Fig. 66.--Constant error and scatter in hitting at a target. The little circle was the target, but the center of the actual distribution of the attempts lies at the cross, which was drawn in afterwards. The constant error could be stated by saying that the center of distribution was so far from the target, and in such and such a direction. The scattering of the attempts can be measured also.
Experimental psychology has taken great pains in measuring the accuracy of different sorts of perception. How small a difference in length can be perceived by the eye, how small a difference of weight by the hand--these are sample problems in this line.
For example, to measure the fineness with which weights can be perceived when "hefted" in the hand, you take two objects that are alike in size and appearance but differing slightly in weight, and endeavor to decide which is the heavier just by lifting them. You try repeatedly and keep track of the number of errors, using this number as a measure of the accuracy of perception. Now, if one weight were twice as heavy as the other (one, for example, weighing 100 grams{449}and the other 200), you would never make an error except through carelessness; but if one were 100 and the other 120 grams, you would make an occasional error, and the number of errors would increase as the difference was decreased; finally, comparing 100 and 101 grams, you would get almost as many wrong as right, so that your perception of that small difference would be extremely unreliable.
ERRORS IN PERCEIVING SMALL DIFFERENCESOF WEIGHT (From Warner Brown)Difference 20 16 12 8 4 8 2 1 gramsErrors 1 2 5 18 28 81 89 44 per hundred trialsThe weights were in the neighborhood of 100 grams; eachweight was compared with the 100-gram weight, and eachsuch pair was lifted and judged 1400 times. Notice thatthe per cent of errors gradually increases as thedifference becomes smaller.
The smaller the difference between two stimuli, the more numerous the errors in perceiving it, or, the less perceptible it is, and there is no sharp line between a difference that can be perceived and one that is too small to be perceived. That is the first great result from the study of the perception of small differences.
The second great result is calledWeber's law, which can be stated as follows: In the same sort of perception, equal relative (not absolute) differences are equally perceptible. For example, from the preceding table we see that 28 per cent. of errors are made in comparing weights of 100 and 104 grams; then, according to Weber's law, 28 per cent, of errors would also be made in comparing 200 grams with 208, or 500 with 520, or 1000 with 1040 grams, or any pair of weights that stood to each other in the ratio of 100 to 104. Weber's law is only approximately true for the perception of weights, since actually fewer errors are committed in comparing 500 and 520 than in comparing 100 and 104 grams; but the discrepancy is not extremely great here, and in{450}some other kinds of perception, as especially in comparing the brightness of lights or the length of seen lines, the law holds good over a wide range of stimuli and only breaks down near the upper and lower extremes. We are familiar, in ordinary life, with the general truth of Weber's law, since we know that an inch would make a much more perceptible addition to the length of a man's nose than to his height, and we know that turning on a second light when only one is already lit gives a much more noticeable increase in the light than if we add one more light when twenty are already burning.
A third great result of this line of study is that different sorts of perception are very unequal in their fineness and reliability. Perception of brightness is about the keenest, as under favorable conditions a difference of one part in one hundred can here be perceived with very few errors. Visual perception of length of line is good for about one part in fifty, perception of lifted weight for about one part in ten, perception of loudness of sound for about one part in three. But the perception of small differences in the pitch of musical tones is keener still, only that, not following Weber's law in the least, it cannot be expressed in the same way. A person with a good ear for pitch can distinguish with very few errors between two tones that differ by only one vibration per second, and can perceive this same absolute difference equally well, whether the total vibration rate is 200, 400, or 800 vibrations per second.
An error of perception is often called an "illusion", though this term is commonly reserved for errors that are large and curious. When one who is being awakened by a bell perceives it as a tom-tom, that is an illusion. An{451}illusion consists in responding to a sensory stimulus by perceiving something that is not really there. The stimulus is there, but not the fact which it is taken to indicate. Illusion is false perception.
The study of illusions is of value, not only as showing how far a given kind of perception can be trusted, but also as throwing light on the process of perception. When a process goes wrong, it sometimes reveals its inner mechanism more clearly than when everything is running smoothly. Errors of any kind are meat to the psychologist.
Illusions may be classified under several headings according to the factors that are operative in causing the deception.
Here the stimulus is distorted by the sense organ and so may easily be taken as the sign of an unreal fact.
Separate the points of a pair of compasses by about three-quarters of an inch, and draw them across the mouth, one point above it and the other below; you will get the illusion of the points separating as they approach the middle of the mouth (where the sensory nerve supply is greatest), and coming together again as they are drawn to the cheek at the other side.
