"I DID it without thinking." When we come to reflect, this remark would apply to most of the actions we perform in our ordinary daily routine. Many of our actions are instinctive or automatic responses to certain situations: thus we blink if a threatening fist suddenly approaches close to the face, we shade our eyes in an unaccustomed glare, and we step out of the way of some obstacle in our path. Many again are matters of habit — having discovered the way to act, either for ourselves or by learning from others, we have performed the action so often that when the appropriate situation occurs our response is almost involuntary and requires no more perhaps than a momentary thought.
But when we are confronted with a difficulty, perplexity, or problem, that is, an unfamiliar situation to which we have no response ready, either instinctive or habitual, then we 'put on our thinking cap'; for thinking is the characteristically human method of seeking a solution, as opposed to the haphazard, hit or miss, trial and error method common in the rest of the animal world. It is this power of dealing with a novel situation by reflection, without overt action, that is the distinguishing mark of homo sapiens.
Thinking therefore should first of all be distinguished from day-dreaming, in which we allow our minds to wander at random or to indulge in idle fancies or to build castles in the air without the direction exercised by the will-power. Thinking is essentially purposive — directed and controlled, at any rate in its earlier stages, by the conscious exercise of will, and set in motion by the conscious realisation of the existence of a problem demanding solution. It is true that if a solution is slow in forthcoming, the thinking process thus initiated may be continued, without any conscious direction or interference on our part, at times when our conscious thoughts are otherwise occupied or even when we are asleep. At these times, the solution might be said to be 'hatching,' so they are known as 'incubation' or 'gestation' periods; and as a result of this non-conscious process, often the solution occurs to the conscious mind when we least expect it — in a flash or inspiration, as we say, comparable to that experienced by Archimedes in his bath. But it is seldom that such Eureka's come 'out of the blue': they are more often the unexpected, but nevertheless merited, results of previous conscious hard thinking and concentration. And 'intuitions,' often regarded as peculiarly characteristic of the feminine mind, probably occur in a similar way — that is, when they are not idle guesses or outlets for prejudice.
The kind of thinking then that we are considering is controlled, constructive thinking, directed towards the solution of a problem. The problem may be a practical or a theoretical one. It may be to repair a faulty piece of mechanism in a bicycle or a motor-car, to find the answer to a problem in Arithmetic or Geometry, to arrest the spread of an epidemic, to discover the secrets of atomic energy, to find the missing 'light' in an acrostic or the hidden clue in a crossword, to ease the congested traffic in a large town, to find an explanation of the existence of evil, to translate a piece of Ovid or La Fontaine, to track down a criminal, to find a quicker, more convenient way home from the office, to decide what candidate to vote for in an election, or to find out why Athens or Rome declined and fell.
But whatever the problem, practical or theoretical, grave or trivial, the thinking process is essentially the same and usually passes through the following stages:
Here is a trivial situation which illustrates the process at work.
Here is another example — this time a more serious problem presented to a medical officer. As you read it, try to pick out the same six stages in the development of its solution.
"A medical officer is summoned to investigate an epidemic of scarlet fever in a town of 20,000 inhabitants. His object is to discover the cause of the outbreak, in order if possible to remove it. He first has a list made of all the cases, with the addresses of the patients and the dates of their coming under medical supervision. There are in all 530 cases. These are not confined to one quarter of the town, but certain streets suffer very severely, although widely separated, while other streets close to one another scarcely suffer at all. Houses seem to be attacked rather than single individuals. There are many houses in which nearly every inmate, with the exception of those immune through having had the disease before, has fallen a victim. A fortnight before there were no cases at all in the town; for the last four days they have been occurring at the rate of over 80 a day."
[Such is the evidence before the Medical Officer. It has been collected by his co-workers. If he doubts either the capacity or the honesty of any one of them, he will, of course, first verify all the testimony received from him. In this case, we will assume that such verification is unnecessary.]
