6. LAW OF VARIATION IN EXTENSION AND INTENSION.
It has been noted that the intension of a term has reference to its qualities while extension considers its application to various objects. It may be wise to experiment with the extension and the intension of certain terms as types with a view of ascertaining how the two ideas are related to each other. For the sake of definiteness let us make use of the following scheme:
| I. | ||||
|---|---|---|---|---|
| Intensional | Extensional | |||
(1) four sides (2) parallel sides (3) equal sides (4) right angles |  | common qualities of |  | (1) squares |
(1) four sides (2) parallel sides (3) equal sides | | common qualities of | | (1) squares (2) rhombs |
(1) four sides (2) parallel sides | | common qualities of | | (1) squares (2) rhombs (3) rectangles (4) rhomboids |
(1) four sides | | common qualities of | | (1) squares (2) rhombs (3) rectangles (4) rhomboids (5) trapezoids (6) trapeziums |
| II. | ||||
(1) heavenly body | | common qualities of | | (1) nebulae (2) fixed stars (3) sun (4) comets (5) meteors (6) moon |
(1) heavenly body (2) self-luminous | | common qualities of | | (1) nebulae (2) fixed stars (3) sun (4) comets |
(1) heavenly body (2) self-luminous (3) fixed | | common qualities of | | (1) nebulae (2) fixed stars (3) sun |
(1) heavenly body (2) self-luminous (3) fixed (4) twinkle | | common qualities of | | (1) nebulae (2) fixed stars |
(1) heavenly body (2) self-luminous (3) fixed (4) twinkle (5) foggy | | common qualities of | | (1) nebulae |
In considering the first illustration we observe that as the number of qualities is decreased, the number of objects increases. While in the second example as the qualities are increased, the number of objects decreases. It would appear from this that the intension and extension of a term are inversely related to each other. As the one increases the other decreases and vice versa. It is customary to state this relation in the form of a law known as the law of variation. “As the intension of a term is increased its extension is decreased and vice versa,” or the extension and intension of a term vary in an inverse ratio to each other. To further illustrate: this book refers to a large number of objects; add to the qualities of book those of text book and the application is much reduced. In other words as we increase the intension, the extension is diminished. Increase the intension further by adding the quality English text book and the extension becomes still less.