Analyzing a Complete Act of Thought

After a brief consideration in the first chapter of the nature of reflective thinking, we turned, in the second, to the need for its training. Then we took up the resources, the difficulties, and the aim of its training. The purpose of this discussion was to set before the student the general problem of the training of mind. The purport of the second part, upon which we are now entering, is giving a fuller statement of the nature and normal growth of thinking, preparatory to considering in the concluding part the special problems that arise in connection with its education.

In the first chapter, we briefly considered the nature of reflective thinking. In the second, we turned to the need to train it. Then we examined the resources, difficulties, and aim involved in that training. This discussion was meant to introduce the student to the general problem of training the mind. The second part, which we now begin, gives a fuller account of the nature and normal development of thinking. This will prepare us to consider the special problems involved in teaching people to think in the final part.

In this chapter we shall make an analysis of the process of thinking into its steps or elementary constituents, basing the analysis upon descriptions of a number of extremely simple, but genuine, cases of reflective experience.¹³

In this chapter, we will break down the thinking process into its basic steps or parts. We will base this analysis on descriptions of several extremely simple but genuine examples of reflective experience.¹³

1. "The other day when I was down town on 16th Street a clock caught my eye. I saw that the hands pointed to 12.20. This suggested that I had an engagement at 124th Street, at one o'clock. I reasoned that as it had taken me an hour to come down on a surface car, I should probably be twenty minutes late if I returned the same way. I might save twenty minutes by a subway express. But was there a station near? If not, I might lose more than twenty minutes in looking for one. Then I thought of the elevated, and I saw there was such a line within two blocks. But where was the station? If it were several blocks above or below the street I was on, I should lose time instead of gaining it. My mind went back to the subway express as quicker than the elevated; furthermore, I remembered that it went nearer than the elevated to the part of 124th Street I wished to reach, so that time would be saved at the end of the journey. I concluded in favor of the subway, and reached my destination by one o'clock."

1. "The other day, I was downtown on 16th Street when a clock caught my eye. Its hands pointed to 12:20. That reminded me that I had an appointment on 124th Street at one o'clock. The streetcar had taken an hour to bring me downtown. So I figured I would probably be twenty minutes late if I took it back. I could save twenty minutes by taking a subway express. But was there a station nearby? If not, I might lose more than twenty minutes looking for one. Then I thought of the elevated train and saw that a line ran within two blocks. But where was the station? If it was several blocks above or below the street I was on, I would lose time instead of gaining it. I turned back to the subway express because it was faster than the elevated train. I also remembered that it went closer to the part of 124th Street I wanted to reach. That would save time at the end of the trip. I decided to take the subway and reached my destination by one o'clock."

2. "Projecting nearly horizontally from the upper deck of the ferryboat on which I daily cross the river, is a long white pole, bearing a gilded ball at its tip. It suggested a flagpole when I first saw it; its color, shape, and gilded ball agreed with this idea, and these reasons seemed to justify me in this belief. But soon difficulties presented themselves. The pole was nearly horizontal, an unusual position for a flagpole; in the next place, there was no pulley, ring, or cord by which to attach a flag; finally, there were elsewhere two vertical staffs from which flags were occasionally flown. It seemed probable that the pole was not there for flag-flying.

2. "A long white pole extends almost horizontally from the upper deck of the ferryboat I take across the river every day. It has a gilded ball at its tip. When I first saw the pole, it reminded me of a flagpole. Its color, shape, and gilded ball fit that idea, and these details seemed to justify my belief. But I soon noticed some problems. The pole was almost horizontal, an unusual position for a flagpole. Also, there was no pulley, ring, or cord for attaching a flag. Finally, two vertical poles stood elsewhere on the boat, and flags were sometimes flown from them. It seemed likely that the long white pole was not there for flying a flag.

"I then tried to imagine all possible purposes of such a pole, and to consider for which of these it was best suited: (a) Possibly it was an ornament. But as all the ferryboats and even the tugboats carried like poles, this hypothesis was rejected. (b) Possibly it was the terminal of a wireless telegraph. But the same considerations made this improbable. Besides, the more natural place for such a terminal would be the highest part of the boat, on top of the pilot house. (c) Its purpose might be to point out the direction in which the boat is moving.

