The Mind and Its Education Part 14

4. THE CONCEPT

Fortunately for our thinking, the great external world, with its millions upon millions of individual objects, is so ordered that these objects can be grouped into comparatively few great cla.s.ses; and for many purposes we can deal with the cla.s.s as a whole instead of with the separate individuals of the cla.s.s. Thus there are an infinite number of individual objects in the world which are composed of _matter_. Yet all these myriads of individuals may be cla.s.sed under the two great heads of _inanimate_ and _animate_. Taking one of these again: all animate forms may be cla.s.sed as either _plants_ or _animals_. And these cla.s.ses may again be subdivided indefinitely. Animals include mammals, birds, reptiles, insects, mollusks, and many other cla.s.ses besides, each cla.s.s of which may be still further separated into its _orders_, _families_, _genera_, _species_, and _individuals_. This arrangement economizes our thinking by allowing us to think in large terms.

THE CONCEPTS SERVE TO GROUP AND CLa.s.sIFY.--But the somewhat complicated form of cla.s.sification just described did not come to man ready-made.

Someone had to _see_ the relations.h.i.+p existing among the myriads of animals of a certain cla.s.s, and group these together under the general term _mammals_. Likewise with birds, reptiles, insects, and all the rest. In order to accomplish this, many individuals of each cla.s.s had to be observed, the qualities common to all members of the cla.s.s discriminated from those not common, and the common qualities retained as the measure by which to test the admission of other individuals into this cla.s.s. The process of cla.s.sification is made possible by what the psychologist calls the _concept_. The concept enables us to think _birds_ as well as bluebirds, robins, and wrens; it enables us to think _men_ as well as Tom, d.i.c.k, and Harry. In other words, _the concept lies at the bottom of all thinking which rises above the seeing of the simplest relations between immediately present objects_.

GROWTH OF A CONCEPT.--We can perhaps best understand the nature of the concept if we watch its growth in the thinking of a child. Let us see how the child forms the concept _dog_, under which he is able finally to cla.s.s the several hundred or the several thousand different dogs with which his thinking requires him to deal. The child's first acquaintance with a dog is, let us suppose, with a pet poodle, white in color, and named _Gyp_. At this stage in the child's experience, _dog_ and _Gyp_ are entirely synonymous, including Gyp's color, size, and all other qualities which the child has discovered. But now let him see another pet poodle which is like Gyp except that it is black in color. Here comes the first cleavage between _Gyp_ and _dog_ as synonyms: _dog_ no longer means white, but may mean _black_. Next let the child see a brown spaniel. Not only will white and black now no longer answer to _dog_, but the roly-poly poodle form also has been lost; for the spaniel is more slender. Let the child go on from this until he has seen many different dogs of all varieties: poodles, bulldogs, setters, shepherds, c.o.c.kers, and a host of others. What has happened to his _dog_, which at the beginning meant the one particular little individual with which he played?

_Dog_ is no longer white or black or brown or gray: _color_ is not an essential quality, so it has dropped out; _size_ is no longer essential except within very broad limits; _s.h.a.gginess_ or _smoothness_ of coat is a very inconstant quality, so this is dropped; _form_ varies so much from the fat pug to the slender hound that it is discarded, except within broad limits; _good nature_, _playfulness_, _friendliness_, and a dozen other qualities are likewise found not to belong in common to _all_ dogs, and so have had to go; and all that is left to his _dog_ is _four-footedness_, and a certain general _form_, and a few other dog qualities of habit of life and disposition. As the term _dog_ has been gaining in _extent_, that is, as more individuals have been observed and cla.s.sed under it, it has correspondingly been losing in _content_, or it has been losing in the specific qualities which belong to it. Yet it must not be thought that the process is altogether one of elimination; for new qualities which are present in all the individuals of a cla.s.s, but at first overlooked, are continually being discovered as experience grows, and built into the developing concept.

