Intension of Concepts.—Certain of our general notions are, however, much more complex than others. When a single attribute such as four-footedness is generalized to represent the class four-footed objects, the notion itself is relatively simple. In other words, a single property is representative of the objects, and in apprehending the members of the class all other properties they chance to possess may be left out of account. In many cases, however, the class notion will evidently be much more complex. The notion dog, for instance, in addition to implying the characteristic four-footedness, may include such qualities as hairy, barking, watchful, fearless, etc. This greater or less degree of complexity of a general notion is spoken of as its intensity. The notion dog, for instance, is more intensive than the notion four-footed animals; the notion lawyer, than the notion man.
Extension of Concepts.—It is to be noted further that as a notion increases in intension it becomes limited to a smaller class of objects. From this standpoint, notions are said to differ in extension. The class lawyer, for instance, is not so extensive as the class man; nor the class dog, as the class four-footed objects. It will appear from the above that an abstract notion viewed as a sign of a class of objects is distinguished by its extension, while a class notion, so far as it implies a synthesis of several abstracted qualities, is marked rather by its intension.
AIMS OF CONCEPTUAL LESSONS
So far as school lessons aim to establish and develop correct class notions in the minds of the pupils, three somewhat distinct types of work may be noted:
1. TO DEFINE CLASSES
In some lessons no attempt is made to develop an utterly new class notion, or concept; the pupils in fact may already know the class of objects in a general way and be acquainted with many of their characteristics. The object of the lesson is, therefore, to render the concept more scientific by having it include the qualities which essentially mark it as a class and especially separate it from other co-ordinate classes. In studying the grasshopper; for instance, in entomology, the purpose is not to give the child a notion of the insect in the ordinary sense of the term. This the pupil may already have. The purpose is rather to enable him to decide just what general characteristics distinguish this from other insects. The lesson may, therefore, leave out of consideration features which are common to all grasshoppers, simply because they do not enter into a scientific differentiation of the class.
2. TO ENLARGE A CONCEPT
In many lessons the aim seems to be chiefly to enlarge certain concepts by adding to their intensiveness. The pupil, for instance, has a scientific concept of a triangle, that is, one which enables him to distinguish a triangle from any other geometrical figure. He may, however, be led to see further that the three angles of every triangle equal two right angles. This is really having him discover a further attribute in relation to triangles, although this knowledge is not essential to the concept as a symbol of the members of the class. In the same way, in grammar the pupil is taught certain attributes common to verbs, as mood and tense, although these are not essential attributes from the standpoint of distinguishing the verb as a special class of words.
3. TO BUILD UP NEW CONCEPTS
A. Presentation of Unknown Individuals.—In many lessons the chief object seems to be, however, to build up a new concept in the mind of the child. This would be the case when the pupil is presented with a totally unknown object, say a platypus, and called upon to examine its characteristics. In such lessons two important facts should be noticed. First, the child finds seemingly little difficulty in accepting a single individual as a type of a class, and is able to carry away from the lesson a fairly scientific class notion through a study of the one individual. In this regard the pupil but illustrates what has been said of the ability of the child to use his early percepts as standards to interpret other individuals. The pupil is able the more easily to form this accurate notion, because he no doubt has already a store of abstract notions with which to interpret the presentation, and also because his interest and attention is directed into the proper channels by the teacher.