"I then tried to imagine all the possible purposes of such a pole. I considered which purpose the pole was best suited for: (a) Perhaps it was an ornament. But all the ferryboats and even the tugboats had similar poles, so I rejected that idea. (b) Perhaps it was a terminal for a wireless telegraph. But the same facts made that unlikely. Besides, a more natural place for a terminal would be the highest part of the boat, on top of the pilot house. (c) The pole might point in the direction the boat was moving.

"In support of this conclusion, I discovered that the pole was lower than the pilot house, so that the steersman could easily see it. Moreover, the tip was enough higher than the base, so that, from the pilot's position, it must appear to project far out in front of the boat. Moreover, the pilot being near the front of the boat, he would need some such guide as to its direction. Tugboats would also need poles for such a purpose. This hypothesis was so much more probable than the others that I accepted it. I formed the conclusion that the pole was set up for the purpose of showing the pilot the direction in which the boat pointed, to enable him to steer correctly."

"In support of this conclusion, I found that the pole was lower than the pilothouse. The steersman could therefore easily see it. Also, the tip was enough higher than the base that, from the pilot's position, it must have appeared to project far in front of the boat. Moreover, because the pilot was near the front of the boat, he would need some such guide to its direction. Tugboats would also need poles for this purpose. This explanation was so much more likely than the others that I accepted it. I concluded that the pole was there to show the pilot which way the boat pointed, so he could steer correctly."

3. "In washing tumblers in hot soapsuds and placing them mouth downward on a plate, bubbles appeared on the outside of the mouth of the tumblers and then went inside. Why? The presence of bubbles suggests air, which I note must come from inside the tumbler. I see that the soapy water on the plate prevents escape of the air save as it may be caught in bubbles. But why should air leave the tumbler? There was no substance entering to force it out. It must have expanded. It expands by increase of heat or by decrease of pressure, or by both. Could the air have become heated after the tumbler was taken from the hot suds? Clearly not the air that was already entangled in the water. If heated air was the cause, cold air must have entered in transferring the tumblers from the suds to the plate. I test to see if this supposition is true by taking several more tumblers out. Some I shake so as to make sure of entrapping cold air in them. Some I take out holding mouth downward in order to prevent cold air from entering. Bubbles appear on the outside of every one of the former and on none of the latter. I must be right in my inference. Air from the outside must have been expanded by the heat of the tumbler, which explains the appearance of the bubbles on the outside.

3. "I was washing tumblers in hot, soapy water and placing them mouth down on a plate. Bubbles appeared on the outside of the tumblers’ mouths and then went inside. Why? The bubbles suggest air, which I realize must come from inside the tumblers. I see that the soapy water on the plate keeps the air from escaping except in bubbles. But why should air leave the tumbler? Nothing was entering to force it out. The air must have expanded. Air expands when heat increases, pressure decreases, or both happen. Could the air have warmed up after the tumbler was taken from the hot soapy water? Clearly not the air that was already trapped in the water. If heated air caused the bubbles, cold air must have entered while I moved the tumblers to the plate. I test this idea by taking out several more tumblers. I shake some to make sure cold air is trapped in them. I take others out with their mouths facing down to prevent cold air from entering. Bubbles appear on the outside of every tumbler I shook, but on none of the others. My conclusion must be right. Air from outside must have expanded because of the tumbler’s heat. This explains why bubbles appeared on the outside.

"But why do they then go inside? Cold contracts. The tumbler cooled and also the air inside it. Tension was removed, and hence bubbles appeared inside. To be sure of this, I test by placing a cup of ice on the tumbler while the bubbles are still forming outside. They soon reverse."

"But why do the bubbles then go inside? Cold makes things contract. The tumbler cooled, and so did the air inside it. The tension was relieved, so bubbles appeared inside. To make sure this is right, I place a cup of ice on the tumbler while bubbles are still forming outside. They soon reverse."

These three cases have been purposely selected so as to form a series from the more rudimentary to more complicated cases of reflection. The first illustrates the kind of thinking done by every one during the day's business, in which neither the data, nor the ways of dealing with them, take one outside the limits of everyday experience. The last furnishes a case in which neither problem nor mode of solution would have been likely to occur except to one with some prior scientific training. The second case forms a natural transition; its materials lie well within the bounds of everyday, unspecialized experience; but the problem, instead of being directly involved in the person's business, arises indirectly out of his activity, and accordingly appeals to a somewhat theoretic and impartial interest. We shall deal, in a later chapter, with the evolution of abstract thinking out of that which is relatively practical and direct; here we are concerned only with the common elements found in all the types.

