical value of extensional context in Pythagorean Numerology is: 5
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"extensional context." Definitions.net. STANDS4 LLC, 2024. Web. 27 Apr. 2024. <https://www.definitions.net/definition/extensional+context>.
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