In the foregoing scheme _building_ refers to a greater number of objects than _barn_, hence the line under _extension_ representing _building_ should be longer than the line for _barn_. Likewise _structure_, referring to a greater number of objects than _building_, is represented by a longer line. Thus when the series is viewed from top to bottom a gradual increase in extension is noted. Giving attention to the intensional use of the series we note that _building_ has fewer qualities than _barn_, _structure_ fewer than _building_ and _object_ fewer than _structure_. Therefore, from top to bottom, the intension of the terms gradually decreases. The variation may be made still more apparent if triangles are used, one triangle being placed upon the other, vertex to base, like the following: Illustration: ( ‡ Intension and Extension ) “Biped” is written near the base or in the broadest part of the extension triangle because it denotes the greatest number of objects, and is, therefore, broadest in extension. “Man” occupies a narrower part of the extension triangle because it refers to fewer objects or is narrower in extension than “biped.” “Arnold” occupies the narrowest part of the extension triangle because it is the narrowest in extension. On the other hand “Arnold” occupies the broadest part of the intension triangle because intensionally it possesses more qualities than the others, while “biped,” having the least depth in intension or possessing the fewest qualities, occupies the narrowest portion of the intension triangle. =7. OUTLINE.= THE EXTENSION AND INTENSION OF TERMS. 1. Two-fold Function of Connotative Terms. 2. Extension and Intension Defined. 3. Extended Comparison of Extension and Intension. 4. A List of Connotative Terms used in Extension and Intension. 5. Other Forms of Expression for Extension and Intension. 6. Law of Variation in Extension and Intension. 6a. Two Important Facts in the Law of Variation. 6b. The Law of Variation Diagrammatically Illustrated. =8. SUMMARY.= 1. Connotative terms are used in a two-fold sense: first, to denote objects; second, to imply qualities. 2. A term is used in extension when it is employed with reference to the objects for which the term stands. A term is used in intension when it is employed with reference to the qualities for which the term stands. 3. The answer to either of the following questions will lead one to use any term in extension: First, what are the kinds? or second, to what objects may the term be applied? The answer to either of the following questions will lead to the use of any term in intension: First, what does it mean? or second, what are the qualities? 4. To illustrate extension and intension it is best to use the class-names in every day speech. 5. The word denotation is commonly used for extension and connotation for intension.