These three cases were deliberately chosen to form a series, from simpler to more complicated examples of reflection. The first illustrates the kind of thinking everyone does in the course of a day’s work. Neither the information nor the ways of handling it go beyond everyday experience. The last presents a problem and a method of solving it that would likely occur only to someone with some prior scientific training. The second case forms a natural transition. Its materials fall well within ordinary, unspecialized experience. But the problem is not directly involved in the person’s work. Instead, it arises indirectly from the person’s activity and therefore appeals to a somewhat theoretical and impartial interest. In a later chapter, we will discuss how abstract thinking develops from relatively practical and direct thinking. Here, we are concerned only with the elements common to all these types of thinking.

Upon examination, each instance reveals, more or less clearly, five logically distinct steps: (i) a felt difficulty; (ii) its location and definition; (iii) suggestion of possible solution; (iv) development by reasoning of the bearings of the suggestion; (v) further observation and experiment leading to its acceptance or rejection; that is, the conclusion of belief or disbelief.

On examination, each example reveals five logically distinct steps, some more clearly than others: (i) a felt difficulty; (ii) identifying and defining the difficulty; (iii) suggesting a possible solution; (iv) reasoning through the implications of the suggestion; (v) further observation and experiment, leading to acceptance or rejection of the suggestion. The conclusion is belief or disbelief.

1. The first and second steps frequently fuse into one. The difficulty may be felt with sufficient definiteness as to set the mind at once speculating upon its probable solution, or an undefined uneasiness and shock may come first, leading only later to definite attempt to find out what is the matter. Whether the two steps are distinct or blended, there is the factor emphasized in our original account of reflection—viz. the perplexity or problem. In the first of the three cases cited, the difficulty resides in the conflict between conditions at hand and a desired and intended result, between an end and the means for reaching it. The purpose of keeping an engagement at a certain time, and the existing hour taken in connection with the location, are not congruous. The object of thinking is to introduce congruity between the two. The given conditions cannot themselves be altered; time will not go backward nor will the distance between 16th Street and 124th Street shorten itself. The problem is the discovery of intervening terms which when inserted between the remoter end and the given means will harmonize them with each other.

1. The first and second steps often merge. The difficulty may be clear enough to make the mind immediately consider a likely solution. Or a vague feeling of unease and shock may come first, leading only later to a definite attempt to discover what is wrong. Whether the two steps are separate or blended, the factor emphasized in our original account of reflection remains: namely, the perplexity or problem. In the first of the three cases cited, the difficulty lies in a conflict between present conditions and a desired and intended result. It is a conflict between an end and the means of reaching it. The aim is to keep an appointment at a certain time, but the present time and location do not fit that aim. The purpose of thinking is to bring the two into agreement. The given conditions cannot themselves be changed. Time will not move backward, and the distance between 16th Street and 124th Street will not shorten itself. The problem is to discover intermediate steps that, when placed between the more distant goal and the given means, will bring them into agreement.

In the second case, the difficulty experienced is the incompatibility of a suggested and (temporarily) accepted belief that the pole is a flagpole, with certain other facts. Suppose we symbolize the qualities that suggest flagpole by the letters a, b, c; those that oppose this suggestion by the letters p, q, r. There is, of course, nothing inconsistent in the qualities themselves; but in pulling the mind to different and incongruous conclusions they conflict—hence the problem. Here the object is the discovery of some object (O), of which a, b, c, and p, q, r, may all be appropriate traits—just as, in our first case, it is to discover a course of action which will combine existing conditions and a remoter result in a single whole. The method of solution is also the same: discovery of intermediate qualities (the position of the pilot house, of the pole, the need of an index to the boat's direction) symbolized by d, g, l, o, which bind together otherwise incompatible traits.

In the second case, the difficulty is that other facts conflict with the suggested and temporarily accepted belief that the pole is a flagpole. Suppose we represent the qualities that suggest flagpole with the letters a, b, c. We represent the qualities that oppose this suggestion with the letters p, q, r. Of course, the qualities themselves are not inconsistent. But they pull the mind toward different, incompatible conclusions. That conflict creates the problem. The goal here is to discover some object (O) for which a, b, c, and p, q, r may all be appropriate traits. Similarly, in the first case, the goal is to discover a course of action that combines existing conditions and a more distant result into a single whole. The method of solving the problem is also the same. We discover intermediate qualities that link the otherwise incompatible traits. These qualities, represented by d, g, l, o, include the positions of the pilot house and the pole, and the need for an indicator of the boat's direction.

