Part 2 — CERTAINTY AND ATTENTION

BY FRANCES H. ROUSMANIERE

The results of the experiments on the feeling of certainty which I have conducted fall into two divisions—those on the nature of the feeling itself, and those on the effect of voluntarily attending to certain aspects of a total experience upon certainty in the judgments as to the constitution of that experience. The problems of the first division are: Are there different kinds of certainty? In any one kind of certainty are there degrees, and if so, are these of a limited or an unlimited number? Can certainty be analyzed into elements? The problems of the second division are: Can it be said that in the report of any experience the judgments made with the highest degree of certainty will be confined to an attended-to group, and if not, will there be more there than elsewhere? In such a report will the direction of voluntary attention toward certain aspects materially alter the distribution of the judgments of the highest order of certainty over the various aspects of any given field?

These two divisions are so distinct in problem and result as to make it seem best to describe them as independent experiments. As some interesting results on the relation of error to the different grades of certainty and to the effect of attention developed in connection with this second division of the experiment, those results are given also.

In general the same subjects took part throughout the experiments. One, an instructor in Harvard University, whom I shall call K, was not subject for the second division of the experiment. Two others, E and H, both graduate students in Harvard University, could not serve as subjects in an important part of the first division. Of those remaining, B was a student in Radcliffe College, F an instructor in Harvard University, and A, C, and D graduate students in Harvard University. These last five were my subjects for all parts of the experiment.

I. THE NATURE OF THE FEELING OF CERTAINTY

The general method here was, of course, the method of introspection. Situations were created about which the subject might be expected to make judgments with different sorts or different degrees of certainty, if such should be possible. He was then questioned as to his experience. The method has the fault of all introspective methods, viz., its results can in no case be verified. The results here are none the less suggestive, and, for the second problem, at any rate, definite enough to be convincing.

Most of the experiments were conducted in connection with visual fields. In working at the first problem which we have now to consider, however, the certainty connected with the dermal sensations and that connected with the simple reasoning process of addition were also examined. The apparatus used consisted of three sets of cards. On one set were pasted geometrical shapes cut from colored paper, and black and white letters or figures. Each of these cards was shown to a subject for a second and a half, or two seconds. After the exposure he told what he judged to be on the card, giving all that he could about the nature of his feeling of confidence (or certainty) for each judgment. On the second set of cards square pieces of tin, smooth rubber, rough rubber, cotton, felt, undressed kid, leather, eiderdown, flannel, coarse and fine sandpaper, and pricked paper were stuck, six on each card. The experimenter passed these cards so that these bits of material rubbed against the forefinger of the subject, while a curtain kept the card and the hand hidden from the subject's sight. Here, again, the subject judged of what had been on the card, just as he had done after seeing each of the first set of cards. Small sample cards, each having pasted upon it a piece of one of the substances used, were also behind the curtain, and the subject was allowed to feel of these as much as he wished while giving his report. Such sample cards were required because of the underdevelopment of the association of names of any kind with the dermal sensations. A single card with three groups of figures for addition upon it made up the third part of the apparatus. Here the subject was asked first to add the columns rapidly and to introspect as to his certainty of the correctness of the different results; then to go over the addition again, and yet a third time, and to compare his feelings of certainty in the different cases. The introspection was developed partly through the help of questions put by the experimenter, but in asking these questions great care was taken to prevent their influencing the judgment of the subject. Some observations made by the subjects during the second division of the experiment (also conducted in connection with visual fields) are, also, introduced here. Apart from this, the experiments on the feeling of certainty connected with this sense of sight were greater in number than the other experiments; and it is those that have given us most of the data for answering the second and third problems.

