An intensional definition gives meaning to a term by specifying necessary and sufficient conditions for when the term should be used. In the case of
nouns, this is equivalent to specifying the
properties that an
object needs to have in order to be counted as a
referent of the term. For example, an intensional definition of the word "bachelor" is "unmarried man". This definition is valid because being an unmarried man is both a necessary condition and a sufficient condition for being a bachelor: it is necessary because one cannot be a bachelor without being an unmarried man, and it is sufficient because 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 terms that have too many referents to list in an extensional definition. It is impossible to give an extensional definition for a term with an
infinite set of referents, but an intensional one can often be stated concisely – there are infinitely many
even numbers, impossible to list, but the term "even numbers" can be defined easily 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. 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"—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. ==Extensional definition==