Under this same general head belong also after-images and contrast colors, and also double vision whenever for any reason the two eyes are not accurately converged upon an object. The fact that a vertical line appears longer than an equal horizontal is supposed to depend upon some peculiarity of the retina. Aside from the use of this class of illusions in the detailed study of the different senses, the chief thing to learn from them is they so seldom are full-fledged illusions, because they are ignored or allowed for, and not taken as the signs of facts. An after-image would constitute a genuine illusion if it were taken for some real{452}thing out there; but as a matter of fact, though after-images occur very frequently--slight ones practically every time the eyes are turned--they are ignored to such an extent that the student of psychology, when he reads about them, often thinks them to be something unusual and lying outside of his own experience. The same is true of double images. This all goes to show how strong is the tendency to disregard mere sensation in the interest of getting objective facts.
When an insane person hears the creaking of a rocking-chair as the voice of some one calling him bad names, it is because he is preoccupied with suspicion. We might almost call this an hallucination, [Footnote:See p. 375.] since he is projecting his own auditory images and taking them for real sensations; it is, at any rate, an extreme instance of illusion. In a milder form, similar illusions are often momentarily present in a perfectly normal person, as when he is searching for a lost object and thinks he sees it whenever anything remotely similar to the desired object meets his eyes; or as when the mother, with the baby upstairs very much on her mind, imagines she hears him crying when the cat yowls or the next-door neighbors start their phonograph. The ghost-seeing and burglar-hearing illusions belong here as well. The mental set facilitates responses that are congruous with itself.
This is probably the commonest source of everyday illusions, and the same principle, as we have seen, is operative in a host of correct perceptions. Perceiving the obliquely presented rectangle as a rectangle is an example of correct perception of this type. Perceiving the buzzing of a fly as an aeroplane is the same sort of response only that it happens to be incorrect. If the present stimulus has something in{453}common with the stimulus which has in the past aroused a certain perception, we may make the same response now as we did before--especially, of course, if the present mantel set favors this response.
Fig. 67.--The Ladd-Franklin illusion of monocular perspective. Close one eye, and hold the book so that the other eye is at the common center from which the lines radiate; this center is about 5 inches from the figure. Hold the book horizontally, and just a little below the eye.
A good instance of this type is the "proofreader's illusion", so called, perhaps, because the professional proofreader is less subject to it than any one else. The one most subjcet to it is the author of a book, for whom it is almost impossible to find every misspelled word and other typographical error in reading the proof. Almost every book comes out with a few such errors, in spite of having been scanned repeatedly by several people. A couple of misprints have purposely been left in the last few lines for the reader's benefit. If the word as printed has enough resemblance to the right word, it arouses the same percept and enables the reader to get the sense and pass on satisfied.{454}Before we began to pore over books and pictures, the lines that we saw usually were the outlines of solid objects, and now it requires only a bare diagram of lines to arouse in us the perception of a solid object seen in perspective. An outline drawing, like those of the cube and staircase used to illustrate ambiguous perspective, is more readily seen as a solid object than as a flat figure.
Fig. 68.--Aristotle's illusion.
Another illusion of this general type dates away back to Aristotle. Cross two fingers, perhaps best the second and third, and touch a marble with the crossed part of both fingers, and it seems to be two marbles; or, you can use the side of your pencil as the stimulus. In the customary position of the fingers, the stimuli thus received would mean two objects.
A much more modern illusion of the same general type is afforded by the moving pictures. The pictures do not actually show an object in motion; they simply show the object in a series of motionless positions, caught by instantaneous photography. The projector shows the series of snap-shots in rapid succession, and conceals them by a shutter while they are shifted, so as to avoid the blur that would occur if the picture were itself moved before the eyes. But the series of snap-shots has so much in common with the visual stimulus got from an actually present moving object that we make the same perceptive response.{455}The same illusion in a rudimentary form can be produced by holding the forefinger upright three or four inches in front of the nose, and looking at it while winking first the one eye and then the other. Looked at with the right eye alone it appears to be more to one side and looked at with the left eye alone it appears to be more to the other side; and when the one eye is closed and the other simultaneously opened, the finger seems actually to move from one position to the other.
Fig. 69.--The pan illusion. The two pan-shaped outlines are practically identical, but it is hard to compare the corresponding sides--hard to isolate from the total figure just the elements that you need to compare.