In the third case, an observer trained to the idea of natural laws or uniformities finds something odd or exceptional in the behavior of the bubbles. The problem is to reduce the apparent anomalies to instances of well-established laws. Here the method of solution is also to seek for intermediary terms which will connect, by regular linkage, the seemingly extraordinary movements of the bubbles with the conditions known to follow from processes supposed to be operative.

In the third case, an observer trained to think in terms of natural laws or regular patterns notices something unusual in the bubbles’ behavior. The problem is to show that these apparent exceptions are examples of well-established laws. The method is to look for intermediate steps that connect the bubbles’ seemingly extraordinary movements to conditions known to result from the processes thought to be at work. These steps must form a regular chain of connections.

2. As already noted, the first two steps, the feeling of a discrepancy, or difficulty, and the acts of observation that serve to define the character of the difficulty may, in a given instance, telescope together. In cases of striking novelty or unusual perplexity, the difficulty, however, is likely to present itself at first as a shock, as emotional disturbance, as a more or less vague feeling of the unexpected, of something queer, strange, funny, or disconcerting. In such instances, there are necessary observations deliberately calculated to bring to light just what is the trouble, or to make clear the specific character of the problem. In large measure, the existence or non-existence of this step makes the difference between reflection proper, or safeguarded critical inference and uncontrolled thinking. Where sufficient pains to locate the difficulty are not taken, suggestions for its resolution must be more or less random. Imagine a doctor called in to prescribe for a patient. The patient tells him some things that are wrong; his experienced eye, at a glance, takes in other signs of a certain disease. But if he permits the suggestion of this special disease to take possession prematurely of his mind, to become an accepted conclusion, his scientific thinking is by that much cut short. A large part of his technique, as a skilled practitioner, is to prevent the acceptance of the first suggestions that arise; even, indeed, to postpone the occurrence of any very definite suggestion till the trouble—the nature of the problem—has been thoroughly explored. In the case of a physician this proceeding is known as diagnosis, but a similar inspection is required in every novel and complicated situation to prevent rushing to a conclusion. The essence of critical thinking is suspended judgment; and the essence of this suspense is inquiry to determine the nature of the problem before proceeding to attempts at its solution. This, more than any other thing, transforms mere inference into tested inference, suggested conclusions into proof.

2. As already noted, the first two steps may merge in a particular case. These are feeling a discrepancy or difficulty and observing it to define its character. But when something is strikingly new or unusually puzzling, the difficulty is likely to appear first as a shock or emotional disturbance. It may be a more or less vague feeling that something is unexpected, odd, strange, funny, or unsettling. In such cases, deliberate observation is needed to reveal exactly what is wrong or clarify the specific nature of the problem. To a large extent, whether this step occurs makes the difference between genuine reflection, or carefully protected critical inference, and uncontrolled thinking. If we do not take enough care to identify the difficulty, suggestions for resolving it must be more or less random. Imagine a doctor called in to prescribe treatment for a patient. The patient tells him some things that are wrong. At a glance, his experienced eye picks up other signs of a particular disease. But suppose he lets the suggestion of this disease take hold too soon and accepts it as a conclusion. His scientific thinking is cut short to that extent. Much of his skill as a practitioner lies in preventing himself from accepting the first suggestions that arise. He may even put off forming any very definite suggestion until he has thoroughly explored the trouble, or the nature of the problem. In a physician's work, this process is called diagnosis. But a similar examination is needed in every new and complicated situation to prevent rushing to a conclusion. The essence of critical thinking is withholding judgment. The essence of withholding judgment is investigating the nature of the problem before trying to solve it. More than anything else, this turns mere inference into tested inference and suggested conclusions into proof.

