Making the Most of One's Mind/Chapter 4
NATURE OF STUDY AND THINKING
WHEN we study we apply our minds to what is going on around us, in order that we may learn how to behave ourselves intelligently in relation to those surroundings. We are not to suppose that study is confined to books. It is true that most people associate the notion of study with schools and colleges, or at the very least with books. But in the broad sense study consists in deliberately acquiring such familiarity with our surroundings as shall enable us to make ourselves thoroughly at home in them. To be sure, conning the multiplication table and learning to read seem remote from the needs of the very complicated adult life that lies before the pupil, but the accomplishments of the schoolroom have all a very definite relation to the pupil's present and future surroundings. Study has for its aim the mastery of the conditions under which we have to live. The student may be misdirected in his study, but the mastery of his surroundings is always his ultimate aim. Indeed, education has been defined as the process by which the educand absorbs and is absorbed by his environment. As we learn we may be said to take possession of the outer world and make it a part of our mental life, while at the same time the outer world is taking possession of us and making us conform to all its conditions; the result being that we gradually find ourselves more and more at home in our surroundings.
Froebel, in speaking of education, tells us that the pupil's activity works in two ways. At one time it is busy taking in material from the outer world: this he calls making the outer inner. At another time it is occupied in impressing its own influence upon things without: this he calls making the inner outer. In the first case the outer world is supplying material for the mind to work upon; in the second the mind, by its reaction on this material, is, at least to some extent, modifying the outer world. Sometimes the first process is called impression and the second expression. To the process of learning, both are necessary.
Herbert Spencer expresses the same truth somewhat differently when he says that "knowledge is turned into faculty as soon as it is taken in, and forthwith aids in the general function of thinking . . . does not lie merely written on the pages of an internal library, as when rote-learnt." In plain English, Spencer regards it as possible to turn fact into faculty. At first sight this seems a hard saying. How can an external fact, say the law of gravitation, become a part of the faculty of a human being? But when you come to think of it, you will realize that you are a different sort of person from what you would be did you not know the law of gravitation. Everybody knows the effects of the law of gravitation, whether they know the law itself or not. The most illiterate man would be a different sort of person if he did not know that when the support of his hand is removed from the jug he is carrying, it will fall to the ground. And in the same way you would be a slightly different person from what you are if you did not know that gravitation exercises its power "inversely as the squares of the distance." If, as a matter of fact, you do not at this moment happen to know the exact law of gravitation, then you will become a slightly different person when you do know it.
When you look into the matter, you will readily see that knowledge is sometimes treated as passive and sometimes as active; or, if you prefer it, knowledge is sometimes static and sometimes dynamic. People often speak of "mental content," by which they mean all the knowledge belonging to a particular mind. Your mental content is made up of all the ideas that are either in your mind now, or have been there before and may be called up again by and by. Investigations have been made, for example, into the contents of the minds of school children. The mental content of a country child is found to be different from that of a town child, and in comparing the two, the investigator makes a sort of inventory in each case and then compares the results. From this point of view we are clearly dealing with knowledge as static. Ideas are regarded as in a way the furniture of the mind, and just as we may make an inventory of tables and chairs and sideboards, so we may make an inventory of ideas of larks, and tram-cars, and hayricks, and asphalt pavements. When we make the outer inner, we are increasing our mental content.
But ideas do not remain sedately where we put them, as chairs and tables do in a room. They are in continual movement, and would almost appear to have a life of their own. You will remember that ideas have been said to be "living creatures having hands and feet." This you will understand is nothing more than a figure of speech. Ideas do not have any power of their own apart from us. It is we who give them whatever force they have. But all the same, ideas will not do exactly what we would like them to do, for they are influenced by what goes on in the outer world. Ideas are related to one another in our mind in a particular way because the things outside that correspond to the ideas are related to one another in that same particular way. The idea of blue and the idea of tomato refuse to be joined together. It is true that we can, by the use of our imagination, make ideas behave in a way that does not correspond to what goes on in the outer world. But we know all the time that if we are to make ourselves at home in our surroundings we must respect what takes place in the world of things. We must recognize facts. When we take in a fact and turn it into faculty, what has happened is that we have realized how certain elements in the outer world act in relation to one another, and that we have made up our minds to act accordingly. If we have a true idea of a dog, this means that we know how to behave intelligently when we meet dogs, or when people speak to us about dogs. The idea of dog is active to that extent. It is not a mere picture inside our mind: it is really our way of dealing with dogs. All the facts that we know about dogs have been turned into the faculty of behaving intelligently wherever dogs are concerned.