DEFINITION OF CONCEPT.--A concept, then, is _our general idea or notion of a cla.s.s of individual objects_. Its function is to enable us to cla.s.sify our knowledge, and thus deal with cla.s.ses or universals in our thinking. Often the basis of a concept consists of an _image_, as when you get a hazy visual image of a ma.s.s of people when I suggest _mankind_ to you. Yet the core, or the vital, functioning part of a concept is its _meaning_. Whether this meaning attaches to an image or a word or stands relatively or completely independent of either, does not so much matter; but our meanings must be right, else all our thinking is wrong.

LANGUAGE AND THE CONCEPT.--We think in words. None has failed to watch the flow of his thought as it is carried along by words like so many little boats moving along the mental stream, each with its freight of meaning. And no one has escaped the temporary balking of his thought by failure to find a suitable word to convey the intended meaning. What the grammarian calls the _common nouns_ of our language are the words by which we name our concepts and are able to speak of them to others. We define a common noun as "the name of a cla.s.s," and we define a concept as the meaning or idea we have of a cla.s.s. It is easy to see that when we have named these cla.s.s _ideas_ we have our list of common nouns. The study of the language of a people may therefore reveal much of their type of thought.

THE NECESSITY FOR GROWING CONCEPTS.--The development of our concepts const.i.tutes a large part of our education. For it is evident that, since thinking rests so fundamentally on concepts, progress in our mental life must depend on a constant growth in the number and character of our concepts. Not only must we keep on adding new concepts, but the old must not remain static. When our concepts stop growing, our minds have ceased to grow--we no longer learn. This arrest of development is often seen in persons who have settled into a life of narrow routine, where the demands are few and of a simple nature. Unless they rise above their routine, they early become "old fogies." Their concepts petrify from lack of use and the constant reconstruction which growth necessitates.

On the other hand, the person who has upon him the constant demand to meet new situations or do better in old ones will keep on enriching his old concepts and forming new ones, or else, unable to do this, he will fail in his position. And the person who keeps on steadily enriching his concepts has discovered the secret of perpetual youth so far as his mental life is concerned. For him there is no old age; his thought will be always fresh, his experience always acc.u.mulating, and his knowledge growing more valuable and usable.

5. JUDGMENT

But in the building up of percepts and concepts, as well as in making use of them after they are formed, another process of thinking enters; namely, the process of _judging_.

NATURE OF JUDGMENT.--Judging enters more or less into all our thinking, from the simplest to the most complex. The babe lies staring at his bottle, and finally it dawns on his sluggish mind that this is the object from which he gets his dinner. He has performed a judgment. That is, he has alternately directed his attention to the object before him and to his image of former nursing, discovered the relation existing between the two, and affirmed to himself, "This is what gives me my dinner." "Bottle" and "what-gives-me-my-dinner" are essentially identical to the child. _Judgment is, then, the affirmation of the essential ident.i.ty of meaning of two objects of thought._ Even if the proposition in which we state our judgment has in it a negative, the definition will still hold, for the mental process is the same in either case. It is as much a judgment if we say, "The day is not-cold," as if we say, "The day is cold."

JUDGMENT USED IN PERCEPTS AND CONCEPTS.--How judgment enters into the forming of our percepts may be seen from the ill.u.s.tration just given.

The act by which the child perceived his bottle had in it a large element of judging. He had to compare two objects of thought--the one from past experience in the form of images, and the other from the present object, in the form of sensations from the bottle--and then affirm their essential ident.i.ty. Of course it is not meant that what I have described _consciously_ takes place in the mind of the child; but some such process lies at the bottom of every perception, whether of the child or anyone else.

Likewise it may be seen that the forming of concepts depends on judgment. Every time that we meet a new object which has to be a.s.signed its place in our cla.s.sification, judgment is required. Suppose the child, with his immature concept _dog_, sees for the first time a greyhound. He must compare this new specimen with his concept _dog_, and decide that this is or is not a dog. If he discovers the ident.i.ty of meaning in the essentials of the two objects of thought, his judgment will be affirmative, and his concept will be modified in whatever extent _greyhound_ will affect it.