The officer now proceeds to frame a tentative or working hypothesis. Is it an instance of simple infection from patient to patient? This hypothesis is at once rejected because of the officer's past experience and the knowledge he has gained from the experience of other observers. It does not account for the suddenness of the outbreak, nor yet for the simultaneous seizure of whole families. An epidemic caused by repeated contact would be gradual, and would probably spread from district to district surely but slowly. The swift onslaught of the epidemic under consideration points to a cause affecting large numbers of people at one and the same time. So the officer frames another hypothesis. He has heard that at a village five miles away scarlet fever has occurred several times during the last few months. Once more the evidence is but testimony depending upon the authority of others, but there seems to be no reason to distrust it. This village sends milk to one of the chief milk distributors of the town. Accordingly the new hypothesis is that the epidemic is due to contaminated milk. The officer knows that outbreaks are often caused in this way. This hypothesis is tested by a deduction which will correspond to facts if the hypothesis be correct. If milk be the cause of the outbreak, the ' fever niap' will correspond to the 'round' of some milkman. Investigation shows that the infected houses are in every case supplied by the milkman who gets his milk from the infected village. The hypothesis is now almost certainly correct, but in order to be quite sure of his ground the officer makes inquiries at the suspected village, and finds one of the chief milkers suffering from scarlet fever in its most infectious stage. This man is isolated, the supply of milk from the village is suspended and the epidemic rapidly declines."(1)
It should not have been difficult to follow the course of that investigation. I propose now to consider each stage in the thinking process separately and in greater detail.
It is also very easy to confuse two questions that are rather like each other on the surface but fundamentally are very different. If, for example. we were interested in the problem of William Joyce ("Lord Haw-Haw") and wondered whether he was really guilty of high treason, we should be careful not to confuse that question with whether or not he deserved to be hanged, for that is really another matter. We should also beware of asking a question framed in such a way that it takes for granted the answer to another question which may in reality be the fundamental one. Until it has been proved beyond doubt that a man has been murdered, it will not lead a detective very far in the investigation of the cause of his death if he propounds to himself the question "Who was the murderer?" Complex questions should therefore be avoided. Again in some problematic situations, the question may be framed for us, and here it is essential that we should spend a little time in pondering over the terms carefully and in finding out exactly what is required. Examination candidates have often been known to come to grief because of failure or neglect to discover the point of a question, with the result that their answers are irrelevant, i.e., they collect the wrong data. Indeed, the data to be collected in the second part of this stage are the data which bear upon the question in which the problem has been formulated: facts acquire significance and importance relative to the questions asked. It is possible, however, that the significance of a fact does not appear until stages 3 and 4, when a tentative solution or hypothesis may send the thinker back to stage 2 for a fact he has overlooked, or even to search for evidence that was not then apparent. For example, the medical officer, when reasoning out his second hypothesis, remembered that he had heard of cases of scarlet fever in a village five miles away from the town, and this fact immediately acquired significance in the light of this hypothesis. In The Memoirs of Sherlock Holmes there is an occasion when the famous detective poked about in the mud and unearthed a half-burnt wax vesta which proved to be the vital clue. The police inspector could not think how it had escaped him; but Holmes said he saw it only because he was looking for it. This is another example of the importance of knowing what we are looking for when we are collecting data — not only as here when we are relying upon personal observation, but also when, as we often have to do, we tap the experience of others by interrogating them in person or by referring to their written works. In either case ability to ask the right questions will serve us well in eliciting the relevant information we require. For example, in C. K. Chesterton's story, The Invisible Man, referred to on p. 109, if the question asked of the four observers had been more explicitly framed in this way, "Has anyone, I do not mean anyone whom you suspect, but anyone at all, entered or left?", then the answers might have been different. It is important, too, that when we have occasion to consult books of reference we should have very clearly at the back of our minds the purpose we have in view and the points on which we require enlightenment.
As I shall have occasion to mention later, fruitful discussion and argument depend largely on sticking to the point, and a necessary preliminary is the careful and precise definition of the issue in dispute. When the issue is formulated in words, it is important to avoid using vague, ambiguous or loose terms, or, if this is not possible, to define strictly the sense and application of such terms for the purpose of the discussion in hand. When the preliminary ground has been thus cleared, very often the cause of a dispute will disappear. It is no less important to see that the question in dispute when formulated does not rest on assumptions that one party or the other is not prepared to accept; for again very often the radical cause of difference may lie, not in the question itself, but in the assumptions on which it is based.