The subjects did not agree in their answers to the first problem. Some found not only that the certainty connected with their belief in the results of their addition seemed to be of a distinct type from that connected immediately with the sense of sight, but also that there were different sorts of certainty connected immediately with the sense of sight itself. Others found but one kind of a feeling of certainty. All agreed, however, that so far as the kind or kinds of certainty associated with them was concerned there was no difference between the sense of sight and the dermal senses, so that it would seem to be true that any distinctions which are to be found within the feeling of certainty will not be distinctions springing from the difference in the sense-organs. Within the sense of sight, however, subjects B, E, and F divided their feelings of certainty into two classes,—an absolute feeling of certainty which they felt could not be shaken, and a feeling of confidence which they would act upon but which they felt might be shaken by questioning, and which seemed different by more than degree from the feeling of certainty proper. Subjects A, C, K and H found no such marked distinction between their feeling of greatest certainty and all lesser feelings of conviction. Subject D at one time felt that the distinction into two such distinct classes, the definitely certain and the more wavering, fitted his experience, and at another time said that it seemed to him that each degree of conviction stood for an unique feeling of certainty and that any two of them were as different from each other as any other two. A second division of the feelings of certainty into two classes is to be found with subjects A, F and H. This developed in connection with the visual experiments again. The distinction here may be called one into psychological and logical certainty. The latter rests on reasoning either from the probable character of the field, or from a feeling as to its general character, to the nature of some detail. We shall notice the characteristics of these two classes later. One subject, A, further distinguished as different the feelings of certainty connected with the two methods of logical certainty just given. The others made no such distinctions. In the experiment with the columns for addition only six subjects, A, B, C, D, F, and K took part. Of these the two who had made the distinction into psychological and logical certainty with the visual experiments (subjects A and F) again made the same distinction. Subject F, however, who had had occasion to do a good deal of important work with statistics, found practically no element of logical certainty in connection with his addition, though it seemed to him that what confidence he felt in his result should be distinguished from the psychological certainty he had had as to the character of the visual fields. Subject B felt no certainty in her results except as she could so hold the process together as to have what seemed to her a simultaneous experience. When she had to judge of the results of a set of successive experiences that could not be so unified, she characterized her state of consciousness not as holding a feeling of certainty or of uncertainty, but as simply lacking any feeling of certainty. The other three subjects found no difference between the feelings of certainty and uncertainty associated with visual experiences and those associated with the process of addition. As a whole, it seems then that we must answer our first problem by saying that the case seems to be different with different individuals. With some the highest grade of certainty associated with a sense-experience is sharply distinct from the other grades, and with some again there appear at least the two general classes of psychological and logical certainty. On the other hand, there seem to be people for whom the feeling of certainty has no such sharp distinctions of kind within it.

The results as to the second problem may be more briefly and more distinctly given. No subject found any evidence that the number of the grades of certainty which he could distinguish would be limited by anything except his keenness in introspection, although in the simple tests given for the experiment, four was the greatest number of grades distinguished at any one time. Two of the subjects (B and F), who set the highest grade of certainty apart from the judgments made with lesser confidence, said that there might be degrees within that higher grade as well as among the "uncertainties." There was no evidence that logical certainty differed from psychological in respect of the grades to be found within it, and some evidence that they were alike in that respect, although logical certainty was less carefully examined. It would seem, then, that our second problem is to be answered thus: There are degrees present in some if not in all kinds of certainty, and there is no evidence that the number of these degrees is limited.

It was not generally found possible to analyze the feeling of certainty into a sum of elements, although certain characteristics seemed to be persistent in it. Here again there is marked individual variation. The general test used for the difference in degrees of confidence was the question "On which judgment would you risk more?" This satisfied every one as a true criterion for such distinctions, but subjects H and C said that for them the feeling of certainty had a much more distinct relation with the past than with the future. Perhaps for that reason, subject H proposed the test "Which judgment could I be converted from most easily and simply?" The distinctness of an image had something to do with the feeling of certainty for subject C. Beyond this, he could not characterize his feeling. Neither was he sure that the degree of certainty varied exactly with the degree of distinctness. Subject D found that all objects about which he made judgments of which he was certain were present to his mind in the form of distinct images; but did not feel that that covered all that was to be said of the feeling of certainty. The number of images present, as visual and auditory, seemed to increase the degree of certainty for him. Subject F could give no characterization of his feeling of psychological certainty. His feeling of logical certainty seemed to spring largely from a feeling of consistency between the present experience and his past experiences. With subjects A, B, and K the vividness of an image was a strong determining factor in the degree of certainty felt in any judgment, but again was not the whole story. Something they could not characterize was also present for A and B, and, as well, a feeling of more or less perfect congruence between an image and the general character of a field. (This introspection developed in connection with the visual experiments.) Among these eight subjects we have but one (K) who is satisfied with reducing certainty to a set of elements.