JUDGMENT LEADS TO GENERAL TRUTHS.--But judgment goes much farther than to a.s.sist in building percepts and concepts. It takes our concepts after they are formed and discovers and affirms relations between them, thus enabling us finally to relate cla.s.ses as well as individuals. It carries our thinking over into the realm of the universal, where we are not hampered by particulars. Let us see how this is done. Suppose we have the concept _man_ and the concept _animal_, and that we think of these two concepts in their relation to each other. The mind a.n.a.lyzes each into its elements, compares them, and finds the essential ident.i.ty of meaning in a sufficient number to warrant the judgment, _man is an animal_. This judgment has given a new bit of knowledge, in that it has discovered to us a new relation between two great cla.s.ses, and hence given both, in so far, a new meaning and a wider definition. And as this new relation does not pertain to any particular man or any particular animal, but includes all individuals in each cla.s.s, it has carried us over into universals, so that we have a _general_ truth and will not have to test each individual man henceforth to see whether he fits into this relation.

Judgments also, as we will see later, const.i.tute the material for our reasoning. Hence upon their validity will depend the validity of our reasoning.

THE VALIDITY OF JUDGMENTS.--Now, since every judgment is made up of an affirmation of relation existing between two terms, it is evident that the validity of the judgment will depend on the thoroughness of our knowledge of the terms compared. If we know but few of the attributes of either term of the judgment, the judgment is clearly unsafe. Imperfect concepts lie at the basis of many of our wrong judgments. A young man complained because his friend had been expelled from college for alleged misbehavior. He said, "Mr. A---- was the best boy in the inst.i.tution."

It is very evident that someone had made a mistake in judgment. Surely no college would want to expel the best boy in the inst.i.tution. Either my complainant or the authorities of the college had failed to understand one of the terms in the judgment. Either "Mr. A----" or "the best boy in the inst.i.tution" had been wrongly interpreted by someone.

Likewise, one person will say, "Jones is a good man," while another will say, "Jones is a rascal." Such a discrepancy in judgment must come from a lack of acquaintance with Jones or a lack of knowledge of what const.i.tutes a good man or a rascal.

No doubt most of us are p.r.o.ne to make judgments with too little knowledge of the terms we are comparing, and it is usually those who have the least reason for confidence in their judgments who are the most certain that they cannot be mistaken. The remedy for faulty judgments is, of course, in making ourselves more certain of the terms involved, and this in turn sends us back for a review of our concepts or the experience upon which the terms depend. It is evident that no two persons can have just the same concepts, for all have not had the same experience out of which their concepts came. The concepts may be named the same, and may be nearly enough alike so that we can usually understand each other; but, after all, I have mine and you have yours, and if we could each see the other's in their true light, no doubt we should save many misunderstandings and quarrels.

6. REASONING

All the mental processes which we have so far described find their culmination and highest utility in _reasoning_. Not that reasoning comes last in the list of mental activities, and cannot take place until all the others have been completed, for reasoning is in some degree present almost from the dawn of consciousness. The difference between the reasoning of the child and that of the adult is largely one of degree--of reach. Reasoning goes farther than any of the other processes of cognition, for it takes the relations expressed in judgments and out of these relations evolves still other and more ultimate relations.

NATURE OF REASONING.--It is hard to define reasoning so as to describe the precise process which occurs; for it is so intermingled with perception, conception, and judgment, that one can hardly separate them even for purposes of a.n.a.lysis, much less to separate them functionally.