Here belong, probably, most of the illusions produced in the psychological laboratory by odd combinations of lines, etc. A figure is so drawn as to make it difficult to isolate the fact to be observed, and when the observer attempts to perceive it, he falls into error. He thinks he is perceiving one fact, when he is perceiving another. The best example is the Müller-Lyer figure, in which two equal lines are embellished with extra lines at their ends; you are supposed to perceive the lengths of the two main lines, but you are very apt to take the whole figure in the rough and perceive the distances between its chief parts. You do not succeed in isolating the precise fact you wish to observe.
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The most familiar form of this striking illusion is made with arrow heads, thus
In attempting to compare the two horizontal lines one is confused so as to regard the line with outward-extending obliques longer than that with inward-extending obliques, though, measured from point to point, they are equal. The same illusion occurs in a variety of similar figures, such as
where the main lines are not drawn, but the distances from point to point are to be compared; or such as
where the two distances between points are again to be compared. Angles, however, are not necessary to give the illusion, as can be seen in this figure
or in this
In the last the lengths to be compared extend (a) from the right-hand rim of circle 1 to the left-hand rim of circle 2, and (b) from this last to the right-hand rim of circle 3. The same illusion can be got with squares, or even with capital letters as
where the distances between the main vertical lines are to be compared.
Here is an another form of the same illusion
the middle lines being affected by those above and below.
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Though these illusions seem like curiosities, and far from every-day experience, they really do enter in some degree into almost every figure that is not perfectly square and simple.
Fig. 70.--The Poggendorf illusion. Are the two obliques parts of the same straight line?
Any oblique line, any complication of any sort, is pretty sure to alter the apparent proportions and directions of the figure. A broad effect, a long effect, a skewed effect, may easily be produced by extra lines suitably introduced into a dress, into the front of a building, or into a design of any sort; so that the designer needs to have a practical knowledge of this type of illusion.
Extra lines have an influence also upon esthetic perception. The esthetic effect of a given form may be quite altered by the introduction of apparently insignificant extra lines.
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Fig. 71.--The barber-pole illusion. The rectangle represents a round column, around which runs a spiral, starting ata. Which of the lines, 1, 2, 3, 4, and 5, comes closest to being a continuation ofa?
Esthetic perception is very much subject to the law of combination, and to the resulting difficulty of isolation.
One of the most interesting illusions, not being visual, can{459}only be described and not demonstrated here.
Fig. 72.--By aid of this simple figure, the Poggendorf and barber-pole illusions can be seen to be instances of the Müller-Lyer illusion, Try to bisect the horizontal line in this figure. The oblique line at the right tends to displace the right-hand end of the horizontal to the right, while the oblique at the left tends to displace the left-hand end of the horizontal also to the right. Similar displacements account for the Poggendorf and barber-pole illusions.
Fig. 73.--The Zoellner illusion. The long lines are really parallel. The illusion is increased by holding the figure so that these main lines shall be neither vertical nor horizontal. It is more difficult to "deceive the eye" in regard to the direction of vertical and horizontal lines, than in regard to the direction of oblique lines. This illusion must be related in some way to the Müller-Lyer and Poggendorf illusions, since the elements employed in constructing the three figures are so much the same.If you treat this figure according to the directions given forFig. 67, and sight along the obliques, you get an illusion of perspective.
It is called the "size-weight illusion", and may be said to be based on the old catch, "Which is heavier, a pound of lead or a pound of feathers?" Of course, we shrewdly answer, a pound's{460}a pound. But lift them and notice how they feel! The pound of lead feels very much heavier. To reduce this illusion to a laboratory experiment, you take two round wooden pill-boxes, one several times as large as the other, and load them so that they both weigh the same; then ask some one to lift them and tell which is the heavier. He will have no doubt at all that the smaller box is the heavier; it may seem two or three times as heavy. Young children, however, get the opposite illusion, assimilating the weight to the visual appearance; but older persons switch over to the contrast effect, and perceive in opposition to the visual appearance. What seems to happen in the older person is a motor adjustment for the apparent weights, as indicated by their visual appearance, with the result that the weight of larger size is lifted more strongly than the weight of smaller size; so that the big one comes up easily and seems light, the little one slowly and seems heavy.
