Extensional Representation

Extensional Representation

The extension of a representation defines things in a different way. An extensional definition defines by enumerating or listing everything that falls under that definition -- an extensional definition of "bachelor" would be a listing of all the unmarried men in the world. Extensional definitions are frequently represented by sets. For example, in the case of our bachelor example, the extensional definition of bachelor would be the set of all bachelors in the world. If we simply listed all the bachelors in the world, this would be an indirect extensional representation. If we rounded up every bachelor in the world and put them all in a large room together, and ensured that the room contained no non-bachelors, then the contents of the room would be the direct extensional representation of bachelors.

Differences between Extensional and Intensional Representation
Intensional definitions are best used when something has a clearly-defined set of properties, and it works 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 category and differentia, in which something is defined by first stating the broad category it belongs to (i.e., its common or shared properties) and then distinguished by its differentia (i.e., it’s private or unshared 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 it is by no means restricted to biology. Suppose we define a miniskirt as "a skirt with a hemline above the knee." We have assigned it to a genus, or larger class of items: it is a type of skirt. Then, we have described the differentia, the specific properties that make it its own sub-type: it has a hemline above the knee.