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An intensional definition may also consist of rules or sets of axioms that define a set by describing a procedure for generating all of its members. For example, an intensional definition of square number can be "any number that can be expressed as some integer multiplied by itself". The rule—"take an integer and multiply it by itself ...
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 .
A language is intensional if it contains intensional statements, and extensional otherwise. All natural languages are intensional. [4] The only extensional languages are artificially constructed languages used in mathematical logic or for other special purposes and small fragments of natural languages.
An intensional definition, also called a connotative definition, specifies the necessary and sufficient conditions for a thing to be a member of a specific set. [3] Any definition that attempts to set out the essence of something, such as that by genus and differentia, is an intensional definition.
in philosophy of mind: an intensional state is a state which has a propositional content; in mathematical logic: see intensional statement. 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 ...
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.
A definition that provides a means for replacing each occurrence of the definiendum with an appropriate instance of the definiens. [131] [132] Contrast implicit definition. explosion The principle in logic that from a contradiction, any statement can be proven, related to the principle of ex falso quodlibet. exportation
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 ...