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1. Outline the chapter.2. Show that the law of combination accounts both for many correct perceptions, and for many illusions.3. Through which of the senses are spatial facts best perceived?4. "At first, the baby very likely perceives a ball simply as something for him to handle and throw; but, through the medium of blocked response, he comes to perceive it more objectively, i.e., as an object related to other objects, and not simply related to himself." Explain and illustrate this statement.5. Give an example from the field of auditory perceptions where "isolation" is very much in evidence.6. Can you see any law analogous to Weber's law in the field of financial profit and loss? Does a dollar gained or lostseemthe same amount, without regard to the total amount possessed?7. Trial and error perception. Go about the room with closed eyes, and identify objects by touching them with the hands. Notice whether your first impression gives place to corrected impressions.8. Perception of form by "active" and "passive" touch. With the eyes closed, try to distinguish objects of different shapes (a) by letting them simply rest upon the skin, and (b) by handling them. What senses coöperate in furnishing data for "active touch"?9. Binocular parallax, or the differing views of the same solid object obtained by the two eyes. Hold a small, three-dimensional object a foot in front of the face, and notice carefully the view of it obtained by each eye separately. A pencil, pointing towards the face, gives very different views. What becomes of the two monocular views when both eyes are open at once?10. Binocular compared with monocular perception of "depth" or distance away. Take a pencil in each hand, and bring the points together a foot in front of the face, while only one eye is open. When the points seem to be nearly touching, open the other eye, and see whether the two points still seem to be close together. Repeat.
Discussions of perception that are in some respects fuller than the present chapter can be found in C. H. Judd'sPsychology, General Introduction, 2nd edition, 1917, pp. 162-194; in Titchener'sTextbook of Psychology, 1909, pp. 303-373; and in Warren'sHuman Psychology, 1919, pp. 232-269.
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We are still on the general topic of "discovery". Indeed, we are still on the topic of perception; we come now to that form of perception which is different from sense perception. The reasoner is an explorer, and the culmination of his explorations is the perception of some fact previously unknown to him.
Reasoning might be described as mental exploration, and distinguished from purely motor exploration of the trial and error variety. Suppose you need the hammer, and go to the place where it is kept, only to find it gone. Now if you simply proceed to look here and there, ransacking the house without any plan, that would be motor exploration. But if, finding this trial and error procedure to be laborious and almost hopeless, you sit down and think, "Where can that hammer be? Probably where I used it last!" you may recall using it for a certain purpose, in a certain place, go there and find it. You have substituted mental exploration of the situation for purely motor exploration, and saved time and effort. Such instances show the use of reasoning, and the part it plays in behavior.
Theprocessof reasoning is also illustrated very well in these simple cases. It is an exploratory process, a searching for facts. In a way, it is a trial and error process. If you don't ransack the house, at least you ransack your memory, in search for facts that will assist you. You recall this fact{463}and that, you turn this way and that, mentally, till some fact is recalled that serves your need. No more in reasoning than in motor exploration can you hope to go straight to the desired goal.
Animal and Human Exploration
Is man the only reasoning animal? The experimental work on animal learning, reviewed in one of our earlier chapters, was begun with this question in mind. Previous evidence on this point had been limited to anecdotes, such as that of the dog that was found opening a gate by lifting the latch with his nose, and was supposed to have seen men open the gate in this way, and to havereasonedthat if a man could do that, why not a dog? The objection to this sort of evidence is that the dog's manner of acquiring the trick was not observed. Perhaps he reasoned it out, and perhaps he got it by accident--you cannot tell without watching the process of learning. You must experiment, by taking a dog that does not know the trick, and perhaps first "showing him" how to open the gate by lifting the latch; but it was found that dogs and cats, and even monkeys, could not learn the trick in this way. If, however, you placed a dog in a cage, the door of which could be opened by lifting a latch, and motivated the dog strongly by having him hungry and placing food just outside, then the dog went to work by trial and error, and lifted the latch in the course of his varied reactions; and if he were placed back in the cage time after time, his unsuccessful reactions were gradually eliminated and the successful reaction was firmly attached to the situation of being in that cage, so that he would finally lift the latch without any hesitation.
The behavior of the animal does not look like reasoning. For one thing, it is too impulsive and motor. The typical{464}attitudes of the reasoner, whether "lost in thought" or "studying over things", do not appear in the dog, or even in the monkey, though traces of them may perhaps be seen in the chimpanzee and other manlike apes. Further, the animal's learning curve fails to show sudden improvements such as in human learning curves follow "seeing into" the problem. In short, there is nothing to indicate that the animal recalls facts previously observed or sees their bearing on the problem in hand. He works by motor exploration, instead of mental. He does not search for "considerations" that may furnish a clue.