3. The third factor is suggestion. The situation in which the perplexity occurs calls up something not present to the senses: the present location, the thought of subway or elevated train; the stick before the eyes, the idea of a flagpole, an ornament, an apparatus for wireless telegraphy; the soap bubbles, the law of expansion of bodies through heat and of their contraction through cold. (a) Suggestion is the very heart of inference; it involves going from what is present to something absent. Hence, it is more or less speculative, adventurous. Since inference goes beyond what is actually present, it involves a leap, a jump, the propriety of which cannot be absolutely warranted in advance, no matter what precautions be taken. Its control is indirect, on the one hand, involving the formation of habits of mind which are at once enterprising and cautious; and on the other hand, involving the selection and arrangement of the particular facts upon perception of which suggestion issues. (b) The suggested conclusion so far as it is not accepted but only tentatively entertained constitutes an idea. Synonyms for this are supposition, conjecture, guess, hypothesis, and (in elaborate cases) theory. Since suspended belief, or the postponement of a final conclusion pending further evidence, depends partly upon the presence of rival conjectures as to the best course to pursue or the probable explanation to favor, cultivation of a variety of alternative suggestions is an important factor in good thinking.

3. The third factor is suggestion. A puzzling situation brings to mind something that is not present to the senses. A person's present location suggests a subway or elevated train. A stick before the eyes suggests a flagpole, an ornament, or equipment for wireless telegraphy. Soap bubbles suggest the law that bodies expand with heat and contract with cold. (a) Suggestion is the heart of inference. It involves moving from what is present to something absent. For this reason, inference is more or less speculative and adventurous. Since inference goes beyond what is actually present, it involves a leap or jump. No matter what precautions we take, we cannot be absolutely sure beforehand that the leap is justified. We can control inference only indirectly. On one hand, this involves developing habits of mind that are both enterprising and cautious. On the other, it involves selecting and arranging the particular facts that give rise to suggestions when perceived. (b) A suggested conclusion becomes an idea when it is not accepted but only considered tentatively. Other words for an idea are supposition, conjecture, guess, hypothesis, and, in more elaborate cases, theory. We suspend belief when we postpone a final conclusion until we have further evidence. Doing so depends partly on having competing guesses about the best course to take or the most likely explanation. Therefore, developing a variety of alternative suggestions is an important part of good thinking.

4. The process of developing the bearings—or, as they are more technically termed, the implications—of any idea with respect to any problem, is termed reasoning.¹⁴ As an idea is inferred from given facts, so reasoning sets out from an idea. The idea of elevated road is developed into the idea of difficulty of locating station, length of time occupied on the journey, distance of station at the other end from place to be reached. In the second case, the implication of a flagpole is seen to be a vertical position; of a wireless apparatus, location on a high part of the ship and, moreover, absence from every casual tugboat; while the idea of index to direction in which the boat moves, when developed, is found to cover all the details of the case.

4. The process of working out how an idea relates to a problem is called reasoning.¹⁴ These relations are technically called implications. Just as an idea is inferred from given facts, reasoning starts with an idea. The idea of an elevated railway leads to other ideas: the difficulty of finding a station, the time the journey takes, and the distance from the station at the other end to the destination. In the second case, a flagpole is seen to imply a vertical position. A wireless apparatus would be located high on the ship and, moreover, would not be found on every passing tugboat. But the idea of an indicator showing the boat's direction of movement, when developed, is found to account for all the details of the case.

Reasoning has the same effect upon a suggested solution as more intimate and extensive observation has upon the original problem. Acceptance of the suggestion in its first form is prevented by looking into it more thoroughly. Conjectures that seem plausible at first sight are often found unfit or even absurd when their full consequences are traced out. Even when reasoning out the bearings of a supposition does not lead to rejection, it develops the idea into a form in which it is more apposite to the problem. Only when, for example, the conjecture that a pole was an index-pole had been thought out into its bearings could its particular applicability to the case in hand be judged. Suggestions at first seemingly remote and wild are frequently so transformed by being elaborated into what follows from them as to become apt and fruitful. The development of an idea through reasoning helps at least to supply the intervening or intermediate terms that link together into a consistent whole apparently discrepant extremes (ante, p. 72).

Reasoning has the same effect on a suggested solution that closer and broader observation has on the original problem. Looking more closely at a suggestion prevents us from accepting it in its first form. Ideas that seem plausible at first often prove unsuitable or even absurd when we trace their full consequences. Even when reasoning through a supposition's implications does not lead us to reject it, the reasoning makes the idea more relevant to the problem. For example, only after thinking through the implications of the idea that a pole was an index-pole could one judge how well it fit the case at hand. Suggestions that at first seem far-fetched and wild often become useful and fruitful when their consequences are worked out. Developing an idea through reasoning helps, at least, to supply the intermediate steps that connect apparently conflicting extremes into a consistent whole (ante, p. 72).

