Extensional and intensional definitions in the context of Definition

⭐ Core Definition: Extensional and intensional definitions

In logic, extensional and intensional definitions are two key ways in which the objects, concepts, or referents a term refers to can be defined. They give meaning or denotation to a term.An intensional definition gives meaning to a term by specifying necessary and sufficient conditions for when the term should be used. An extensional definition gives meaning to a term by specifying every object that falls under the definition of the term in question.

For example, in set theory one would extensionally define the set of square numbers as {0, 1, 4, 9, 16, $\dots$ }, while an intensional definition of the set of the square numbers could be { $x\mid x$ is the square of an integer}.

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⭐ Core Definition: Extensional and intensional definitions
Extensional and intensional definitions in the context of Class (philosophy)
Extensional and intensional definitions in the context of Genus-differentia

Extensional and intensional definitions in the context of Class (philosophy)

A class is a collection whose members either fall under a predicate or are classified by a rule. Hence, while a set can be extensionally defined only by its elements, a class has also an intensional dimension that unites its members. When the term 'class' is applied so that it includes those sets whose elements are intended to be collected without a common predicate or rule, the distinction can be indicated by calling such sets "improper class."

Philosophers sometimes distinguish classes from types and kinds. The class of human beings is discussed, as well as the type (or natural kind), human being, or humanity. While both are typically treated as abstract objects and not different categories of being, types not classes are usually treated as universals. Whether natural kinds ought to be considered universals is vexed; see natural kind.

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Extensional and intensional definitions in the context of Genus-differentia

A genus–differentia definition is a type of intensional definition, and it is composed of two parts:

a genus (or family): An existing definition that serves as a portion of the new definition; all definitions with the same genus are considered members of that genus.
the differentia: The portion of the definition that is not provided by the genus.

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Extensional and intensional definitions in the context of Definition

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⭐ Core Definition: Extensional and intensional definitions

Extensional and intensional definitions in the context of Class (philosophy)

Extensional and intensional definitions in the context of Genus-differentia