Extensional and intensional definitions: Difference between revisions

Revision as of 21:09, 25 July 2022

Revision as of 14:36, 26 September 2022

Line 15:

[[Genus–differentia definition|Definition by genus and difference]], in which something is defined by first stating the broad category it belongs to and then distinguished by specific properties, is a type of intensional definition. As the name might suggest, this is the type of definition used in [[Linnaean taxonomy]] to categorize living things, but is by no means restricted to [[biology]]. Suppose one defines a miniskirt as "a skirt with a hemline above the knee". It has been assigned to a ''genus'', or larger class of items: it is a type of skirt. Then, we've described the ''differentia'', the specific properties that make it its own sub-type: it has a hemline above the knee.

elmo p0rn

An intensional definition may also consist of rules or sets of [[axiom]]s that define a [[set (mathematics)|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"—always generates members of the set of square numbers, no matter which integer one chooses, and for any square number, there is an integer that was multiplied by itself to get it.

Similarly, an intensional definition of a game, such as [[chess]], would be the rules of the game; any game played by those rules must be a game of chess, and any game properly called a game of chess must have been played by those rules.