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.
(2) As a second fact: the increase and decrease is not a mathematical one. That is, by doubling the extension the 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 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.