We may, however, define reasoning provisionally as _thinking by means of a series of judgments with the purpose of arriving at some definite end or conclusion_. What does this mean? Professor Angell has stated the matter so clearly that I will quote his ill.u.s.tration of the case:

"Suppose that we are about to make a long journey which necessitates the choice from among a number of possible routes. This is a case of the genuinely problematic kind. It requires reflection, a weighing of the _pros_ and _cons_, and giving of the final decision in favor of one or other of several alternatives. In such a case the procedure of most of us is after this order. We think of one route as being picturesque and wholly novel, but also as being expensive. We think of another as less interesting, but also as less expensive. A third is, we discover, the most expedient, but also the most costly of the three. We find ourselves confronted, then, with the necessity of choosing with regard to the relative merits of cheapness, beauty, and speed. We proceed to consider these points in the light of all our interests, and the decision more or less makes itself. We find, for instance, that we must, under the circ.u.mstances, select the cheapest route."

HOW JUDGMENTS FUNCTION IN REASONING.--Such a line of thinking is very common to everyone, and one that we carry out in one form or another a thousand times every day we live. When we come to look closely at the steps involved in arriving at a conclusion, we detect a series of judgments--often not very logically arranged, to be sure, but yet so related that the result is safely reached in the end. We compare our concept of, say, the first route and our concept of picturesqueness, decide they agree, and affirm the judgment, "This route is picturesque."

Likewise we arrive at the judgment, "This route is also expensive, it is interesting, etc." Then we take the other routes and form our judgments concerning them. These judgments are all related to each other in some way, some of them being more intimately related than others. Which judgments remain as the significant ones, the ones which are used to solve the problem finally, depends on which concepts are the most vital for us with reference to the ultimate end in view. If time is the chief element, then the form of our reasoning would be something like this: "Two of the routes require more than three days: hence I must take the third route." If economy is the important end, the solution would be as follows: "Two routes cost more than $1,000; I cannot afford to pay more than $800; I therefore must patronize the third route."

In both cases it is evident that the conclusion is reached through a comparison of two or more judgments. This is the essential difference between judgment and reasoning. Whereas judgment discovers relations between concepts, _reasoning discovers relations between judgments, and from this evolves a new judgment which is the conclusion sought_. The example given well ill.u.s.trates the ordinary method by which we reason to conclusions.

DEDUCTION AND THE SYLLOGISM.--Logic may take the conclusion, with the two judgments on which it is based, and form the three into what is called a _syllogism_, of which the following is a cla.s.sical type:

All men are mortal; Socrates is a man, Therefore Socrates is mortal.

The first judgment is in the form of a proposition which is called the _major premise_, because it is general in its nature, including all men.

The second is the _minor premise_, since it deals with a particular man.

The third is the _conclusion_, in which a new relation is discovered between Socrates and mortality.

This form of reasoning is _deductive_, that is, it proceeds from the general to the particular. Much of our reasoning is an abbreviated form of the syllogism, and will readily expand into it. For instance, we say, "It will rain tonight, for there is lightning in the west." Expanded into the syllogism form it would be, "Lightning in the west is a sure sign of rain; there is lightning in the west this evening; therefore, it will rain tonight." While we do not commonly think in complete syllogisms, it is often convenient to cast our reasoning in this form to test its validity. For example, a fallacy lurks in the generalization, "Lightning in the west is a sure sign of rain." Hence the conclusion is of doubtful validity.

INDUCTION.--Deduction is a valuable form of reasoning, but a moment's reflection will show that something must precede the syllogism in our reasoning. The _major premise must be accounted for_. How are we able to say that all men are mortal, and that lightning in the west is a sure sign of rain? How was this general truth arrived at? There is only one way, namely, through the observation of a large number of particular instances, or through _induction_.

Induction is the method of proceeding from the particular to the general. Many men are observed, and it is found that all who have been observed have died under a certain age. It is true that not all men have been observed to die, since many are now living, and many more will no doubt come and live in the world whom _we_ cannot observe, since mortality will have overtaken us before their advent. To this it may be answered that the men now living have not yet lived up to the limit of their time, and, besides, they have within them the causes working whose inevitable effect has always been and always will be death; likewise with the men yet unborn, they will possess the same organism as we, whose very nature necessitates mortality. In the case of the premonitions of rain, the generalization is not so safe, for there have been exceptions. Lightning in the west at night is not always followed by rain, nor can we find inherent causes as in the other case which necessitates rain as an effect.

