Formerly the words extension and intension were applied to concepts while denotation and connotation were applied to terms representing the concepts, but now the words are interchangeable. Denotation, the noun, and denote, the verb, signify, etymologically, a marking off. To denote is to mark off or indicate the objects or classes of objects for which the term stands. Connotation, the noun, and connote, the verb, signify to mark along with. To connote is to mark along with the object, its attributes.

The terms which should be remembered are

extensionandintension
oror
denotationconnotation

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.

6a. TWO IMPORTANT FACTS IN THE LAW OF VARIATION.

In studying the law of variation two facts are especially evident. (1) The law applies only to a series of terms representing notions of the same family. The extension and intension of “text book,” for example, could not be compared with the extension and intension of “house” as they belong to a different class of words, the genus of text book being book, while the genus of house is building.

To illustrate the law of variation, determine upon any class name, then think of its proximate genus (the next higher-up class to which it belongs). Continue this till the series is sufficiently complete to illustrate the law. Or proceed in the opposite direction. That is, after selecting the class name think of the next lower term in the class and thus continue till series is complete. Illustration: The class name man is determined upon; the proximate genus of man is biped, the proximate genus of biped is animal, and so on. Or thinking downward: a proximate species of man is white man, of white man. European, etc.