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notions.

the qualities of things that they have been accustomed to consider as essential, and to recognize as necessary some that they have heretofore overlooked, so that they may perceive the general notion or law involved. It is very important to realize that, though logical notions can never be fully reached, instruction is always striving to attain them as nearly as possible; they are really the goal of instruction. A general notion, as its name implies, does not refer to one Distinguishparticular object and to no other, but to many of the ing marks of same sort, as the word river to a whole class of ob- and general jects. It differs from individual notions just as common nouns differ from proper names. The latter apply, in each case, to only one certain object, as Illinois to one of the Central states, while the former refer to any one of a class, as child to any one of millions of persons. Proper names compose a relatively small class of words; almost all other words stand for generalizations; for instance, the verb run signifies a certain class of actions; sweet, a quality common to a great number of objects; the preposition underneath, a kind of relationship that may frequently exist between objects. Each of these notions, instead of applying to a single case and to no other, covers a multitude of individual cases or classes.

Knowing now the nature of individual and general notions, it is comparatively easy to recognize each in its various forms. Numerous examples of the former have been given. As to the latter, not only do al

most all words signify generalizations, but the rules of grammar and arithmetic do the same. The definitions of mathematics, as of triangle, plane, etc.; the laws of physics, as the laws of pulleys and of gravitation; the principles of science, as the economical principle that man is by nature lazy, and moral maxims, as that we should do unto others as we would have them do unto us, are all general notions: they are all reached by the same process, by the separation of non-essential characteristics from those that are essential. Definitions, rules, laws, proverbs, principles, and maxims are general truths or notions: the individual instances illustrating them are individual truths or notions. In the second place, general notions distinguish themselves from individuals by the fact that the latter can be imaged or pictured concretely, while the former cannot.

Any particular chair presents a certain appearance; it has definite form, weight, color, etc., and the mental picture of it contains these particular characteristics. Any historical event has a peculiar setting; it was performed at a certain time and place, by a certain person or persons, under particular conditions, in a definite manner, etc. When it is reproduced mentally it must be accompanied with its peculiar environment. Objects and events that have never been actually witnessed, but only imagined, must also be pictured in detail in the same way. But general notions and laws cannot be thus clearly imaged or seen concretely. They do not apply to just one object, event, or relation, but to any and all of a class; in fact, they have no external objective existence, hence they cannot be limited to any certain form, color, time, place, setting, etc. The word chair signifies the common essential characteristics of chair without reference to any particular example; the preposition underneath, a relationship that may frequently exist between nouns or pronouns and other words without naming any specific case; the moral maxim, honesty is the best policy, calls to mind a general truth without mentioning any instances that illustrate it. Frequently, however, these instances are so close at hand that, when the general notion is presented, one or more of the individuals that fall under it come immediately to consciousness. When we think horse, it is impossible not to call some favorite horse into mind.

The last statement indicates the relationship properly existing between individual and general notions. The latter are not creations entirely separated from the former, but are intimately associated with them. 1" The general notion is not a new mental product Relationship

between existing apart from and outside of the concrete no

individual tions, but it is thought out each time, inasmuch as a and general person from among the numerous ideas of the same kind (or also from only one idea) lifts exclusively the essential characteristics into the centre of conscious

notions,

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ness, and endeavors to isolate them from the others, which recede or withdraw (an attempt that is always, of course, only partially successful). It is like a melody that can be easily distinguished in a piece of music of several parts on account of special emphasis or peculiar registering, while, however, it never ceases to form a constituent part of the separate accords. It happens to us regularly, when we attempt really to think a concept and not simply to repeat the words of the definition, that we involuntarily glide down among its individual notions; that we hasten through these quickly and emphasize what is common and essential, rejecting the non-essential. The general is not really separated from the particular, but only distinguished from it; for deep down in consciousness it is always united with what is concrete."

CHAPTER IV

WHY GENERAL NOTIONS OR CONCEPTS ARE THE GOAL

OF INSTRUCTION

THE declaration that logical notions are the goal of all instruction is so far-reaching in its bearings that it deserves further consideration, Pestalozzi called the attention of teachers emphatically to this truth, but he failed signally to apply it to his own teaching. Since his time men have commonly accepted his assertion as true, but, like him, have expended little effort in applying it to school instruction. In consequence, one of the weightiest thoughts in education has been largely overlooked by educators. How effect reform in this direction ? It is certain that teachers will not labor persistently to reach after and apply generalizations in the classroom until they have learned both to distinguish between individual and general notions, and to appreciate the great value of the latter. The preceding chapter treated of the first of these two points

attempting to explain the difference between the two kinds of notions; the present chapter takes up

the second point and aims to show why instruction · culminates in generalizations.

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