It is worth noting that not all facts become faculty to the same degree. Many facts have so little bearing upon our life that they hardly seem to have any effect at all. You could sit down with a sheet of foolscap and in a few minutes fill it with facts about the room in which you are sitting, that are of no consequence to anyone, even to yourself. The facts that count are what may be called significant facts, facts that have a meaning, facts that are so related to other facts as to be capable of giving practical guidance in our thinking, acting or feeling. Now in our studies we are supposed to deal only with significant facts, facts that can and ought to be turned into faculty. No better test, indeed, could be applied to discover whether certain subjects should be included in the school curriculum than the question: "Can and should the facts included under these subjects be turned into faculty?" The multiplication table, for example, certainly supplies facts that ought to be turned into faculty. We are different sorts of persons because we know these facts. It would be a different sort of world if seven times eight were sometimes fifty-six and sometimes sixty-four.
These considerations give us some help when we come to our actual study. We find that, broadly speaking, our work is of two kinds. Sometimes our main business seems to be to acquire knowledge: certain matters are placed before us in books or by our teachers, and we are required to master them, to make them part of our stock of knowledge. At other times we are called upon to use the knowledge we already possess in order to attain some end that is set before us. In a general way, the two may be classed as acquisitive and constructive work. In Geography, for example, so long as we are merely learning the bare facts of the subject, the size and contours of the different continents, the political divisions, the natural features, we are at the acquisitive stage. We are making the outer inner. But when we go on to try to find out the reasons why certain facts that we have learnt should be as they are and not otherwise, we pass to the constructive stage. We are working constructively when we seek to discover why it is that great cities are so often found on the banks of rivers, why peninsulas more frequently turn southward than northward, why the jute industry settled down in Dundee. You will readily realize that all this manipulation of knowledge and its application to new cases marks out what are called "problems" as the special sphere of constructive study. In acquisition we depend largely upon the memory, in constructive work we depend more upon the reason.
In our study we must not lose sight of the effect that our mental content produces upon the new matter that is presented to it. We learn with our minds, no doubt, but we also learn by means of the knowledge we have already acquired. We receive and understand new facts in different ways according to our mental content. A big word is sometimes used to represent this action of the mind as modified by its acquired knowledge. This word is apperception, and indicates the process by which our present knowledge acts upon any new fact that is presented to the mind. Some writers object to this word as being unnecessarily technical. They say that there is another word at present in use that will serve our purpose extremely well. They say that just as the mind takes in and acts upon knowledge, so the body takes in and acts upon food. Assimilation is the name given to the process by which the body takes in food, acts upon it, and makes some of it part of itself. Accordingly we need have no difficulty in accepting assimilation as a better word than acquisi- tion to represent the process by which the mind takes in facts and transforms at least some of them into faculty. The new ternı emphasizes the point that the two processes, assimilation and construction, are not so widely opposed as the term acquisition would suggest. For purposes of exposition I began by using the term acquisition, because I wanted to make the contrast a sharp one, but now that we understand the two kinds of study better, we can fall back upon the more accurate term assimilation.
For a very little reflection will make you see that while there is a distinct difference between the two kinds of study-work, they must not be regarded as entirely separate from or independent of each other: they are not mutually exclusive; they necessarily interpenetrate. Assimilation does not consist entirely in gathering in new facts, nor does construction confine itself to the manipulation and application of facts already acquired. The two processes to some extent overlap. In acquiring new facts we must always use a little reason; while in constructive work we cannot always rely upon having all the necessary matter ready to hand: we have frequently to stop our constructive work for a little in order to acquire some new facts that we find to be necessary. Thus we acquire a certain number of new facts while we are reasoning about things; and while we are engaged in acquiring new matter we must use our reason at least to some small extent.