To my mind the most valuable thing to be gained from this division of the experiment is the suggestion that there are definite types of certainty, and that people may be classified by these. There are obviously marked individual variations as to the characteristics of this feeling. I should expect from my work this year that two pretty distinct types could be discovered. For one of these, certainty in a judgment as to an experience would rest very largely upon the vividness of an image; for the other, upon the congruence of an image with other previously accepted images, that is, the absence of conflicting images when the experience judged about is imagined part of a wide setting of past experiences. I should not expect either element of certainty to appear absolutely, without the other form. For many people one element would predominate in certain fields, as in judgments regarding sense-experiences, the other in the more logical fields. For some, again, perhaps, the two would be nearly coördinate in every experience of certainty. But for some subjects, as, I think, for subject K here, the vividness of the image would always be the determining factor, while for others, as for subject H, congruence with wider experience would be much more important. This classification of subjects according to their types of certainty might develop into a much more complicated affair. The experiments described here have gone no farther than to suggest lines along which it may perhaps run. There may be other elements equally important with these two. A set of experiments consisting of attempts to raise uncertainty to certainty would bring out the essentials of certainty from a new point of view, and would, perhaps, test this theory that individuals may be classified according to the types of their certainty, in the most satisfactory manner.

II. THE EFFECT OF VOLUNTARILY ATTENDING TO CERTAIN ASPECTS OF A TOTAL EXPERIENCE UPON CERTAINTY IN THE JUDGEMENTS CONSTITUTION OF THAT TOTAL EXPERIENCE.

As has been said, judgments as to the elements of visual fields were tested for this part of the experiment. The apparatus used was the following: The subject was seated before a low table which was shut from his view by curtains and boards. He looked down upon the table through an opening into which a camera-shutter had been fitted. This shutter was set for a two seconds' exposure and opened by means of a bulb which the subject held in his hand. Just before each exposure, the experimenter placed a card on the table below the camera-shutter. The set of twenty cards so used were alike in that the background for all was gray and the objects pasted upon the cards black letters and numerals and simple geometrical figures of chosen shapes and colors. No color was repeated on any one card. The cards were different in the choice and arrangement and in the number of objects used. The number of letters and numerals on any one card varied from two to five, the total number of objects from eight to twelve. A white card on which were pasted dark gray samples of each of the eleven shapes used, together with a card of the background of those shown in the experiment on which were pasted torn scraps of the eleven colored papers used, was always in sight at the subject's side. A camera-shutter, experiment cards and sample cards thus made up the apparatus.

The presence of the sample cards needs explanation. They stood for the attempt to place the colors and shapes on the same footing as the letters and numerals. Their presence, in the first place, and, as well, the limitation of the number of letters and numerals used, did away somewhat with the advantage that letters and numerals naturally have for ease of naming. In the second place, the use of a new color for the sample shapes and the absence of definite shape in the sample colors helped to keep the colors and shapes more distinct. With the help of these cards it seemed that we could properly hold we had a a visual field of three very nearly coördinate sets of elements.

The experiment as a whole, as conducted, had four phases which, except for one particular, were exactly alike. The subject's attention was directed toward a certain aspect of the field by (1) asking him before each exposure (or less often if that appeared unnecessary) to attend to that aspect, as, for instance, to the colors present, and (2) taking care that any questions asked should tend to strengthen rather than counteract the effect of that voluntary attention. At a given signal the subject pressed the bulb which opened the shutter. On the closing of the shutter he reported what he had seen. This report the experimenter recorded almost in the subject's own words, and later tabulated in the manner described presently. So far as giving the objects present was concerned, the report was given almost invariably without any suggestion by the experimenter as to the possibilities of the field. To help the subject distinguish the amount of confidence which he had in the judgments that such or such objects were present, however, the experimenter frequently asked such questions as, "Would you risk more on the fact that there was a square in the field than on the fact there was something blue there?" In giving his report the subject pointed to the sample cards or spoke, as he might wish. He was also allowed to be as leisurely or as rapid in giving it as he chose. A half-minute interval elapsed between the end of each report and the signal that the shutter be opened again. No persistent effort to distract the subject's attention was made then, though conversation on other topics was frequently carried on. The point in which the phases of the experiment differed was in the aspect of the field to which attention was called. In the first, this was the shapes, in the second, the colors, in the third, the letters and numerals, and in the fourth, the number of objects in the field. Fixing the attention upon the number of objects in the field served to distribute it equally over all the groups represented there. The general method of calling attention to the different aspects and of learning the effect of such attention was, as has just been said, the same for all phases.