The behavior of human beings, placed figuratively in a cage, sometimes differs very little from that of an animal. Certainly it shows plenty of trial and error and random motor exploration; and often the puzzle is so blind that nothing but motor exploration will bring the solution. What the human behavior does show that is mostly absent from the animal is (1) attentive studying over the problem, scrutinizing it on various sides, in the effort to find a clue; (2) thinking, typically with closed eyes or abstracted gaze, in the effort to recall something that may bear on the problem; and (3) sudden "insights" when the present problem is seen in the light of past experience.
Though reason differs from animal trial and error in these respects, it still is a tentative, try-and-try-again process. The right clue is not necessarily hit upon at the first try; usually the reasoner finds one clue after another, and follows each one up by recall, only to get nowhere, till finally he notices a sign that recalls a pertinent meaning. His exploration of the situation, though carried on by aid of recalled experience instead of by locomotion, still resembles finding the way out of a maze with many blind alleys. In short, reasoning may be called a trial and error process in the sphere of mental reactions.
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The reader familiar with geometry, which is distinctly a reasoning science, can readily verify this description. It is true that the demonstrations are set down in the book in a thoroughly orderly manner, proceeding straight from the given assumption to the final conclusion; but such a demonstration is only a dried specimen and does not by any means picture the living mental process of reasoning out a proposition. Solving an "original" is far from a straight-forward process. You begin with a situation (what is "given") involving a problem (what is to be proved), and, studying over this lay-out you notice a certain fact which looks like a clue; this recalls some previous proposition which gives the significance of the clue, but often turns out to have no bearing on the problem, so that you shift to another clue; and so on, by what is certainly a trial and error process, till some fact noted in the situation plus some knowledge recalled by this fact, taken together, reveal the truth of the proposition.
When you have described reasoning as a process of mental exploration, you have told only half the story. The successful reasoner not only seeks, but finds. He not only ransacks his memory for data bearing on his problem, but he finally "sees" the solution clearly. The whole exploratory process culminates in a perceptive reaction. What he "sees" is not presented to his senses at the moment, but he "sees that somethingmustbe so". This kind of perception may be calledinference.
To bring out distinctly the perceptive reaction in reasoning, let us cite a few very simple cases. Two freshmen in college, getting acquainted, ask about each other's fathers and find that both are alumni of this same college. "What class was your father in?" "In the class of 1900. And{466}yours?" "Why, he was in 1900, too. Our fathers were in the same class; they must know each other!" Here two facts, one contributed by one person and the other by another person, enable both to perceive a third fact which neither of them knew before. Inference, typically, is a response to two facts, and the response consists in perceiving a third fact that is bound up in the other two.
You do not infer what you can perceive directly by the senses. If Mary and Kate are standing side by side, you canseewhich is the taller. But if they are not side by side, but Mary's height is given as so much and Kate's as an inch more, then from these two facts you know, by inference, that Kate is taller than Mary.
"Have we set the table for the right number of people?" "Well, we can see when the party comes to the table." "Oh! but we can tell now by counting. How many are there to be seated? One, two, three--fifteen in all. Now count the places at table--only fourteen. You will have to make room for one more." This reducing of the problem to numbers and then seeing how the numbers compare is one very simple and useful kind of inference.
Indirect comparison may be accomplished by other similar devices. I can reach around this tree trunk, but not around that, and thus I perceive that the second tree is thicker than the first, even though it may not look so. If two things are each found to be equal to a third thing, then I see they must be equal to each other; if one is larger than my yardstick and the other smaller, then I see they must be unequal.
Of the two facts which, taken together, yield an inferred fact, one is often a general rule or principle, and the inference then consists in seeing how the general rule applies to a special case. A dealer offers you a fine-looking diamond ring for five dollars, but you recall the rule that "all genuine diamonds are expensive", and perceive that this{467}diamond must be an imitation. This also is an instance of indirect comparison, the yardstick being the sum of five dollars; this ring measures five dollars, but any genuine diamond measures more than five dollars, and therefore a discrepancy is visible between this diamond and a genuine diamond. You can't see the discrepancy by the eye, but you see it by way of indirect comparison, just as you discover the difference between the heights of Mary and Kate by aid of the yardstick.
