No word is more constantly on our lips than the word think. A hundred times a day we tell what we think about this thing or that. Any exceptional power of thought classes us among the efficient of our generation. It is in their ability to think that men stand preËminently above the animals.

1. DIFFERENT TYPES OF THINKING

The term think, or thinking, is employed in so many different senses that it will be well first of all to come to an understanding as to its various uses. Four different types of thinking which we shall note are:[5] (1) chance, or idle, thinking; (2) thinking in the form of uncritical belief; (3) assimilative thinking; and (4) deliberative thinking.

Chance or Idle Thinking.—Our thinking is of the chance or idle kind when we think to no conscious end. No particular problem is up for solution, and the stream of thought drifts along in idleness. In such thinking, immediate interest, some idle fancy, the impulse of the moment, or the suggestions from our environment determine the train of associations and give direction to our thought. In a sense, we surrender our mental bark to the winds of circumstance to drive it whithersoever they will without let or hindrance from us. Since no results are sought from our thinking, none are obtained. The best of us spend more time in these idle trains of thought than we would like to admit, while inferior and untrained minds seldom rise above this barren thought level. Not infrequently even when we are studying a lesson which demands our best thought power we find that an idle chain of associations has supplanted the more rigid type of thinking and appropriated the field.

Uncritical Belief.—We often say that we think a certain thing is true or false when we have, as a matter of fact, done little or no thinking about it. We only believe, or uncritically accept, the common point of view as to the truth or untruth of the matter concerned. The ancients believed that the earth was flat, and the savages that eclipses were caused by animals eating up the moon. Not a few people today believe that potatoes and other vegetables should be planted at a certain phase of the moon, that sickness is a visitation of Providence, and that various "charms" are potent to bring good fortune or ward off disaster. Probably not one in a thousand of those who accept such beliefs could give, or have ever tried to give, any rational reason for their point of view.

But we must not be too harsh toward such crude illustrations of uncritical thinking. It is entirely possible that not all of us who pride ourselves on our trained powers of thought could give good reasons discovered by our own thinking why we think our political party, our church, or our social organization is better than some other one. How few of us, after all, really discover our creed, join a church, or choose a political party! We adopt the points of view of our nation or our group much as we adopt their customs and dress—not because we are convinced by thinking that they are best, but because they are less trouble.

Assimilative Thinking.—It is this type of thinking that occupies us when we seek to appropriate new facts or ideas and understand them; that is, relate them to knowledge already on hand. We think after this fashion in much of our study in schools and textbooks. The problem for our thought is not so much one of invention or discovery as of grasp and assimilation. Our thinking is to apprehend meanings and relations, and so unify and give coherence to our knowledge.

In the absence of this type of thinking one may commit to memory many facts that he does not understand, gather much information that contains little meaning to him, and even achieve very creditable scholastic grades that stand for a small amount of education or development. For all information, to become vital and usable, must be thought into relation to our present active, functioning body of knowledge; therefore assimilative thinking is fundamental to true mastery and learning.

Deliberative Thinking.—Deliberative thinking constitutes the highest type of thought process. In order to do deliberative thinking there is necessary, first of all, what Dewey calls a "split-road" situation. A traveler going along a well-beaten highway, says Dr. Dewey, does not deliberate; he simply keeps on going. But let the highway split into two roads at a fork, only one of which leads to the desired destination, and now a problem confronts him; he must take one road or the other, but which? The intelligent traveler will at once go to seeking for evidence as to which road he should choose. He will balance this fact against that fact, and this probability against that probability, in an effort to arrive at a solution of his problem.

Before we can engage in deliberative thinking we must be confronted by some problem, some such "split-road" situation in our mental stream—we must have something to think about. It is this fact that makes one writer say that the great purpose of one's education is not to solve all his problems for him. It is rather to help him (1) to discover problems, or "split-road" situations, (2) to assist him in gathering the facts necessary for their solution, and (3) to train him in the weighing of his facts or evidence, that is, in deliberative thinking. Only as we learn to recognize the true problems that confront us in our own lives and in society about us can we become thinkers in the best sense. Our own plans and projects, the questions of right and wrong that are constantly arising, the social, political and religious problems awaiting solution, all afford the opportunity and the necessity for deliberative thinking. And unhappy is the pupil whose school work does not set the problems and employ the methods which will insure training in this as well as in the assimilative type of thinking. Every school subject, besides supplying certain information to be "learned," should present its problems requiring true deliberative thinking within the range of development and ability of the pupil, and no subject—literature, history, science, language—is without many such problems.

2. THE FUNCTION OF THINKING

All true thinking is for the purpose of discovering relations between the things we think about. Imagine a world in which nothing is related to anything else; in which every object perceived, remembered, or imagined, stands absolutely by itself, independent and self-sufficient! What a chaos it would be! We might perceive, remember, and imagine all the various objects we please, but without the power to think them together, they would all be totally unrelated, and hence have no meaning.

Meaning Depends on Relations.—To have a rational meaning for us, things must always be defined in terms of other things, or in terms of their uses. Fuel is that which feeds fire. Food is what is eaten for nourishment. A locomotive is a machine for drawing a train. Books are to read, pianos to play, balls to throw, schools to instruct, friends to enjoy, and so on through the whole list of objects which we know or can define. Everything depends for its meaning on its relation to other things; and the more of these relations we can discover, the more fully do we see the meaning. Thus balls may have other uses than to throw, schools other functions than to instruct, and friends mean much more to us than mere enjoyment. And just in the degree in which we have realized these different relations, have we defined the object, or, in other words, have we seen its meaning.