Students differ in the way they regard the two forms of study. Assimilative work is generally regarded as easier than constructive. The more commonplace student rather likes to sit down deliberately to master a certain amount of detail, to lay in a good store of definite information. He knows where he is with this sort of work. It does not exhaust him: he is not worried with that call for initiative that marks work of the constructive kind. On the other hand, many capable students find it almost intolerable to sit down and steadily amass material. They want rather to keep on applying material that they have already at their disposal. Now with such students it may be possible to arrange that they shall do most of their assimilation in the process of working out problems. Instead of sitting down systematically to acquire certain bits of knowledge which may then be applied to problems, they may begin with the problems and then acquire, as they need them, the necessary facts. In this case they would always have the stimulus of a definite purpose in acquiring any necessary piece of information. The danger of getting information in this way is that there is almost certain to be various gaps left in the pupil's knowledge. The purely assimilative student ordinarily studies his subjects in a very systematic way, and thus secures that his facts are logically arranged and that there are no gaps. It is highly desirable, therefore, that those who prefer to acquire their knowledge in the active process of doing constructive work, should arrange for a short supplementary course extending over the ground covered by that constructive work, so that the inevitable gaps may be decently filled.
Though of the two forms of study-work the assimilative is sometimes spoken of as being less important than the other, we must not forget that both are essential for a real mastery of any subject. We shall see later that for examination work too great importance is attached to the merely assimilative side, though even in examinations there is now a tendency to change matters so as to give greater prominence to the constructive side. But apart from examination requirements, there is need for the somewhat more systematic study involved in the ordinary assimilative process. If we do nothing but use material already acquired, and add new material only incidentally, we run the danger of getting a one-sided view of certain subjects, and of missing some facts that, though not likely to be disclosed in the constructive process, yet would be of great value in giving a fresh direction to that process. In any case, the man who desires to have a really all-round acquaintance with a subject must be prepared to devote a certain amount of time to the direct acquisition of facts as facts.
Some subjects lend themselves specially to the constructive form of study. These are they in which from certain known facts it is possible to infer a great many more. In such subjects we are continually making assumptions with regard to the matter in hand, and proceeding to verify or correct these assumptions. This is really a process of guessing, carried on under legitimate conditions. As a rule, schoolmasters and professors have a deadly animosity against guessing. It is their custom to complain bitterly about foolish answers as the result of mere guessing. But the introduction of the word mere makes an important difference, for it implies that there is a kind of guessing that is not open to obloquy. Indeed, we have to recognize the fact that in their ordinary work students are guessing very nearly all the time. Unless they are dealing with matters that they have learned by the mere process of assimilation, all their answers are reached by a system of guesswork. It is true that this guessing has a sound foundation, and is, in fact, the only way in which real progress can be made. If a question is put in such a way that we are able to remember the exact answer that we know it requires, we can answer with the certainty of being right. But in most of our other answers we have little more than a feeling of probability.
It has to be admitted that in certain lines of reasoning we are able to come to conclusion after conclusion with certainty, even though we have never had occasion to deal with the matters in question on any previous occasion. Such is the state of affairs when we are concerned with what is technically known as reasoning. This consists in the application of certain very vague but universal laws of thinking, usually known as the Laws of Thought as Thought. When these laws are written out they appear to be very empty and formal, and indeed to be somewhat silly, or at the best superfluous.
The first of these portentous laws is known as the Law of Identity, which maintains that whatever is, is; or that A is A. It is sometimes represented by the formula, that does not seem to get us much further forward, A = A.
The second is called the Law of Non-Contradiction: it runs—whatever is contradictory is unthinkable. It, too, has a formula: A = not - A = O. Or if this does not please you, then you may choose: A - A = O. To help you to attach some meaning to these perplexing formulæ, you may take as an example the fact that any statement you may make cannot be true and false at the same time, and tested in the same way. We have to put in those two qualifications, since it is possible, for example, for John Smith to be both guilty and not guilty of the murder of Richard Robinson. He may have known that Robinson was about to walk during a fog over a railway bridge that had been broken in the middle during a recent gale. By giving no warning, Smith was morally guilty of murdering Robinson. But since, as a matter of fact, Smith had done nothing at all in the matter, he is not legally guilty of the murder. In the same way, a watch may be both right and wrong at the same moment: right with the town clock, but wrong by the Greenwich standard.