If all French writers are clear, then Binet, a French writer, must be clear. Here "French writers" furnish your yardstick. Perhaps it would suit this case a little better if, instead of speaking of indirect comparison by aid of a mental yardstick, we spoke in terms of "relations". When you have before your mind the relation of A to M, and also the relation of B to M, you may be able to see, or infer, a relation between A and B. M is the common point of reference to which A and B are related. Binet stands in a certain relation to "French writers", who furnish the point of reference; that is, he is one of them. Clear writing stands in a certain relation to French writers, being one of their qualities; from which combination of relations we perceive clear writing as a quality of Binet.
Just as an illusion is a false sense perception, so a false inference is called a "fallacy". One great cause of fallacies consists in the confused way in which facts are sometimes presented, resulting in failure to see the relationships clearly. If you read that
"Smith is taller than Brown; andJones is shorter than Smith; and thereforeJones is shorter than Brown,"
the mix-up of "taller" and "shorter" makes it difficult to get the relationships clearly before you, and you are likely{468}to make a mistake. Or again, if Mary and Jane both resemble Winifred, can you infer that they resemble each other? You are likely to think so at first, till you notice that resemblance is not a precise enough relation to serve for purposes of indirect comparison. Mary may resemble Winifred in one respect, and Jane may resemble her in another respect, and there may be no resemblance between Mary and Jane.
Or, again,
"All French writers are clear; butJames was not a French writer; and thereforeJames was not a clear writer,"
may cause some confusion from failure to notice that the relation between French writers and clear writing is not reversible so that we could turn about and assert that all clear writers were French.
The reasoner needs a clear head and a steady mental eye; he needs to look squarely and steadily at his two given statements in order to perceive their exact relationship. Diagrams and symbols often assist in keeping the essential facts clear of extraneous matter, and so facilitate the right response.
To sum up: the process of reasoning culminates in two facts being present as stimuli, and the response, called "inference", consists in perceiving a third fact that is implicated in the two stimulus-facts. It is a good case of the law of combination, and at the same time it is a case where "isolation" is needed, otherwise the response will be partly aroused by irrelevant stimuli, and thus be liable to error.
Reasoning as a whole is a process of mental exploration culminating in inference. Now, without regard to possible{469}variations of the perceptive response of inference, there are at least different varieties of the exploratory process leading up to inference. The situation that arouses reasoning differs from one case to another, the motive for engaging in this rather laborious mental process differs, and the order of events in the process differs. There are several main types of reasoning, considered as a process of mental exploration.
A "problem" is a situation for which we have no ready and successful response. We cannot successfully respond by instinct or by previously acquired habit. We mustfind outwhat to do. We explore the situation, partly by the senses and actual movement, partly by the use of our wits. We observe facts in the situation that recall previous experiences or previously learned rules and principles, and apply these to the present case. Many of these clues we reject at once as of no use; others we may try out and find useless; some we may think through and thus find useless; but finally, if our exploration is successful, we observe a real clue, recall a pertinent guiding principle, and see the way out of our problem.
Two boys went into the woods for a day's outing. They climbed about all the morning, and ate their lunch in a little clearing by the side of a brook. Then they started for home, striking straight through the woods, as they thought, in the direction of home. After quite a long tramp, when they thought they should be about out of the woods, they saw clear space ahead, and, pushing forward eagerly, found themselves in the same little clearing where they had eaten their lunch! Reasoning process No. 1 now occurred: one of the boysrecalledthat when traversing the woods without any compass or landmark, the traveller is very likely to go in a circle; inference, "That is what we have done and{470}we probably shall do the same thing again if we go ahead. We may as well sit down and think it over."
Mental exploration ensued. "How about following the brook?" "That won't do, for it flows down into a big swamp that we couldn't get through". "How about telling directions by the sun?" "But it has so clouded over that you can't tell east from west, or north from south." "Yes, those old clouds! How fast they are going! They seem to go straight enough." "Well, say! How about following the clouds? If we keep on going straight, in any direction, for a couple of hours, we shall surely get out of the woods somewhere." This seems worth trying and actually brings the boys out to a road where they can inquire the way home.
What we find in this case is typical of problem solution. First, a desire is aroused, and it facilitates the observation and recall of facts relevant to itself. One pertinent fact is observed, another pertinent fact, or rule, is recalled; and in these two taken together the key to the problem is found.