When the medical officer has propounded the problem, he proceeds to collect, or to have collected by his assistants, all the relevant information bearing on it — the number of cases, their geographical distribution, the dates on which the cases were notified, etc. If necessary he would take steps to see that the information was verified; for he knows how essential it is that it should be based on facts and should be the result of accurate and objective observation. He would probably have the information classified, arranged and tabulated, and a large-scale map of the infected area made showing the distribution of the cases: he would thus have the data in a handy and accessible form for reference and consideration. As to what facts are relevant, his previous knowledge and experience of similar situations will have guided him. He knows, for instance, that the Christian names and surnames of the victims are not likely to have any significance, nor the fact that one infected district is a continuous row of houses with basements and another a tree-lined avenue of semidetached villas. He also realises the importance of negative evidence, e.g., information about areas not visited by the epidemic.
In thus selecting the data for examination, the clear thinker is guided by two primary considerations — they must be based upon objective fact and they must be relevant. He does not allow his personal feelings to enter into his choice. He does not, after a casual glance at the evidence, jump to any conclusion, nor does he approach the problem with a preconceived opinion, with the result of confining his attention to those data only which seem to point to this conclusion or to confirm this opinion. In other words, he is not actuated by prejudice, but by a genuine desire to get at the truth. This second stage in the process of thinking is often made ineffective by prejudice, for prejudice tends to concentrate attention in one direction and to inhibit attention in others. The prejudiced person selects facts, not for their relevance, but because they fit in with preconceived opinion; and he shuts his eyes to inconvenient facts. Prejudice, too, may be operative at this stage in affecting the thinker's power of objective observation under its influence he may see, not what really exists, but what he wants to see; and his interpretations of his sense impressions will be coloured or distorted by his feelings.
In selecting data for examination we must also beware of other possible irrational influences. In much of our thinking, we are necessarily dependent on second-hand sources of information — on what we read in books or newspapers, on what we hear on the wireless, or on what we see on the cinematograph screen. Judging the value and validity of such evidence is no easy matter. To doubt everything and to believe everything we read, hear or see in these ways are equally convenient but equally irrational solutions, as both dispense with the necessity for reflection and circumspection. Nevertheless we need to be aware of the human susceptibility to suggestion and reiteration which are part of the stock-in-trade of propagandists and used by them to influence our choice of facts and the course of our thinking generally.
I have mentioned two possible sources of data — the raw material, so to speak, used in the thinking process. There is a third — the knowledge stored in the mind and accumulated in the course of experience — the records not only of past personal observation, but of previous teaching, reading, study, and interchange of knowledge and ideas with others in the way of conversation and discussion. The value of such data will depend upon their reliability and that of the memory, for memory can magnify, minimise and distort. And their availability for use will depend upon the efficiency of the power of recall, on the way they are organised in the mind, and the kind of associatory links connecting them.
The thinker will also be able to put to use the judgments he has previously made: his previous experience will have furnished him with a number of general rules, formulae or principles which enable him not only to choose relevant data, but also to draw inferences from them and to extract meaning out of them, either taken separately or in conjunction. A detective, for example, in the course of his inquiries (i.e., collection of data) has learnt that the man whose death he is investigating was an autocrat. From his experience he has formed a judgment or opinion of the sort of behaviour to expect of an autocrat, e.g., that he likes his own way, does not suffer fools gladly, is inconsiderate of other people's feelings, resists stubbornly when attacked, brooks no opposition, and so on. He says to himself, "Autocrats, from my knowledge and experience, act in such and such a way: the dead man was an autocrat; therefore probably he acted in one or other of these ways. Similarly a broken vase may mean to a detective that it had been knocked over by accident, or smashed in the course of a scuffle, or carelessly dislodged by a maid-servant, or hit by a ricochet bullet, or blown over by a sudden gust of wind. All these possibilities of meaning occur to him as a result of judgments he has made from previous experience, in which he has noted, not only facts, but also causes and effects, similarities, contrasts, degrees, differences, incompatibilities and relationships of all kinds. Which of these meanings is to be attached to the object in the particular case under investigation will depend upon other data and other judgments. One of the latter may have been, "Results such as the rucking of the carpet, the over-toppling of a chair, the spilling of ink, the disarrangement of papers, etc., frequently follow scuffles in rooms like this one." If these phenomena were present as well as the broken vase, then he might make the inference that probably the vase was broken in the course of a scuffle. But he will not rule out the possibility that all these things were caused either by someone, perhaps the criminal, acting deliberately to cover up his tracks, or by a raving lunatic who had nothing whatever to do with the crime.