THE NECESSITY FOR BROAD INDUCTION.--Thus it is seen that our generalizations, or major premises, are of all degrees of validity. In the case of some, as the mortality of man, millions of cases have been observed and no exceptions found, but on the contrary, causes discovered whose operation renders the result inevitable. In others, as, for instance, in the generalization once made, "All cloven-footed animals chew their cud," not only had the examination of individual cases not been carried so far as in the former case when the generalization was made, but there were found no inherent causes residing in cloven-footed animals which make it necessary for them to chew their cud. That is, cloven feet and cud-chewing do not of necessity go together, and the case of the pig disproves the generalization.

In practically no instance, however, is it possible for us to examine every case upon which a generalization is based; after examining a sufficient number of cases, and particularly if there are supporting causes, we are warranted in making the "inductive leap," or in proceeding at once to state our generalization as a working hypothesis.

Of course it is easy to see that if we have a wrong generalization, if our major premise is invalid, all that follows in our chain of reasoning will be worthless. This fact should render us careful in making generalizations on too narrow a basis of induction. We may have observed that certain red-haired people of our acquaintance are quick-tempered, but we are not justified from this in making the general statement that all red-haired people are quick-tempered. Not only have we not examined a sufficient number of cases to warrant such a conclusion, but we have found in the red hair not even a cause of quick temper, but only an occasional concomitant.

THE INTERRELATION OF INDUCTION AND DEDUCTION.--Induction and deduction must go hand in hand in building up our world of knowledge. Induction gives us the particular facts out of which our system of knowledge is built, furnishes us with the data out of which general truths are formed; deduction allows us to start with the generalization furnished us by induction, and from this vantage ground to organize and systematize our knowledge and, through the discovery of its relations, to unify it and make it usable. Deduction starts with a general truth and asks the question, "What new relations are made necessary among particular facts by this truth?" Induction starts with particulars, and asks the question, "To what general truth do these separate facts lead?"

Each method of reasoning needs the other. Deduction must have induction to furnish the facts for its premises; induction must have deduction to organize these separate facts into a unified body of knowledge. "He only sees well who sees the whole in the parts, and the parts in the whole."

7. PROBLEMS IN OBSERVATION AND INTROSPECTION

1. Watch your own thinking for examples of each of the four types described. Observe a cla.s.s of children in a recitation or at study and try to decide which type is being employed by each child. What proportion of the time supposedly given to study is given over to _chance_ or idle thinking? To _a.s.similative_ thinking? To _deliberative_ thinking?

2. Observe children at work in school with the purpose of determining whether they are being taught to _think_, or only to memorize certain facts. Do you find that definitions whose meaning is not clear are often required of children? Which should come first, the definition or the meaning and application of it?

3. It is of course evident from the relation of induction and deduction that the child's natural mode of learning a subject is by induction.

Observe the teaching of children to determine whether inductive methods are commonly used. Outline an inductive lesson in arithmetic, physiology, geography, civics, etc.

4. What concepts have you now which you are aware are very meager? What is your concept of _mountain?_ How many have you seen? Have you any concepts which you are working very hard to enrich?

5. Recall some judgment which you have made and which proved to be false, and see whether you can now discover what was wrong with it. Do you find the trouble to be an inadequate concept? What const.i.tutes "good judgment"? "poor judgment"? Did you ever make a mistake in an example in, say, percentage, by saying "This is the base," when it proved not to be? What was the cause of the error?

6. Can you recall any instance in which you made too hasty a generalization when you had observed but few cases upon which to base your premise? What of your reasoning which followed?

7. See whether you can show that validity of reasoning rests ultimately on correct perceptions. What are you doing at present to increase your power of thinking?

8. How ought this chapter to help one in making a better teacher? A better student?