As a preliminary to making up the tables here given, from which we are to answer our problems, the experimenter first tabulated the reports of the subjects in such a way as to show how many judgments (correct and incorrect) of each of the four grades of certainty adopted for this division of the experiment were made by each subject on each card for each group on the card (shape, color, or letter or numeral). From these tabulations the tables that follow were in turn compiled.

The number of grades of certainty adopted for this division of the experiment is obviously decidedly arbitrary. Grades of certainty there surely are. The introspection of the subjects develops that clearly, as has been stated. But there is no reason in the conditions of the case for holding to the number four, as is done here. In giving the results for which the experiment was undertaken, I shall, indeed, confine myself to studying the range of the judgments made with as high a grade of confidence as the subject believed he should ever have. This is called certainty (1) or certainty proper. But for the tributary discussion on the relation of certainty and error, the consideration of three other grades used in the report and early tabulation, is also introduced. This lowest grade (4) might better be named "as complete uncertainty as will admit of one's making any judgment." The other two are intermediate. It was at first intended to give the results with regard to the effect of voluntary attention upon the place of these grades of certainty, also, but such a discussion has been omitted because it promised to add very little more than complexity to the report. Besides this, the classification into these lower grades is too purely approximate to make the distinction there of great value. For judgments of the order certainty (1) we have the test, "Are you as certain of this as you can imagine being in an experiment of this sort?" but no such test for the other grades could be found. Yet, though he tended to omit judgments of the lower grades of certainty, each subject seemed to find four grades a convenient number to use in giving his report.

The number of experiment cards used varied with the subjects. E had so clear a memory of the cards that after as many as ten had been shown, he found difficulty in distinguishing his memory of the one which he had just seen from that of others seen earlier. Ten cards only were used in his case. A, B, D, and F showed signs of fatigue after fifteen cards which made the value of any later results questionable. C and K showed no such signs of fatigue. The same set of cards was, of course, shown any one subject for all four phases of the experiment. Those omitted were the last ten or the last five of the complete set as the case might be.

TABLE I

% of cards where certainty (1) appears in the attended-to group. % of cards where certainty (1) appears elsewhere than in the attended-to group only. % of cards where certainty (1) in attended-to group only. % of cards where certainty (1) is stronger outside than within the attended-to group.

A 91% 49% 49% 13.3%

B 97 91 83 28

C 95 67 30 16.6

D 93.3 69 24.5 11.2

E 96.6 83.3 13.3 26.6

F 88.8 30 53.3 8.3

H 91.6 70 26.6 10

Table I answers the first part of our first problem promptly. Every subject gave judgments of the order certainty (1) about groups other than that attended to, in the case of a very considerable percentage of the cards. True, again in the case of a considerable (though generally smaller) percentage of those cards, each subject confined his judgments to the group attended to. The fact of individual variation stands out again here; and, moreover, the conclusions drawn should be qualified slightly because of the fact that it was often possible for the subjects to give all the letters and numerals on the cards, and still have, as it were, some attention left over for the other, supposedly non-attended-to groups. Such reaching beyond the properly attended-to group never seemed to be possible with either shapes or colors. Aside from this, however, it is clear that judgments of the highest grade of certainty were by no means limited to the group attended to.

This same table answers, also, the second part of the problem. Each subject found certainty of the highest grade sometimes stronger outside than within the group which held his attention. It is, of course, practically impossible to make absolutely certain that each subject's attention was invariably held to the group toward which it was turned, yet the percentage where certainty was stronger outside than within such groups seems large enough, in some cases, at least, as with subjects A, B, and H, to warrant our answering this second part of the problem in the negative. I should feel, however, that this was answered less definitely than was the first part of the problem. We may say, then, that the judgments made with the highest degree of certainty about a visual field will not be confined to the group attended to, and that we have strong evidence pointing toward the belief that we cannot expect there will invariably be more of such judgments within the group attended to than outside it.