The processes just described are two: judgments, generalisations, formulae, principles, etc., are arrived at by INDUCTION, i.e., the extraction of a general rule from a number of particular instances, and applied by DEDUCTION to the particular circumstances under investigation. There are two possibilities of error: if the generalisation is based upon limited experience, it may be unreliable and thus diminish the reliability of deductions made from it; and if the generalisation is incorrectly applied, the conclusions drawn will not be warranted and may be untrue. But the oftener a generalisation is correctly applied and the conclusion drawn turns out to be true, the more reliable the generalisation becomes, and, of course, vice versa.
Let me now sum up Stage 2. It can be called the analytic stage: the situation out of which the difficulty arises is broken up; the problem is isolated and formulated; the various facts and conditions bearing upon it are collected, verified, sorted, arranged, and examined; and their significance, singly or in groups, assessed in the light of previous judgments.
It is at this and the following stages that prejudice and other irrational influences may again be operative, both in the choice of hypotheses to be considered and in the final selection for acceptance. The clear thinker will choose a solution according to its tenability in relation to the facts and its power to account for them. The prejudiced person, on the other hand, is influenced by his feelings to choose the most agreeable or the most comfortable solution and to discard that which he dreads or dislikes. Other irrational people are apt to be influenced by all sorts of irrelevant considerations — — they may, for example, choose a solution because it is novel, arresting, or sensational, or merely because it resembles other solutions recently arrived at in different situations, or because it exhibits striking coincidences, or because it seems to confirm suspicions widely spread or popularly held at the moment, or because it is in keeping with some pet superstition.
Thus at these stages also it is necessary to issue a warning against 'jumping to conclusions.' It is true, as has already been pointed out, that sometimes the satisfactory solution may suggest itself unexpectedly; but judgment on a hypothesis thus suggested should be suspended until its consequences have been reasoned out in the way described in Stage 4.
This procedure on the part of a detective is analogous to a 'controlled' experiment in a scientific laboratory, i.e., an experiment in which all the ingredients and conditions of a problem are exactly reproduced to see if the same original situation is repeated. Failing the successful issue of such a test in actual experience there is no certitude that the solution arrived at is the correct one. The greatest uncertainty will prevail where human beings and human relationships provide the raw material of the problem confronting the thinker, for not only are they infinitely variable and difficult to analyse or classify exhaustively, but they are not easy to weigh, calculate or assess with objective exactitude. No generalisation concerning them can ever be otherwise than incomplete or at best more than a roughly approximate guide to future behaviour or happenings. In human affairs the incalculable is always to be reckoned with and any general rules and principles can only be applied with allowances and reservations.
This uncertainty is often made an excuse for not coming to a conclusion at all, or for refusing to put a conclusion rationally reached to a practical test. Some people when faced with a choice of alternatives will not commit themselves to one or the other, either because they fear the unpleasant consequences of being wrong, or because they mistake the attitude of 'sitting on the fence' for one of commendable impartiality. Others when faced with the consequences of a conclusion that appears to follow from a rational examination of the available facts shrink from putting it to a practical trial on the ground that 'it's all very well in theory, but it won't work in practice.' If such are the results of 'thinking' for such people, then it would be better if they saved themselves the trouble; for unless a conclusion is reached and used as the basis of subsequent action or further experiment, thinking is not complete and its primary object unattained. Those who suspend judgment indefinitely because immediate certainty is not attainable are waiting for the Greek Calends. The clear thinker suspends his judgment only as long as the circumstances of his problem permit, and no longer: when the time comes to act, he will act with courage and firmness, even if only on a balance of probabilities. He may be wrong, but it is better to be wrong than perpetually indecisive; and if he is wrong then, as Huxley says, some day he will be lucky enough to knock his head against a new fact that will set him right again. The clear thinker knows his task is never finished. He knows that there is no contradiction involved in making decisions and at the same time preserving an open mind. He knows that his judgments will have to be submitted to the test of new facts and new experience as they come along and be strengthened, modified, or abandoned accordingly.
