Intensional and extensional definitions

Examples of intensional definitions:

• "Man is a featherless biped"
• "Man is an animal"
• "Even numbers divide by 2, with a null remainder"
• "Extensional definition consists in naming all or a certain number of individuals of a set, and adding 'etc.' if necessary" (this constitutes an intensional definition of "extensional definition")

Examples of extensional definitions (the paragraph above constitutes a extensional definition of "intensional definition"):

• "Man is Alfred, Marie, Albert, Richard, Louis, etc."
• "Even numbers are 0, 2, 4, 6, 8, 10, etc., but not 1, 3, 5, 7, 9, etc."

The paragraph above constitutes a extensional definition of "extensional definition".

Extensional orientation

In mathematics, extensional orientation started immediately as a consequence of the structure of the language used. By construction, mathematics does not tolerate any exception to its theorems: one single counter-example is sufficient to prove that a theorem is wrong. On another side, no example can prove that a theorem is right, except if all cases were examined.

In physics, extensional orientation started in fact with Galileo, the first experimental physicist. We know the price he paid for developing this orientation. A second step was reached with Einstein's theories, by the rejection of the formulations of 'absolute space' and 'absolute time'. Space-time replaced these old elementalistic formulations.

In everyday life, an extensional orientation improves the way we perceive the uniqueness of events: it keeps us, for example, from reacting to a present event as if it were about a past event, the basic mechanism of neurosis. It also allows us to broaden our point of view, by leaving room for the un-said, the unknown, etc.

General semantics proposes a certain number of tools promoting this orientation.