The third law is that of the Excluded Third, or the Excluded Middle. This tells us that of two repugnant notions that cannot both exist together, one or other of them must exist. It has been thus expressed: "Of contradictory attributions we can affirm only one of a thing; and if one be explicitly affirmed, the other is implicitly denied. A either is or is not. A either is or is not B." Either there are mermaids or there are not mermaids. There is no intermediate state. John Smith cannot in the eyes of the law be both guilty and not guilty of the murder of Richard Robinson, but he must be one or the other.
Now I do not expect that you will have the least inclination to question any of these laws. You could not break them even if you tried. What troubles you, no doubt, is that you do not quite see the necessity to state them at all. They seem so empty as to be quite useless. And yet it is because these laws are there and cannot be broken that we can argue with one another and be quite sure that our minds will work uniformly.
But if we must all obey these Laws of Thought as Thought, and if all our minds work uniformly on the same principles, how does it come about that we ever reach different conclusions? Have you ever considered how it is that an honest Radical and an honest Conservative, from an examination of the same facts, come to diametrically opposite conclusions? From what we have said about these laws, we might naturally expect that from the same facts only one conclusion could be drawn, and if it depended merely on the laws, this would be true; but other things have to be taken into consideration. The English philosopher John Locke was of the opinion that two men must come to the same conclusion on any subject if the following conditions were observed: (1) they must know all the circumstances of the case; (2) they must be free from bias; (3) they must give their minds seriously to the subject. Men differ in their opinions because they cannot observe all these conditions, and in fact, when we look into the matter, we find that very few people observe any one of them.
It is obviously impossible for any man to hope to know all the circumstances of any case, for this would really imply that he knew all about everything in the universe since, after all, everything is related to everything else in some way or other, however remote. It would be enough, indeed, if our honest Radical and qur honest Conservative knew exactly the same facts, but even this is all but impossible, since all the knowledge that each possesses about other things would affect his knowledge about the particular facts that are under discussion on any one occasion.
But the second condition is quite as hard to fulfil. It is almost impossible for a man to empty himself of his preferences and dislikes. He may make the most strenuous efforts to keep a perfectly fair mind, yet he will find that his likes and dislikes do come in and interfere with the soundness of his decision. It has to be remembered that this does not mean that he always favours his own side. The effort to be quite fair may result in the Radical or the Conservative giving an unfair advantage to the view he dislikes. When a fair man gives to an opponent the benefit of the doubt, it almost always means that the opponent is getting the advantage of a bias. Thus in the effort to be fair to all his pupils, a schoolmaster who has a son in his class is apt to be more severe on his son than on the other boys.
It is when we come to the third condition that there is hope, for the honest man can at least give his mind to the subject. Most of the opinions of the ordinary man come to him more or less ready-made. He accepts the opinions of others, or if he strikes out on his own account, he often does so after a merely superficial examination of the facts of the case. As a student, it is your first business to give your mind seriously to all those matters submitted to you on which you are expected to pass an opinion. In the purely assimilative process you may, under certain conditions, regard the material supplied as already guaranteed, but the moment you enter upon constructive work you must be prepared to give your mind to a critical examination of the matters presented to you.
So long as we are working within the realm of the Laws of Thought we can be quite certain of our answers. We have no need to hesitate. There is no room for guesswork. If I am told that, at the age of seventy-two, John Locke died in the same year that the Battle of Blenheim was fought, and that this battle was fought in the year 1704, there is no guesswork whatever in my saying that he was born in the year 1632. Thackeray tells a story about an abbé who called upon a certain count, and while waiting for the arrival of the host did his best to amuse the count's other guests by telling them of some of his experiences. He mentioned how interesting it was to hear the confessions of sinners, and added piquancy to his talk by saying that his first penitent was a murderer. When the count arrived he was very glad to see his friend, and turning to his guests, remarked that the abbé was one of his oldest friends. "In fact," he concluded, "I was the abbé's first penitent." The guests could draw only one conclusion. The count had proclaimed himself a murderer. There was no possible room for doubt.