Thus however careful, conscientious, and thorough the thinker's investigation may be, he may not arrive at the truth; but his solution may contribute to ultimate truth in one or other of the following ways: it may provide a further verification of an existent theory; it may modify or correct such a theory in some detail; or it may prove to be the first step in the evolution of a new theory and thus make a new contribution to human knowledge. Clear thinking may not succeed in arriving at the truth; but the truth cannot be arrived at without clear thinking. Clear thought is not necessarily creative thought, but it is the first step and the indispensable preliminary to it.
Familiarity with the nature of thinking and what it involves is necessary not only that we may practise it ourselves in trying to solve the problems that confront us, but also that we may follow with understanding and critical appreciation the course and results of the thinking of others — especially of those whose discoveries and achievements in scholarship, philosophy and science have added to human knowledge and have been recorded for our use and benefit in the books they have written. When we read and study their works, we shall do so with better advantage, if we realise that their results have been achieved by the exercise of the same powers, though perhaps in a greater degree, as those which we seek to acquire in order to make the management of our own ordinary affairs more effective; and we shall be in a better position to evaluate their achievements, if we can follow closely in the tracks of the thinking by which they were arrived at.
We should also realise and make use of the fact that the thinking process just described is not restricted to any particular field of study, but is an element common to all. Thinking follows the same lines, whether in Geometry or Geography, in Science or History, in Biology or Sociology, in the lecture room or in the laboratory; the procedures of induction and deduction apply equally to all; and 'hypothesis' and are not terms peculiar to the natural sciences. It is a great mistake to regard any of the processes of constructive thought as being the proprietary characteristic of any particular branch of learning or research. Knowledge is all one: thinking is the interchangeable handle to the tools used in its various branches; and the attainment of human welfare is the common integrating aim.
It is said that we tend progressively to know more and more about less and less. Knowledge is continually developing and expanding, and specialisation is the order of the day. There is a danger therefore that knowledge may develop in watertight departments and thus suffer fragmentation. For many years now this danger has been present to the minds of philosophers. who have put forward this or that ' subject' as the true co-ordinator and integrator, embracing the whole. But that is only inviting the development in turn of this 'subject ' into another fragment. Is it not preferable to develop an interchangeable technique of thought and to orientate all departments of study to a common aim? Then if the specialists share this common aim and system and research deeply enough into their own subjects, they will eventually discover how they interact and are interdependent, by regarding themselves as fellow-workers in a common held, dividing the labour. For this common aim and technique will provide a common ground on which they can meet to interchange the fruits of their work, and thus by communal and collaborative thinking, knowledge may escape disintegration and unreality, and retain its essential coherence and relevance to life and its pressing problems.
1. Decipher the following cryptogram, giving full particulars of your thinking at each stage in the process:
DSVIV ZIV GSV HMLDH LU BVHGVIBVZI?
2. Something happens (e.g., a change of occupation or residence) which necessitates a considerable change in your normal daily routine. State in full how you think out the best way to adapt yourself to it.
3. Thomas A. Edison said that creative genius involved 2% inspiration and 98% perspiration. What do you think he meant?
4. "Let me call your attention to the curious incident of the dog in the night-time."
"The dog did nothing at all in the night-time."
"That was the curious incident," said Sherlock Holmes. — Comment.
5.Here are three problems. In one, all the relevant data necessary for solution no more given. Of the other two, one contains some irrelevant data, and the other omits some relevant data.
Solve the first and the second. Re-state the second, omitting the irrelevant data. Try to solve the third, and by doing so discover what data must he supplied if a solution is to be found. Then re-state this one also.
N.B. — The problems are not set out in this order.
(a) On the 15th of April, 1946, the day after the commencement of British Summer Time, a man started from his house at 2.30 p.m. and walked to a village, arriving there when the church clock indicated 3.15 p.m. and when, according to the sundial on the front of the church, it was just after o'clock. After staying 25 minutes, he borrowed a bicycle and cycled back against a m.p.h. head wind by another road, half as long again as the first, at a speed twice as fast as he had walked, and reached home at 4.5 p.m. How far wrong was the church clock?
