Thus the series:
animal
biped
man
white man
European
(2) As a second fact: the increase and decrease is not a mathematical one. That is, by doubling the extensionthe intension is not halved. Or if the intension is decreased by one quality the extension is not necessarily increased by one object. Thus “man” stands for one billion seven hundred million beings or objects. Decrease the intension of “man” by the one quality of rationality and the extension would include all bipeds—many billion objects.
6b. THE LAW OF VARIATION DIAGRAMMATICALLY ILLUSTRATED.
In a general way lines may be used to represent the variation in extension and intension. For example: we may let a line an inch long represent the extension of man, one two inches long represent the extension of biped, three inches long represent the extension of animal, etc. While on the other hand, if a line an inch long represents the intension of man, a line one-half inch long may be used to represent the intension of biped, one a quarter of an inch long to represent the intension of animal, etc. The following illustrates this scheme in connection with another series of words:
| Extension | Intension | |
| —— | barn | ———————— |
| ———— | building | —————— |
| —————— | structure | ———— |
| ———————— | object | —— |
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 longerline. 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:
“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.