But we are not always in a position to adopt this tone of certainty. We have to balance one thing against another, and come to a conclusion that seems on the whole the most probable in the circumstances. This process of trying to get at the truth by estimating probabilities is not open to the objections usually brought against guessing. If you are asked some question the answer to which you do not know, and make a shot at random, this is guessing, and is objectionable. But if you have some reason for giving one answer rather than any other, you cannot be said to be guessing in the bad sense of that term, even though you are not at all sure that your answer is right. Guessing in the better sense of the term may be said to be the jumping to a conclusion on insufficient grounds, but with a full knowledge of the uncertainty of the result. The conclusion is the best we can reach with the material at our disposal. This form of guessing is not to be discouraged. It is a step towards the solution of a problem, as is suggested in the lines:
"The golden guess,
That's morning star to the fair round of truth."
What scientific men call hypothesis is merely a carefully guarded form of guessing. If we assume a certain state of affairs such as seems likely to explain a particular fact, and then test the state of affairs to see how far it does explain the fact and how far it is consistent with what we know of other things, we are said to form an hypothesis and to test it. Between the random shot with no justification and the reasoned certainty that we have in applying the Laws of Thought there is to be found a wide range of answers of varying degrees of certainty, and the manipulation of this doubtful region is the realm of practical thinking.
By practical thinking we mean that kind that leads to new knowledge. There is a kind of thinking that consists in bringing out clearly what is implied in what we know already. When we think in this way, we are said to think deductively, and we have the encouraging assurance that in deduction we cannot go wrong. If we are assured that all dogs have the heart divided into four compartments and that our Cæsar is a dog, then we can infer with absolute certainty that our Cæsar has his heart divided into four compartments. Here we pass from two statements called premises to a third statement called a conclusion, with the absolute conviction that if the premises are true the conclusion cannot help being true. If all great admirals are blind of one eye, and if Blake is a great admiral, then nothing can shake the belief of the deductive logician that Blake has only one eye. It is of no use pointing out cases of great admirals who are not blind of an eye. The logician repeats, "If all great admirals," etc., then Blake must be blind of an eye. If the premises are true the conclusion must be true: but for the truth of the premises the logician of this type does not hold himself responsible. Let others see to that.
It is in securing the truth of the premises that we engage in what we have called practical thinking. If we confine ourselves to deductive logic, we shall certainly never make any mistakes. We shall attain to greater clearness about what we already know, and this is rather an important matter; but we shall make no progress: we shall never get any further forward. The kind of logic that takes a little risk of error, but promises a chance of progress, is called inductive. All our reasoning in deductive logic depends upon the truth of the statement that, "whatever is true of a whole class is true of every member of that class." No one can deny this truth. It is self-evident. When we say that every member of a class possesses certain qualities it is only saying the same thing over again to maintain that any one member of that class possesses these qualities.
In induction there is a corresponding general statement on which all our reasoning is based, and this is that nature acts uniformly: that is, that whatever happens under certain conditions will happen again in exactly the same way if all the conditions are repeated exactly as they existed in the first case. Our belief in the uniformity of nature is strong. All our experience strengthens us in our faith in the uniformity with which she works, but we do not have that absolute certainty that we have about the workings of deductive logic. These depend on the applications of the Laws of Thought as Thought, and we have found that no one can even think of denying these. In induction, on the other hand, we depend practically on our experience, and our experience frequently misleads us, because we are not always able to interpret it aright. Men's experience showed them for centuries that swans were always white, but by and by it was found that the swans in Australia are black. So that centuries of experience are not enough to make us quite sure of conclusions that we reach by induction.
The black swan supplies a very good illustration of the working of the two kinds of logic. With a black swan before him, the deductive logician goes through his ceremonial:
All swans are white.