(b) At an election 10% of the people on the voting list did not vote, and 60 votes recorded were rejected as invalid. The successful candidate's majority was 308, and it was found that he had been supported by 47% of the whole number on the voting list. What was the number of valid votes cast for each candidate?
(c) In a certain district there are two evening schools. In the first 20% of the students are adults, 50% are boys and the rest are girls. If the two schools were amalgamated there would be 8% adults and 56% boys. Find the percentage of boys and girls in the second school.
6. Here are two obiter dicta of Sherlock Holmes. What have you to offer in the way of criticism?
(a) "When you have eliminated the impossible, whatever remains, however improbable, must he the truth."
(b) "When a fact appears to be opposed to a long train of deductions, it invariably proves to be capable of bearing some other interpretation."
7."But you spoke just now of observation and deduction. Surely the one to some extent implies the other."
"Why, hardly," Sherlock Holmes answered. "For example, observation shows me that you have been to the Wigmore Street post office this morning, but deduction lets me know that when there you despatched a telegram."
"Right on both points. But I confess that I don't see how you arrived at it."
"It is simplicity itself," he remarked, chuckling, "so absurdly simple that an explanation is superfluous; and yet it may serve to define the limits of observation and deduction. Observation tells me that you have a little reddish mould adhering to your instep. Just opposite the Wigmore Street office they have taken up the pavement and thrown up some earth, which lies in such a way that it is difficult to avoid treading in it on entering. The earth is of this peculiar reddish tint which is found nowhere else in the neighbourhood. So much is observation. The rest is deduction. I knew that you had not written a letter, since I sat opposite to you all morning. I see also in your open desk that you have a sheet of stamps and a thick bundle of post cards. What could you go into the post office for, then, but to send a wire? Eliminate all other factors, and the one which remains must be the truth." — Conan Doyle, The Sign of Four (abridged).
Critical comments, please.
From the earliest times the mechanism of fire had been a matter of some experiment and much speculation among the curious-minded. By the end of the seventeenth century it was generally accepted that:
In 1731 Georg Ernst Stahl put forward "The Phlogiston Theory" to account for these facts. His ideas were
This theory was widely accepted because it seemed to explain many quantitative facts about burning; but it did not account for the increase in weight on the calcination of metals. When this was pointed out to the holders of the 'phlogiston theory,' they gave four 'explanations':
Give a reasoned critical estimate of the value of each of these 'explanations.'
In 1777 Lavoisier, as the result of many years careful experiment on the calcination of metals, in which he attached great importance to weighing and measuring volumes, and enlightened by Priestley's discovery of oxygen, put forward the 'Oxygen Theory' of burning. His chief points were:
Lavoisier's theory was so utterly opposed to the 'phlogiston theory,' which had been accepted for so many years and was firmly held by such famous chemists as Priestley (d. 1804) and Cavendish (d. 1810) until their deaths, that it met with the bitterest opposition. However, Lavoisier embarked on a series of confirmatory experiments, so brilliantly conceived and executed and so conclusive in result, that his theory was finally accepted.
His chief experiments were as follows:
He heated mercury in contact with 40 cu. ins, of air until no further change took place. This took twelve days and nights. He found that the mercury became covered with a red powder, mercury calx, all of which he carefully collected; and that 8 cu. ins, of air had disappeared.
He then strongly heated all the mercury calx which he had collected. He obtained a small quantity of mercury and 8 cu. ins, of a gas which was identical with the gas, oxygen, which had recently been discovered by Priestley. He also showed that the 32 cu. ins, of gas left in his original apparatus would not support any form of burning.
What other confirmatory experiments were required to make the theory completely 'watertight'?
10. "One of the most interesting examples of scientific thinking is to be found in the history of malaria. Malaria is a fever which from the very earliest times has afflicted dwellers in the neighbourhood of marshes. Naturally the ancients concluded that the disease was caused by the water, or by exhalations from it. This view was held until quite recent times, and as the avoidance of marshes was followed by excellent results, there did not seem to be any reason to abandon the theory. But modern science was not satisfied and search was made for another hypothesis."Continue the story.
11. You are entrusted with the task of investigating the cause of
Outline your method of procedure. (N.B. Such an inquiry could be staged as a class exercise.)
12. Outline the means you would adopt to solve the following problems: