Intensional and extensional
"It is common sense to take a method and try it. If it fails, admit it frankly and try another. But above all, try something."
— Franklin D. Roosevelt, quoted in Nathan Miller's F.D.R.: An Intimate History, p. 263, Doubleday & Co.(1983).

"Aristotle could have avoided the mistake of thinking that women have fewer teeth than men, by the simple device of asking Mrs. Aristotle to keep her mouth open while he counted."
— Bertrand Russell, “An Outline of Intellectual Rubbish,” Unpopular Essays (1950).

"I have not failed. I've just found 10,000 ways that won't work."
— Thomas Edison

"A man who carries a cat by the tail learns something he can learn in no other way."
— Mark Twain

"Example isn't another way to teach, it is the only way to teach."
— Albert Einstein

"The value of an idea lies in the using of it."
— Thomas A. Edison

"Few things are harder put up with than the annoyance of a good example."
— Mark Twain, Pudd’nhead Wilson, ch. 19, “Pudd’nhead Wilson’s Calendar,” (1894).

"Genius is one per cent inspiration, ninety-nine per cent perspiration."
— Thomas Alva Edison, Remark by Edison c. 1903. Harper’s (New York, Sept. 1932).

"Experience: that most brutal of teachers. But you learn, my God you learn."
— C. S. Lewis

"Principally I hate and detest that animal called man; although I heartily love John, Peter, Thomas, and so forth."
— Jonathan Swift, letter, Sept. 29, 1725, to Alexander Pope. The Correspondence of Jonathan Swift, vol. 3, ed. H. Williams (1963).

 Intensional and extensional definitions 

Examples of intensional definitions:


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


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 general proposition is false. On another side, no example can prove that a general proposition 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.

 Typical errors about Intensional and Extensional 

The most usual error can be stated as "intensional is bad, extensional is good." As with observations and inferences, both are useful and needed. It happens that, with the Aristotelian system, we are more trained in intensional orientation than in extensional orientation. The practice of general semantics and extensional devices should balance that tendency and train us more in the extensional orientation.

Another rare blunder is to consider that "intensional is inside my head, extensional is outside my head," as if what happen inside one's head was only 'abstract.' Of course it is not and we have some vivid PET imagery to prove it. The error was made in a notorious French book listed in the French bibliography.

© ESGS, 2002