This creature is a swan.
Therefore this creature is white.
The common-sense person objects that the creature is obviously black. All that the deductive logician has to say is that if it is black it is not a swan, and he is quite right: for deductive logic always starts with an agreement about the terms used. It is quite true that if the term swan includes among the other recognized qualities that of whiteness, then the blackness of this creature precludes it from sharing the name of swan with other creatures that do fit in with the definition deliberately adopted. It is left for the inductive logician to point out that this black creature has all the other qualities that are essential to swanhood, and that therefore the definition of swan should be so changed as to include this black specimen.
We thus see that Induction takes upon itself to modify premises. It seeks to provide new material that enables us to pass on to new generalizations. Naturally it wants to be as sure of its ground as is possible under the circumstances. It cannot get rid of all chance of error, and must be prepared for occasional mistakes, but by taking reasonable precautions it reduces the chance of error to a minimum. One of the chief precautions is to see that we do not draw an induction from too few cases. We want to have a great number of examples before we come to a general conclusion. A child lets a book fall and finds that the binding has been injured, and that part of the paper pasted on the inside of the cover has been torn off, revealing a picture underneath. The picture happens to be there merely because the binder, in using scrap-paper, chanced upon a bit that had a picture on it. The child, however, being unacquainted with the conditions of wise induction, at once jumps to the conclusion that if you remove the paper from the inside of the covers of a book you will disclose a picture. After injuring a few books without disclosing another picture, the child finds it necessary to reverse his first decision, and thus learns one of his first lessons in applying the inductive method.
There must be a sufficient number of cases to warrant us in drawing a conclusion, but however great the number of cases we can never be quite sure that an exception may not occur at any moment; so we must be prepared to consider whether there is any value in a rule to which there are exceptions. Obviously such a rule may be of the greatest practical service. It is very important to know how to behave "in most cases," even if we cannot reach a rule that will work in all cases. It is only natural that the fewer the exceptions to a given rule, the greater reliance may be placed on that rule. Yet it is just those rules that have very few exceptions that are most apt to lead us into serious difficulties. For in cases of this kind we are apt to depend too much on the rule. It works almost always with excellent results, but when it does fail we are apt to be led to disaster; whereas, with a rule that is less reliable, we are always more or less on our guard, and therefore less likely to make a complete smash.
There is another consideration that ought to have weight with us in our use of induction. We must take account of the natural connexion between different phenomena. If on three different occasions we return from a week-end visit to an aunt to find that something has gone wrong with the plumber-work of our house, we will do wisely to content our- selves with a remark on the curious coincidence. There is no natural connexion between aunts and plumber-work. But if, after each of the three oссаsions on which we have eaten a new kind of cereal food, we experience an internal pain, we are entitled to connect the food with the pain and to take measures accordingly. Food and internal pain are frequently related to one another as cause and effect. Superficial resemblances, too, are apt to produce misleading conceptions. Thus it is not uncommon for a child to think that milk is white because it comes from a white cow, if the first cow that comes into his experience is of that colour. Such a child will often express great surprise the first time that he sees white milk coming from a brown cow.
This last example suggests a special kind of induction that is of practical interest because it is so frequently used in ordinary life. It is called analogy, and has given rise to an inordinate amount of quarrelling among philosophers. Here we need not enter into the details of the arguments about its exact nature. For practical purposes it may be marked off from ordinary induction by the fact that while induction is based upon a great number of different cases in which the same law is seen at work, analogy is usually regarded as limited to two cases that resemble each other in a certain number of points, and because of this resemblance are assumed to be alike in certain other points. If we compare the planet Mars with the earth and find that the two resemble each other in a great many respects, such as size, rotation, distribution of land and water, conditions of temperature and atmosphere, we may by analogy infer that Mars has inhabitants somewhat like ourselves. As a rule, analogy does not lead to a very definite conclusion, but is rather useful in indicating general similarities and probable uniformities. The great danger of analogy is that of choosing two cases that have a certain number of resemblances that are really superficial, and drawing conclusions as if the two cases were fundamentally alike. We are very apt to carry over from the one case to the other, elements that are quite incongruous in the new set of circumstances to which they are transferred. Thus, when it is argued that under our present laws a wife is merely an unpaid servant, elements are introduced in the case of the wife that are quite foreign to the case of the servant. The important point to be kept in view in analogy is that it is sufficient if the two cases can be shown to be parallel in the points that are essential to the matter under discussion. If, for example, the flow of ideas through the mind is compared to a stream it is a silly objection to say that this is incorrect, since ideas are not wet.