TABLE II

Label 1: % of judgments of certainty (1) given to each group in phase I (or when shapes were attended to). Label 2: % of judgments of certainty (1) given to each group in phase II (or when colors were attended to). Label 3: % of judgments of certainty (1) given to each group in phase III (or when letters and numerals were attended to). Label 4: % of judgments of certainty (1) given to each group in phase IV (or when the attention was equally distributed over all the groups)

1 2 3 4

Subject Shapes (a) 94% 38% 18% 31%

A Colors (b) 5 61 20 59

Letters and Numerals (c) 0 0 61 9

Subject (a) 48 39 21 33

B (b) 43 60 29 38

(c) 8 0 51 28

Subject (a) 88 15 26 34

C (b) 8 77 28 8

(c) 5 7 47 58

Subject (a) 60 13 11 40

D (b) 19 67 2 37

(c) 19 19 86 23

Subject (a) 51 15 0 37

E (b) 22 56 8 29

(c) 26 28 91 34

Subject (a) 66 12 0 50

F (b) 14 77 0 27

(c) 19 10 100 23

Subject (a) 43 21 7 24

H (b) 29 52 4 19

(c) 27 26 88 57

The most interesting part of this division of the experiment is brought out in Table II in answer to the problem, "Will the place of voluntary attention materially alter the distribution of judgments of the highest order of certainty among the given groups?" In every case the percentage is affected, in most cases, greatly affected. Take the case of subject A, for instance. Although, when his attention is equally distributed over the field 59% of the judgments we consider were of colors, yet when his attention was fixed on shapes and on letters and numerals this fell to 5% and 20% respectively. When it was fixed on colors, it rose, indeed, only to 61%. When, however, subject A fixed his attention upon the letters and numerals, 61% of the judgments were confined to the group attended to,—the same percentage as when colors were the attended-to group,—although, when his attention was distributed over the whole field, the percentage of these judgments about the group of letters and numerals was 9% only. When shapes were attended to, the 31% of the fourth phase of the experiment rose to 94%,—almost all of the judgments of the highest grade of certainty that were given were judgments about shapes. A similar study of the results given in the table can be made for the other subjects. The degree of change varies with the subject and with the group, but always there is some change, and often a very marked one. In this experiment the place of voluntary attention clearly did alter, and alter materially, the proportion of judgments of the highest order of certainty made about any given group.

That, indeed, would seem to me to be the answer of this experiment to the question as to the effect of voluntary attention upon certainty in one's judgments. Every subject showed a tendency to have more certainty in those judgments which were made about that aspect of the field toward which his attention was directed. Yet, on the other hand, this was a tendency only, one not strong enough to make it possible to predict beforehand exactly how great a proportion of the judgments in which he had the highest degree of confidence would be limited to that field, or even to be sure in every case that the greater proportion of those judgments would be so limited. The place of voluntary attention has an influence upon the subject-matter of the judgments made with certainty about a visual field just seen, but an influence of varying and uncertain strength.

TABLE III

x = no judgments of that kind given. % of mistakes in judgments of certainty (1). % of mistakes in judgments of certainty (2). % of mistakes in judgments of certainty (3). % of mistakes in judgments of certainty (4).

Subject (in giving shapes) (a) 7% 10% 0% 100%

A (in giving colors) (b) 2 14 23 0

(in giving letters and numerals) (c) 0 0 x x

Subject (a) 2 10 10 0

B (b) 3 6 20 25

(c) 4 50 0 x

Subject (a) 1 8 10 0

C (b) 4 14 14 0

(c) 1 0 16 0

Subject (a) 3 4 0 16

D (b) 1 6 0 0

(c) 5 0 0 0

Subject (a) 2 10 25 50

E (b) 1 33 40 0

(c) 0 0 0 0

Subject (a) 1 25 7 25

F (b) 4 15 29 26

(c) 3 0 0 x

Subject (a) 3 6 5 0

H (b) 6 2 15 15

(c) 4 0 0 20

TABLE IV

General % of mistakes in judgments of certainty (1). % of mistakes in judgments of certainty (1) about attended-to groups. General % of mistakes in judgments not of certainty (1). % of mistakes in judgments not of certainty (1) about attended-to groups.