The Function of Thinking is to Discover Relations.—Now it is by thinking that these relations are discovered. This is the function of thinking. Thinking takes the various separate items of our experience and discovers to us the relations existing among them, and builds them together into a unified, related, and usable body of knowledge, threading each little bit on the string of relationship which runs through the whole. It was, no doubt, this thought which Tennyson had in mind when he wrote:

Flower in the crannied wall,
I pluck you out of the crannies,
I hold you here, root and all, in my hand,
Little flower—but if I could understand
What you are, root and all, and all in all,
I should know what God and man is.

Starting in with even so simple a thing as a little flower, if he could discover all the relations which every part bears to every other part and to all other things besides, he would finally reach the meaning of God and man. For each separate thing, be it large or small, forms a link in an unbroken chain of relationships which binds the universe into an ordered whole.

Near and Remote Relations.—The relations discovered through our thinking may be very close and simple ones, as when a child sees the relation between his bottle and his dinner; or they may be very remote ones, as when Newton saw the relation between the falling of an apple and the motion of the planets in their orbits. But whether simple or remote, the seeing of the relationships is in both cases alike thinking; for thinking is nothing, in its last analysis, but the discovering of the relationships which exist between the various objects in our mental stream.

Thinking passes through all grades of complexity, from the first faint dawnings in the mind of the babe when it sees the relation between the mother and its feeding, on to the mighty grasp of the sage who is able to "think God's thoughts after Him." But it all comes to the same end finally—the bringing to light of new meanings through the discovery of new relations. And whatever does this is thinking.

Child and Adult Thinking.—What constitutes the difference in the thinking of the child and that of the sage? Let us see whether we can discover this difference. In the first place the relations seen by the child are immediate relations: they exist between simple percepts or images; the remote and the general are beyond his reach. He has not had sufficient experience to enable him to discover remote relations. He cannot think things which are absent from him, or which he has never known. The child could by no possibility have seen in the falling apple what Newton saw; for the child knew nothing of the planets in their orbits, and hence could not see relations in which these formed one of the terms. The sage, on the other hand, is not limited to his immediate percepts or their images. He can see remote relations. He can go beyond individuals, and think in classes. The falling apple is not a mere falling apple to him, but one of a class of falling bodies. Besides a rich experience full of valuable facts, the trained thinker has acquired also the habit of looking out for relations; he has learned that this is the method par excellence of increasing his store of knowledge and of rendering effective the knowledge he has. He has learned how to think.

The chief business of the child is the collection of the materials of thought, seeing only the more necessary and obvious relations as he proceeds; his chief business when older grown is to seek out the network of relations which unites this mass of material, and through this process to systematize and give new meanings to the whole.

3. THE MECHANISM OF THINKING

It is evident from the foregoing discussion that we may include under the term thinking all sorts of mental processes by which relations are apprehended between different objects of thought. Thus young children think as soon as they begin to understand something of the meaning of the objects of their environment. Even animals think by means of simple and direct associations. Thinking may therefore go on in terms of the simplest and most immediate, or the most complex and distant relationships.

Sensations and Percepts as Elements in Thinking.—Relations seen between sensations would mean something, but not much; relations seen between objects immediately present to the senses would mean much more; but our thinking must go far beyond the present, and likewise far beyond individual objects. It must be able to annihilate both time and space, and to deal with millions of individuals together in one group or class. Only in this way can our thinking go beyond that of the lower animals; for a wise rat, even, may come to see the relation between a trap and danger, or a horse the relation between pulling with his teeth at the piece of string on the gate latch, and securing his liberty.

But it takes the farther-reaching mind of man to invent the trap and the latch. Perception alone does not go far enough. It is limited to immediately present objects and their most obvious relations. The perceptual image is likewise subject to similar limitations. While it enables us to dispense with the immediate presence of the object, yet it deals with separate individuals; and the world is too full of individual objects for us to deal with them separately. It is in conception, judgment, and reasoning that true thinking takes place. Our next purpose will therefore be to study these somewhat more closely, and see how they combine in our thinking.

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 classes; and for many purposes we can deal with the class as a whole instead of with the separate individuals of the class. 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 classed under the two great heads of inanimate and animate. Taking one of these again: all animate forms may be classed as either plants or animals. And these classes may again be subdivided indefinitely. Animals include mammals, birds, reptiles, insects, mollusks, and many other classes besides, each class 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 Classify.—But the somewhat complicated form of classification just described did not come to man ready-made. Someone had to see the relationship existing among the myriads of animals of a certain class, 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 class had to be observed, the qualities common to all members of the class discriminated from those not common, and the common qualities retained as the measure by which to test the admission of other individuals into this class. The process of classification 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, Dick, 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 class 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, cockers, 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; shagginess 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 classed 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 class, 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 class of individual objects. Its function is to enable us to classify our knowledge, and thus deal with classes 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 mass 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 class," and we define a concept as the meaning or idea we have of a class. It is easy to see that when we have named these class 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 constitutes 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 accumulating, 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 identity 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 illustration 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 identity. 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 assigned its place in our classification, 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 identity 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 assist 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 classes 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 analyzes each into its elements, compares them, and finds the essential identity 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 classes, 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 class, 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, constitute 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 institution." It is very evident that someone had made a mistake in judgment. Surely no college would want to expel the best boy in the institution. 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 institution" 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 constitutes a good man or a rascal.

No doubt most of us are prone 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 analysis, 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 illustration 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 circumstances, 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 illustrates 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 classical 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 class 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 assimilative 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 constitutes "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?