We have seen that by experience, observation, induction and analogy we, acquire certain materials for the framing of premises by means of which we may reach clearly expressed conclusions. But in the course of our ordinary life we are not so much concerned with finding out and enunciating general truths as in making practical applications of these truths. No doubt these general truths are there, but they are very frequently acted upon without being clearly realized, and practical persons are sometimes inclined rather to pride themselves on not troubling with general principles, and on confining themselves to methods that they have found to work. This is the attitude of the person who works by rule of thumb, and by the results of actual experience unguided by thought. People of this type who have acquired a knowledge of big words like to call themselves empirics: other people call them quacks.
It has to be remembered that it is possible to use all the machinery of thought and remain intensely practical. What is commonly called practical thinking is differentiated from any other kind of thinking only by the fact that it has a definite practical end which is obvious to other people. But there is only one kind of thinking, whether the process ends in discovering the best way of mending a boot, or in the solution of a metaphysical problem. Thinking has been defined in many ways, but the definition that best suits our present purpose is "the application of means to ends, so long as we work by means of ideas." We cannot be said to think when we merely fumble. If the clock on the mantelpiece has stopped, and we have no idea how to make it go again, but mildly shake it in the hope that something will happen to set it going, we are merely fumbling. But if, on moving the clock gently so as to set the pendulum in motion, we hear it wobbling about irregularly, and at the same time observe that there is no ticking of any kind, we come to the conclusion that the pendulum has somehow or other escaped the little catch that connects it with the mechanism, we have been really thinking. From the fact that the pendulum wobbles irregularly we infer that it has lost its proper catch. From the fact that there is no ticking at all we infer the same thing, for even when there is something wrong with the clock that will prevent it from going permanently, if the pendulum is set in motion by force from without it will tick for a few seconds before it comes to rest again. The important point to observe is that there must be inference. This is always indicated by the word therefore or its equivalent. If you reach a conclusion without having to use or at any rate imply a therefore, you may take it for granted that you have not been really thinking, but only jumping to conclusions.
Not all fitting of means to ends is thinking. The story is told of a man who set out with his dog to have a sail. His boat was about a mile from home, and when he reached it he was disappointed to find it three-quarters full of water. His chagrin was increased when he found that the dipper was not there, so that it was impossible to bale out the water. Unwilling to walk the mile home to fetch the dipper, he thought he would enlist the services of the dog. Looking at the animal, he put his hollowed hand into the water and threw out a handful or two, in the hope that the dog would understand that the dipper was needed. The dog nodded, went home, and returned with the dipper. This is so wonderful that the ordinary reader is apt to be a little incredulous. But the story is vouched for by a competent psychologist whose comment, however, is that it was not a case of thinking at all, but only the completing of a picture previously seen by the dog. On many previous occasions the dog had seen the same picture—his master, the boat, the water, the dipper, the water being thrown out. The picture on this occasion was incomplete, for the dipper was lacking. What the dog did was merely to complete the picture to which he had become accustomed. He was fitting means to ends no doubt, but not by the use of ideas. There was no therefore in the case. Had there been real thinking, it would have gone something like this. The dog reaches home, and to his disappointment does not find the dipper in the outhouse where he expected to see it. There is nothing that looks sufficiently like the dipper to be substituted for it on its mere general resemblance. Is there anything else that will serve the master's purpose? Well, there is the sponge in the bath-room. If it were dipped in the water it would take up a great deal, which might then be squeezed out, and in this way the boat might be emptied almost as quickly with the sponge as with the dipper. Had the dog acted upon these considerations and returned with the sponge, the exacting psychologist would have admitted that there had been a case of thinking.