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.
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.