While in the preceding case reasoning showed what to do, here it is called upon to justify what has been done, or what is going to be done anyway. The question is, what reason to assign for the act; we feel the need of meeting criticism, either from other people or from ourselves. The real motive for the act may be unknown to ourselves, as it often is unless we have made a careful study of motives; or, if known, it may not be such as we care to confess. We require areasonablemotive, some acceptable general principle that explains our action.
A child is unaccountably polite and helpful to his mother some day, and when asked about it replies that he simply wants to help--while his real motive may have been to score against his brother or sister, who is to some extent his rival.
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If I have work requiring attention but want to go to the game, I should certainly be lacking in reasoning ability if I could not find something in the situation that made my attendance at the game imperative. I am stale, and the game will freshen me up and make me work better afterward. Or, I am in serious danger of degenerating into a mere "grind", and must fight against this evil tendency. Or, my presence at the game is necessary in order to encourage the team.
Thus, aspects of the situation that are in line with our desire bob to the surface and suggest acceptable general principles that make the intended action seem good and even necessary. Finding excuses for acts already performed is a reasoning exercise of the same sort. Man is a rationalizing animal as well as a rational animal, and his self-justifications and excuses, ludicrous though they often are, are still a tribute to his very laudable appreciation of rationality.
This form of reasoning, like the preceding, takes its start with something that raises the question, "Why?" Only, our interest in the question is objective rather than subjective. It is not our own actions that call for explanation, but some fact of nature or of human behavior. Why--with apologies to the Southern Hemisphere!--is it so cold in January? The fact arouses our curiosity. We search the situation for clues, and recall past information, just as in the attempt to solve a practical problem. "Is it because there is so much snow in January?" "But what, then, makes it snow? This clue leads us in a circle." "Perhaps, then, it is because the sun shines so little of the time, and never gets high in the sky, even at noon." That is a pretty good clue; it recalls the general principle that, without a continued supply of heat, cold is inevitable. To explain a phenomenon is to deduce it from{472}an accepted general principle; to understand it is to see it as an instance of the general principle. Such understanding is very satisfactory, since it rids you of uncertainty and sometimes from fear, and gives you a sense of power and mastery.
The reasoning processes discussed up to this point have taken their start with the particular, and have been concerned in a search for the general principle that holds good of the given particular case. Reasoning may also take its start at the other end, in a general statement, and seek for particular cases belonging under this general rule. But what can be the motive for this sort of reasoning? What is there about a general proposition to stimulate exploration?
Several motives may be in play. First, there may be a need for application of the general principle. Somebody whose authority you fully accept enunciates a general proposition, and you wish to apply it to special cases, either for seeing what practical use you can make of it, or simply to make its meaning more real and concrete to yourself. Your exploration here takes a different form from that thus far described. Instead of searching a concrete situation for clues, and your memory for general principles, you search your memory for particular cases where the general law should apply. If all animals are cold-blooded, excepting only birds and mammals, then fish and frogs and lizards are cold-blooded, spiders, insects, lobsters and worms; having drawn these inferences, your understanding of the general proposition becomes more complete.
A general proposition may stimulate reasoning because you doubt it, and wish to find cases where it breaks down. Perhaps somebody makes the general statement whose authority you do not accept; perhaps he says it in an assertive way that makes you want to take him down{473}a peg. Perhaps you are in the heat of an argument with him, so that every assertion he may make is a challenge. You search your memory for instances belonging under the doubted general statement, in the hope of finding one where the general statement leads to a result that is contrary to fact. "You say that all politicians are grafters. Theodore Roosevelt was a politician, therefore, according to you, he must have been a grafter. But he was not a grafter, and you will have to take back that sweeping assertion."
This same general type of reasoning, which takes its start with a general proposition, and explores particular instances in order to see whether the proposition, when applied to them, gives a result in accordance with the facts, has much more serious uses; for this is the method by which ahypothesisis tested in science. A hypothesis is a general proposition put forward as a guess, subject to verification. If it is thoroughly verified, it will be accepted as a true statement, a "law of nature", but at the outset it is only a guess that may turn out to be either true or false. How shall its truth or falsity be demonstrated? By deducing its consequences, and testing these out in the realm of observed fact.
