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An extensional definition gives meaning to a term by specifying its extension, that is, every object that falls under the definition of the 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 extensional statement is a non-intensional statement. Substitution of co-extensive expressions into it always preserves logical value. A language is intensional if it contains intensional statements, and extensional otherwise. All natural languages are intensional. [4]
Intensional logic is an approach to predicate logic that extends first-order logic, which has quantifiers that range over the individuals of a universe , by additional quantifiers that range over terms that may have such individuals as their value .
In logic, extensionality, or extensional equality, refers to principles that judge objects to be equal if they have the same external properties. It stands in contrast to the concept of intensionality , which is concerned with whether the internal definitions of objects are the same.
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 — 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 the ideas, properties, or corresponding signs that are implied ...
See also extensionality, and also intensional definition versus extensional definition; Intensional logic embraces the study of intensional languages: at least one of their functors is intensional. It can be contrasted to extensional logic; Intensional fallacy, committed when one makes an illicit use of Leibniz's law in an argument; See also ...
Editor’s note: Before beginning any new exercise program, consult your doctor.Stop immediately if you experience pain. As you head into the gym, you likely already have a workout plan in mind ...
According to an extensional definition, they are abstract groups, sets, or collections of objects. According to an intensional definition, they are abstract objects that are defined by values of aspects that are constraints for being member of the class. The first definition of class results in ontologies in which a class is a subclass of ...