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- Intensional_definition abstract "In logic and mathematics, an 'intensional definition' gives the meaning of a term by specifying all the properties required to come to that definition, that is, the necessary and sufficient conditions for belonging to the set being defined.For example, an intensional definition of bachelor is \"unmarried man\". Being an unmarried man is an essential property of something referred to as a bachelor. It is a necessary condition: one cannot be a bachelor without being an unmarried man. It is also a sufficient condition: any unmarried man is a bachelor.This is the opposite approach to the extensional definition, which defines by listing everything that falls under that definition – an extensional definition of bachelor would be a listing of all the unmarried men in the world.As becomes clear, intensional definitions are best used when something has a clearly defined set of properties, and they work well for sets that are too large to list in an extensional definition. It is impossible to give an extensional definition for an infinite set, but an intensional one can often be stated concisely – there is an infinite number of even numbers, impossible to list, but they can be defined by saying that even numbers are integer multiples of two.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.Intensional definition also applies to rules or sets of axioms that generate all members of the set being defined. 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.".
- Intensional_definition wikiPageID "794036".
- Intensional_definition wikiPageLength "3276".
- Intensional_definition wikiPageOutDegree "26".
- Intensional_definition wikiPageRevisionID "667160827".
- Intensional_definition wikiPageWikiLink Axiom.
- Intensional_definition wikiPageWikiLink Biology.
- Intensional_definition wikiPageWikiLink Category:Definition.
- Intensional_definition wikiPageWikiLink Category:Necessity.
- Intensional_definition wikiPageWikiLink Chess.
- Intensional_definition wikiPageWikiLink Comprehension_(logic).
- Intensional_definition wikiPageWikiLink Definition.
- Intensional_definition wikiPageWikiLink Extension_(semantics).
- Intensional_definition wikiPageWikiLink Extensional_definition.
- Intensional_definition wikiPageWikiLink Extensionality.
- Intensional_definition wikiPageWikiLink Genus–differentia_definition.
- Intensional_definition wikiPageWikiLink Infinity.
- Intensional_definition wikiPageWikiLink Integer.
- Intensional_definition wikiPageWikiLink Intension.
- Intensional_definition wikiPageWikiLink Linnaean_taxonomy.
- Intensional_definition wikiPageWikiLink Logic.
- Intensional_definition wikiPageWikiLink Mathematics.
- Intensional_definition wikiPageWikiLink Meaning_(linguistics).
- Intensional_definition wikiPageWikiLink Necessity_and_sufficiency.
- Intensional_definition wikiPageWikiLink Ostensive_definition.
- Intensional_definition wikiPageWikiLink Parity_(mathematics).
- Intensional_definition wikiPageWikiLink Set_(mathematics).
- Intensional_definition wikiPageWikiLink Square_number.
- Intensional_definition wikiPageWikiLinkText "Intensional definition".
- Intensional_definition wikiPageWikiLinkText "defined".
- Intensional_definition wikiPageWikiLinkText "definition".
- Intensional_definition wikiPageWikiLinkText "intension".
- Intensional_definition wikiPageWikiLinkText "intensional definition".
- Intensional_definition wikiPageWikiLinkText "intensional".
- Intensional_definition wikiPageUsesTemplate Template:Defining.
- Intensional_definition wikiPageUsesTemplate Template:Reflist.
- Intensional_definition subject Category:Definition.
- Intensional_definition subject Category:Necessity.
- Intensional_definition type Concept.
- Intensional_definition comment "In logic and mathematics, an 'intensional definition' gives the meaning of a term by specifying all the properties required to come to that definition, that is, the necessary and sufficient conditions for belonging to the set being defined.For example, an intensional definition of bachelor is \"unmarried man\". Being an unmarried man is an essential property of something referred to as a bachelor. It is a necessary condition: one cannot be a bachelor without being an unmarried man.".
- Intensional_definition label "Intensional definition".
- Intensional_definition sameAs Q1026899.
- Intensional_definition sameAs Intensión.
- Intensional_definition sameAs تعریف_معنایی.
- Intensional_definition sameAs m.03ckrx.
- Intensional_definition sameAs Q1026899.
- Intensional_definition sameAs 描述法_(集合论).
- Intensional_definition wasDerivedFrom Intensional_definition?oldid=667160827.
- Intensional_definition isPrimaryTopicOf Intensional_definition.