5. The concluding and conclusive step is some kind of experimental corroboration, or verification, of the conjectural idea. Reasoning shows that if the idea be adopted, certain consequences follow. So far the conclusion is hypothetical or conditional. If we look and find present all the conditions demanded by the theory, and if we find the characteristic traits called for by rival alternatives to be lacking, the tendency to believe, to accept, is almost irresistible. Sometimes direct observation furnishes corroboration, as in the case of the pole on the boat. In other cases, as in that of the bubbles, experiment is required; that is, conditions are deliberately arranged in accord with the requirements of an idea or hypothesis to see if the results theoretically indicated by the idea actually occur. If it is found that the experimental results agree with the theoretical, or rationally deduced, results, and if there is reason to believe that only the conditions in question would yield such results, the confirmation is so strong as to induce a conclusion—at least until contrary facts shall indicate the advisability of its revision.

5. The final and decisive step is some kind of experimental confirmation, or verification, of the proposed idea. Reasoning shows that if we accept the idea, certain consequences follow. So far, the conclusion is hypothetical or conditional. Suppose we look and find all the conditions the theory requires. Suppose we also find that the features expected from competing explanations are absent. Then the tendency to believe and accept the idea is almost irresistible. Sometimes direct observation provides confirmation, as in the case of the pole on the boat. In other cases, as with the bubbles, an experiment is needed. In an experiment, conditions are deliberately arranged as an idea or hypothesis requires, to see whether the results it predicts actually occur. Suppose the experimental results match the results deduced from the theory through reasoning. Suppose there is also reason to believe that only the conditions in question would produce those results. Then the confirmation is strong enough to lead to a conclusion, at least until contrary facts suggest revising it.

Observation exists at the beginning and again at the end of the process: at the beginning, to determine more definitely and precisely the nature of the difficulty to be dealt with; at the end, to test the value of some hypothetically entertained conclusion. Between those two termini of observation, we find the more distinctively mental aspects of the entire thought-cycle: (i) inference, the suggestion of an explanation or solution; and (ii) reasoning, the development of the bearings and implications of the suggestion. Reasoning requires some experimental observation to confirm it, while experiment can be economically and fruitfully conducted only on the basis of an idea that has been tentatively developed by reasoning.

Observation occurs at both the beginning and the end of the process. At the beginning, observation helps define the difficulty more clearly and precisely. At the end, it tests the value of a tentative conclusion. Between these two points of observation, we find the more distinctly mental aspects of the whole thought cycle: (i) inference, the suggestion of an explanation or solution, and (ii) reasoning, the development of the suggestion’s relevance and implications. Reasoning requires some experimental observation to confirm it. An experiment, in turn, can be conducted efficiently and fruitfully only on the basis of an idea tentatively developed through reasoning.

The disciplined, or logically trained, mind—the aim of the educative process—is the mind able to judge how far each of these steps needs to be carried in any particular situation. No cast-iron rules can be laid down. Each case has to be dealt with as it arises, on the basis of its importance and of the context in which it occurs. To take too much pains in one case is as foolish—as illogical—as to take too little in another. At one extreme, almost any conclusion that insures prompt and unified action may be better than any long delayed conclusion; while at the other, decision may have to be postponed for a long period—perhaps for a lifetime. The trained mind is the one that best grasps the degree of observation, forming of ideas, reasoning, and experimental testing required in any special case, and that profits the most, in future thinking, by mistakes made in the past. What is important is that the mind should be sensitive to problems and skilled in methods of attack and solution.

Education aims to develop a disciplined, logically trained mind. Such a mind can judge how far to carry each of these steps in a particular situation. There are no rigid rules. Each case must be handled as it arises, according to its importance and context. Taking too much care in one case is as foolish and illogical as taking too little in another. At one extreme, almost any conclusion that ensures prompt, unified action may be better than one reached after a long delay. At the other extreme, a decision may have to be postponed for a long time, perhaps for a lifetime. A trained mind best understands how much observation, idea formation, reasoning, and experimental testing each case requires. It also makes the best use of past mistakes in future thinking. What matters is that the mind be alert to problems and skilled in methods of tackling and solving them.