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As we have seen, a certain specified energy in a given form of activity produces individual triangles. The number of triangles thus produced form the whole, and the individual triangles are the parts. The producing activity, the common nature, of the individuals is called the content of the class, or general notion; while the number of individuals thus produced and thus unified is called the extent of the class, or general notion. Thus the content of a general idea is the sum of attributes common to a number of individuals, whose sum forms the extent of the idea. The content of the class quadruped is the sum of the attributes, sensation, voluntary motion, vertebral structure, peculiar nervous and circulatory system, quadrupedal, etc., including whatever else may be found in each animal of that class. The number of animals containing this sum of common attributes forms the extent of the class quadruped. The mind, in thinking the content of a class, must at the same time think the individuals in which the content finds its concrete being, — must think the extent of the class.
The content of a class determines its extent. One bears an inverse ratio to the other. If the class animal has for its content the sum of the two attributes sensation and voluntary motion, and a third attribute be added, say warm-blooded, thus increasing the content, the extent is decreased by having to drop from the idea animal the cold blooded animals. With each addition of a new attribute to the content, there is a subtraction from its extent, — a subtraction of the number not having the attribute added. Continuing this process the richest content would be reached in the least extent, which is the individual. The content thus determines the class whole or the class unity, and the first step in exposition corresponds to that in description and narration, — namely, the presentation of the theme as a whole by means of its attributive content.
THE CONTENT OF THE THEME.
The content of a general idea consists of two relations —the universal and the particular, or its likenesses to and its differences from other ideas.
If we take from this particular book all the attributes it has in common with other books, or in common with any other class of objects, we have destroyed our thought of the book. If we should take from the class book all the attributes common to books only, our thought of book is likewise destroyed. Again, if we should take from this particular book all the attributes peculiar to it, or from the class book all the attributes peculiar to it as a class, we have destroyed our thought of this book and the class book. Thus every object or idea has its being in the union of the two relations of particular and universal. Therefore, exposition, in presenting the content of a class, or general idea, must do so through these two relations. These two relations are formally presented by the process of
Definition. – Definition is the process of presenting to another mind the content of a class by a statement of the universal and the particular truth of that class.
The universal truth is presented in definition by referring the class to be defined to the known larger class of which it is a part. Whenever an object or a class is said to be in a larger class, however small the larger class, a connection is established with the universe. To say that a noun is a substantive is to say that it is the arbitrary expression of an object, and to say this is to say that it is the arbitrary expression of an idea, which further implies that it at least is the expression of an idea. Now this last fact is true of every object in the universe. All express thought. Nothing can be correctly defined without connecting it with the sun, moon, and stars, and the definitions which have power to the student are those in which he can feel his way back to, is conscious of, the universal element. This reference of an idea to a larger whole is only a concise and an abbreviate form of giving the universal. Otherwise the universal elements would have to be enumerated.
It follows from what has been said that the larger class to which reference is made must be a known class, and such as will give the clearest and fullest notion of the class defined. Reference is made to the known class to abbreviate the process ; but if this class need explanation, the purpose is defeated. For the same reason, the class to which reference is made should have the greatest content, and therefore the least extent of any class to which reference can be made. Reference is made to the larger class to save enun erating and explaining common attributes of the class cefined ; and the greater the number found in the larger class, the greater is the economy. For instance, in defining a pronoun it may be referred to the class words or to the smaller class substantives. The choice will be determined first by which is better known ; second, by which has the greater content. If the substantive has been previously defined, it must be selected, because it contains one more attribute in common with the pronoun than does the class words. In saying that a pronoun is a word is saying only that it expresses an idea; but in saying that it is a substantive is saying that it expresses an idea of an object.
There is no exception to the rule that the class defined must be referred to a larger class; yet nothing is more common than for statements which look like definitions to lack this quality : as, “ A preposition shows relation.” Not what a thing shows, how it looks, or what it does, but what it is, must be the form of every definition; what are its connections with the universal truth out of which it springs.
The universal truth having been presented, the truth which gives to the class its particular, separate being must follow. This truth consists of the sum of the particular, but common, attributes of the individuals in the class to be defined. It will be readily seen that these common attributes which bind the individuals into a class are also those which separate the class defined from the whole to which it is referred. If these common attributes had been found in the larger class, they would have been exhausted in the reference to that class. So that the attributes here to
be given both unite the individuals of the class and separate them from all other individuals.
Summing up, we have the following rule for making a definition:
First, present the universal nature of the class by referring it to the smallest known class of which it is a part.
Second, present the particular nature of the class by stating the common, essential attributes which bind the individuals together, and which, at the same time, distinguish the class from the whole of which it is a part.
Definition being a statement of unity among individuals, the law of unity here is exacting, and its violation can be definitely detected. This law requires that, in defining, none but common attributes be given. If an attribute be given which belongs only to a part of the class, two classes are presented instead of one. For instance, “A verb is a word that expresses action, state, or being.” Action does not belong to all verbs, neither does state or being. If all the verbs of the language be taken and placed before us in groups as the foregoing definitions require, there would be three distinct groups. The attributes named in the definition should belong to each and every verb in the language, but to no other part of speech. When it is said that a verb expresses action, state, or being, other parts of speech are included, for other parts of speech may include the same ideas. But if it be said that a verb is a word that asserts, all other words are excluded. By giving an attribute which extends be