Subject A 4% 1% 17% 27%

Subject B 3 2 10 7

Subject C 2 3 9 24

Subject D 3 4 4 0

Subject E 1 2 22 34

Subject F 3 1 21 23

Subject H 4 6 6 10

The results given in Tables III and IV were compiled from the same records as those of the two Tables just discussed. They give the relation of error to certainty and to attention, as that relation was developed in this experiment. No experiments were conducted with these relations of error primarily in view, but the results developed in connection with the problem of the effect of attention upon certainty in one's judgments.

Both Tables show again marked individual variation. They suggest to me, in the first place, a further line of investigation in the same field and for the same purpose as those investigations which L. William Stern outlines in an article[101] entitled Aussagestudium. This further line is the testing subjects to learn the probable relative correctness of the judgments made with different degrees of confidence. Although a comparison of the first and third columns in Table IV makes it clear that the proportion of mistakes for the highest grade of confidence is lower than for the other grades taken together, there is a very marked difference among the subjects to be noticed. The difference in the two percentages is, for instance, very slight in the cases of D and H, and very great in the case of E. It is interesting to notice with regard to E that while he has the lowest percentage of mistakes for certainty (1), he has the highest percentage for the group of certainties (2), (3), and (4). In the more detailed percentages given in Table III we see further that in certain fields and sometimes in all fields (as with subject C) judgments made with the lowest grade of confidence were invariably correct. Such Tables might be of help in a case where the evidence of eye-witnesses conflicted. We might perhaps learn that witness N made a large proportion of mistakes where he was absolutely certain, whereas witness M was seldom wrong in judgments in which he had a low degree of confidence. Even when the probity of both was unquestioned, we should not then assume that N was more probably right because he had so much more confidence in his judgments than M had in his. A much longer and more comprehensive set of experiments would be necessary before we could feel that we had at hand a table from which to work in this way.

The question of the effect of voluntary attention upon error, for answering which Table IV was compiled, brings out again the marked individual variation among these seven subjects which has shown itself in practically all parts of the experiment. Some effect seems to have been produced always, but this was sometimes to give a larger percentage of mistakes in the attended-to groups and sometimes a smaller. With A, B, and F the percentage of mistakes in certainty (1) was lower for the groups attended to than for the total number of judgments of that order. Only with subject B, however, is this true of the group of lower grades of certainties also. On the other hand, with subjects C, D, E, and H the percentage is greater for certainty (1) in the groups attended to than for certainty (1) in the collection of all the judgments of certainty (1) taken together. Here, too, in the case of subject D, the results with regard to the lower grades of certainty reverse those for certainty (1). Thus all four possibilities as to the kind of influence of voluntary attention upon certainty appear. We cannot say that the place of voluntary attention will tend to affect the percentage of error in any given way. We can only say that apparently it made some difference with each subject. It might be found by further experimenting that the character of this difference is associated with some other characteristic of either attention or the feeling of certainty, as, for instance, with the ease with which attention is held to the chosen field or with the type of the subject's certainty.

Like all experiments, these open up further questions quite as much as they answer those toward which they are aimed. To repeat something of what has already been said, I feel that what it has established is (1) that introspection develops distinct grades of certainty in the case of every individual, (2) that the particular characteristics of the feeling of certainty vary markedly among individuals; (3) that the feelings of certainty associated with the different senses are not, as feelings of certainty, to be distinguished from each other; (4) that the judgments of the highest degree of certainty which are made about the constitution of any visual field just seen will not be confined to the group in that field toward which the attention is directed; and (5) that such fixing of the attention will, nevertheless, materially alter the subject-matter of such judgments of greatest certainty. The rather vague statement that the percentage of error is not surely less with the judgments of a group because attention is fixed on that group may perhaps be added as a sixth conclusion. The most interesting and promising of the problems which the experiments seem to me to raise are: (1) the problem, are there such definite types of the feeling of certainty that people may be classified according to their types, and, if so, what are the types and what their relation to other psychological characteristics of the individual? (2) the problem, what will be the result of careful and trained introspection as to the relation of so-called logical and psychological certainty and in what fields do these appear for different individuals? (3) the problem, how can a test for grading the probable percentage of error in the judgments of different grades of certainty made by any one person be constructed? and (4) the problem, how are such facts as those given in Table IV to be connected with the effort required for attention, the type of certainty of each subject, etc.? Other problems could, of course, be suggested, but these, I feel, mark the steps that naturally follow the experiments described here.

PLATE VIII.