An example from the history of science is afforded by Harvey's discovery of the circulation of the blood, which was at first only a hypothesis, and a much-doubted one at that. If the blood is driven by the heart through the arteries, and returns to the heart by way of the veins, then the flow of blood in any particular artery must be away from the heart, and in any particular vein towards the heart. This deduction was readily verified. Further, there should be little tubes leading from the smallest arteries over into the smallest veins, and this discovery also was later verified, when the invention of the microscope made observation of the capillaries possible. Other deductions also were verified,{474}and in short all deductions from the hypothesis were verified, and the circulation of the blood became an accepted law.
Most hypotheses are not so fortunate as this one; most of them die by the wayside, since it is much easier to make a guess that shall fit the few facts we already know than to make one that will apply perfectly to many other facts at present unknown. A hypothesis is a great stimulus to the discovery of fresh facts. Science does not like to have unverified hypotheses lying around loose, where they may trip up the unwary. It is incumbent on any one who puts forward a hypothesis to apply it to as many special cases as possible, in order to see whether it works or not; and if the propounder of the hypothesis is so much in love with it that he fails to give it a thorough test, his scientific colleagues are sure to come to the rescue, for they, on the whole, would be rather pleased to see the other fellow's hypothesis come to grief. In this way, the rivalry motive plays a useful part in the progress and stabilizing of science.
When you are sure at the outset of your general proposition, and need only to see its application to special cases, your reasoning is said to be "deductive". Such reasoning is specially used in mathematics. But in natural science you are said to employ "inductive reasoning". The process has already been described. You start with particular facts demanding explanation or generalization, and try to find some accepted law that explains them. Failing in that, you are driven to guess at a general law, i.e., to formulate a hypothesis that will fit the known facts. Then, having found such a conjectural general law, you proceed to deduce its consequences; you see that,ifthe hypothesis is true, such and such facts must be true. Next you go out and see whether these facts are true, and if they are, your hypothesis{475}is verified to that extent, though it may be upset later. If the deduced facts are not true, the hypothesis is false, and you have to begin all over again.
The would-be natural scientist may fail at any one of several points. First, he may see no question that calls for investigation. Everything seems a matter-of-course, and he concludes that science is complete, with nothing left for him to discover. Second, seeing something that still requires explanation, he may lack fertility in guessing, or may be a poor guesser and set off on a wild-goose chase. Helmholtz, an extremely fertile inventor of high-grade hypotheses, describes how he went about it. He would load up in the morning with all the knowledge he could assemble on the given question, and go out in the afternoon for a leisurely ramble; when, without any strenuous effort on his part, the various facts would get together in new combinations and suggest explanations that neither he nor any one else had ever thought of before. Third, our would-be scientific investigator may lack the clear, steady vision to see the consequences of his hypothesis; and, fourth, he may lack the enterprise to go out and look for the facts that his hypothesis tells him should be found.
Psychology is not the only science that studies reasoning; that is the subject-matter of logic as well, and logic was in the field long before psychology. Psychology studies theprocessof reasoning, while logic checks up the result and shows whether it is valid or not. Logic cares nothing about the exploratory process that culminates in inference, but limits itself to inference alone.
Inference, in logical terminology, consists in drawing a conclusion from two given premises. The two premises are the "two facts" which, acting together, arouse the{476}perceptive response called inference, and the "third fact" thus perceived is the conclusion. [Footnote: The "two facts" or premises need not be true; either or both may be assumed or hypothetical, and still they may lead to a valid conclusion, i.e., a conclusion implicated in the assumed premises.] Logic cares nothing as to how the premises were found, nor as to the motive that led to the search for them, nor as to the time and effort required, nor the difficulty encountered; these matters all pertain to psychology.
Logic sets forth the premises and conclusion in the form of the "syllogism", as in the old stand-by:
Major premise: All men are mortalMinor premise: Socrates is a manConclusion: Therefore, Socrates is mortal
The syllogism includes three "terms", which in the above instance are "Socrates", "mortal", and "man" or "men". Logic employs the letters, S, P, and M to symbolize these three terms in general. S is the "subject" (or, we might say, the "object" or the "situation") about which something is inferred. P is the "predicate", or what is inferred about S; and M is the "middle term" which corresponds to our "yardstick" or "point of reference", as we used those words at the beginning of the chapter. S is compared with P through the medium of M; or, S and P are both known to be related to M, and therefore (when the relations are of the right sort) they are related to each other. It is part of the business of logic to examine what relations are, and what are not, suitable for yielding a valid inference.
In symbols, then, the syllogism becomes:
Major premise: M is PMinor premise: S is MConclusion: Therefore, S is P