Ontario Normal School Manuals: Science of Education

by Ontario. Department of Education

B. Division of Known Classes.—A second common mode of developing new concepts in school work is in breaking up larger classes into co-ordinate sub-classes. This, of course, involves the developing of new concepts to cover these sub-classes. In such cases, however, the new notions are merely modified forms of the higher class notion. When, for example, the pupil gains general notions representative of the classes, proper noun and common noun, the new terms merely add something to the intension of the more extensive term noun. This will be evident by considering the difference between the notions noun and proper noun. Both agree in possessing the attribute used to name. The latter is more intensive, however, because it signifies used to name a particular object. Although in such cases the lesson seems in a sense to develop new general notions, they represent merely an adding to the intension of a notion already possessed by the child.

Use of the Term.—A further problem regarding the process of conception concerns the question of the significance of a name. When a person uses such a term as dog, whale, hepatica, guava, etc., to name a certain object, what is the exact sense, or meaning, in which the name is to be applied? A class name, when applied scientifically to an object, is evidently supposed to denote the presence in it of certain essential characteristics which belong to the class. It is clear, however, that the ordinary man rarely uses these names with any scientific precision. A man can point to an object and say that it is a horse, and yet be ignorant of many of the essential features of a horse. In such cases, therefore, the use of the name merely shows that the person considers the object to belong to a certain class, but is no guarantee that he is thinking of the essential qualities of the class. It might be said, therefore, that a class term is used for two somewhat different purposes, either to denote the object merely, or to signify scientifically the attributes possessed by the object. It is in the second respect that danger of error in reasoning arises. So far as a name represents the attributes of a class, it will signify for us just those attributes which we associate with that class. So long, therefore, as the word fish means to us an animal living in the water, we will include in the class the whale, which really does not belong to the class, and perhaps exclude from the class the flying fish, although it is scientifically a member of the class.

THE DEFINITION

It has been noted that, when man discovers common characteristics in a number of objects, he tends on this basis to unite such objects into a class. It is to be noted in addition, however, that in the same manner he is also able, by examining the characteristics of a large class of objects, to divide these into smaller sub-classes. Although, for example, we may place all three-sided figures into one class and call them triangles, we are further able to divide these into three sub-classes owing to certain differences that may be noted among them. Thus an important fact regarding classification is that while a class may possess some common quality or qualities, yet its members may be further divided into sub-classes and each of these smaller classes distinguished from the others by points of difference. Owing to this fact, there are two important elements entering into a scientific knowledge of any class, first, to know of what larger class it forms a part, and secondly, to know what characteristics distinguish it from the other classes which go with it to make up this larger class. To know the class equilateral triangle, for instance, we must know, first, that it belongs to the larger class triangle, and secondly, that it differs from other classes of triangles by having its three sides equal. For this reason a person is able to know a class scientifically without knowing all of its common characteristics. For instance, the large class of objects known as words is subdivided into smaller classes known as parts of speech. Taking one of these classes, the verb, we find that all verbs agree in possessing at least three common characteristics, they have power to assert, to denote manner, and to express time. To distinguish the verb, however, it is necessary to note only that it is a word used to assert, since this is the only characteristic which distinguishes it from the other classes of words. When, therefore, we describe any class of objects by first naming the larger class to which it belongs, and then stating the characteristics which distinguish it from the other co-ordinate classes, we are said to give a definition of the class, or to define it. The statement, "A trimeter is a verse of three measures," is a definition because it gives, first, the larger class (verse) to which the trimeters belong, and secondly, the difference (of three measures) which distinguishes the trimeter from all other verses. The statement, "A binomial is an algebraic expression consisting of two terms," is a definition, because it gives, first, the larger class (algebraic expression) to which binomials belong, and secondly, the difference (consisting of two terms) which distinguishes binomials from other algebraic expressions.

JUDGMENT

Nature of Judgment.—A second form, or mode, of thinking is known as judgment. Our different concepts were seen to vary in their intension, or meaning, according to the number of attributes suggested by each. My notion triangle may denote the attributes three-sided and three-angled; my notion isosceles triangle will in that case include at least these two qualities plus equality of two of the sides. This indicates that various relations exist between our ideas and may be apprehended by the mind. When a relation between two concepts is distinctly apprehended in thought, or, in other words, when there is a mental assertion of a union between two ideas, or objects of thought, the process is known as judgment. Judgment may be defined, therefore, as the apprehension, or mental affirmation, of a relation between two ideas. If the idea, or concept, heaviness enters as a mental element into my idea stone, then the mind is able to affirm a relation between these concepts in the form, "Stone is heavy." In like manner when the mind asserts, "Glass is transparent" or "Horses are animals," there is a distinct apprehension of a relation between the concepts involved.

Judgment Distinguished from Statement.—It should be noted that judgment is the mental apprehension of a relation between ideas. When this relation is expressed in actual words, it is spoken of as a proposition, or a predication. A proposition is, therefore, the statement of a judgment. The proposition is composed of two terms and the copula, one term constituting the subject of the proposition and the other the predicate. Although a judgment may often be expressed in some other form, it can usually be converted into the above form. The proposition, "Horses eat oats," may be expressed in the form, "Horses are oat-eaters"; the proposition, "The sun melts the snow," into the form, "The sun is a-thing-which-melts-snow."

Relation of Judgment to Conception.—It would appear from the above examples that a judgment expresses in an explicit form the relations involved within the concept, and is, therefore, merely a direct way of indicating the state of development of any idea. If my concept of a dog, for example, is a synthesis of the qualities four-footed, hairy, fierce, and barking, then an analysis of the concept will furnish the following judgments:

	{ A four-footed thing.
	{ A hairy thing.
A dog is	{ A fierce thing.
	{ A barking thing.

Because in these cases a concept seems necessary for an act of judgment, it is said that judgment is a more advanced form of thinking than conception. On the other hand, however, judgment is implied in the formation of a concept. When the child apprehends the dog as a four-footed object, his mind has grasped four-footedness as a quality pertaining to the strange object, and has, in a sense, brought the two ideas into relation. But while judgment is implied in the formation of the concept, the concept does not bring explicitly to the mind the judgments it implies. The concept snow, for instance, implies the property of whiteness, but whiteness must be apprehended as a distinct idea and related mentally with the idea snow before we can be said to have formed, or thought, the judgment, "Snow is white." Judgment is a form of thinking separate from conception, therefore, because it does thus bring into definite relief relations only implied in our general notions, or concepts. One value of judgment is, in fact, that it enables us to analyse our concepts, and thus note more explicitly the relations included in them.