Criminal Psychology; a manual for judges, practitioners, and students Part 33

Examples of this sort of thing are innumerable and they teach that whenever any questionable a.s.sertion is made about a thing heard the doctor must be called in to determine whether the witness heard it under abnormal, though not diseased conditions. Again, merely accidental or habitual general excitability tends to intensify all sounds, and whether the witness under consideration was in such condition can be determined only by the expert physician.

The illusions of hearing which completely normal people are subject to are the most difficult of all. Their number and frequency is variously estimated. The physician has nothing to do with them. The physicist, the acoustician and physiologist do not care about the criminalist's needs in this matter, and we ourselves rarely have time and opportunity to deal with it. As a result our information is very small, and no one can say how much is still undiscovered. One of my friends has called my attention to the fact that when the beats of the clock are counted during sleepiness, one too many is regularly counted. I tested this observation and my experience confirmed it. If, now, we consider how frequently the determination of time makes the whole difference in a criminal case and how easily it is possible to mistake a whole hour, we can get some notion of the importance of this illusion. Its explanation is difficult and it may be merely a single instance of a whole series of unknown auditory illusions resting on the same basis. Another and similar phenomenon is the "double beat of the hammer." If you have an a.s.sistant strike the table with a hammer while you hold both ears with your fingers and then open them half a second or a second after the blow, you hear the blow again. And if you open and shut your ears quickly you can hear the blow several times. This is explained through the fact that a number of reflections of the sound occur in the room, and that these are perceivable only by the unfatigued ear. The explanation is unsatisfactory because the experiment is sometimes successful in the open. Taken in itself, this matter seems very theoretical and without practical value. But this kind of action may occur

automatically. It is well known that swallowing closes the Eustachian tubes for a moment, especially if done when lying down. Now, if this occurs during a blow, a shot, etc., the sound must be heard twice. Again, it may easily happen that because of the noise a man wakes up half asleep and, frightened, swallows the collected saliva; then this accident, which in itself seems unimportant, may lead to very significant testimony. Such occurrences are not infrequent.

The intensity of a sound already heard may be of considerable influence. Certain experimenters have indicated the remarkable character of slightly intensive effects of sound. If you hold a watch so far from the ear as to hear it clearly but weakly, the sound decreases until finally it is not heard at all, and after awhile it is again heard, etc. This may lead to hearing distinct sounds made up of many tones, and need not evince any great illusion with regard to the ticking of a watch. But the thing may occur also in connection with more powerful and more distant sounds, e. g., the murmur of a brook, the rush of a train, the pounding in a distant factory. Noises far removed are influenced by reflections of sound, waves of air, etc., and it is possible that all kinds of things may be heard in a completely monotonous noise. This can be easily learned by listening to the soft murmur of a distant brook at night. Given the disposition and supposing the existence of the brook unknown, it is easy to hear in its monotonous murmur, human voices, sighs, shrieks, etc.

Another remarkable observation shows that in the dark very distinct things are heard during the playing of delicate instruments, such as mouth-organs. The humming approaches and withdraws, then it comes on various sides, and finally one has the feeling that the whole room is full of humming and winging insects. And this may go on indefinitely. There is a large collection of reasons for this reduplication of monotonous sounds. Everybody knows the accord of the

only one cry. Difference in distance and alterations in the air cause the chords.

The difficulties in distinguishing the intensity or weakness of a sound are of importance. Fechner learned from the violinist Wasilewski that he observed that a male choir of four hundred voices did not sound essentially louder than one of two hundred. At the same time one clock is not heard at a great distance, a hundred clocks are heard. One locust can not be heard eating; when 1000 eat they are heard; hence each one must make a definite noise.[1] Early authorities have already indicated how difficult it is to distinguish the number of bells ringing together. Even musicians will often take two or three to be five or six.

Certain dispositions make some difference in this respect. The operating physician hears the low groaning of the patient after the operation without having heard his loud cries during the operation. During the operation the physician must not hear anything that is likely to disturb his work, but the low groan has simply borne in upon him. The sleeping mother often is deaf to considerable noise, but wakes up immediately when her child draws a deeper breath than usual. Millers and factory hands, travellers, etc., do not hear the pounding of their various habitual environmental noises, but they perceive the slightest call, and everybody observes the considerable murmur of the world, the sum of all distant noises, only in the silence of the night that misses it.

Illusions of direction of sound are very common. It is said that even animals are subject to them; and everybody knows how few human beings can distinguish the source and direction of street music, a rolling wagon, or a ringing bell. Even when long practice enables one to determine direction with correctness, an accidental event, perhaps the weather, especial sounds, a different grouping of individuals on the street, may result in serious mistakes. I tried to learn to judge from my office-desk whether the ring of the horse- car came from above or below. I succeeded so well that I could not understand how it was difficult not to learn the difference, and yet I failed many a time altogether in judgment. The reason for it I do not know.

All these enumerated circ.u.mstances must show how very uncertain all acoustic perceptions are, and how little they may be trusted if they are not carefully tested under similar conditions, and if-what is most important-they are not isolated. We are here led back

[1] Max Meyer: Zur Theorie der Ger

to the old principle that every observation is not proof but means of proof, and that it may be trusted only when it is confirmed by many parallel actions which are really consistent. That even after that mistakes are possible, is true, but "after that" is when we have done all that lies within human power.

Section 101. (4) Illusions of Touch.

The high standing of the sense of touch which make it in certain directions even the organ of control of the sense of sight, is well known, and Condillac's historic attempt to derive all the senses from this one is still plausible. If what is seen is to be seen accurately there is automatic resort to the confirmatory aid of the sense of touch, which apprehends what the eye has missed. Hence we find many people touching things, whose vision is not altogether reliable- i. e., people of considerable age, children unpracticed in seeing, an uneducated people who have never learned to see quickly and comprehensively. Moreover, certain things can be determined only by touching, i. e., the fineness of papers, cloth, etc., the sharpness or pointedness of instruments, or the rawness of objects. Even when we pat a dog kindly we do so partly because we want to see whether his skin is as smooth and fine as the eye sees it; moreover, we want to test the visual impression by that of touch.

But important and reliable as the sense of touch is, it is nevertheless not to be trusted when it is the sole instrument of perception. We must never depend on the testimony of a witness based entirely on perceptions by touch, and the statements of a wounded person concerning the time, manner, etc., of his wound are unreliable unless he has also seen what he has felt. We know that most knife and bullet wounds, i. e., the most dangerous ones, are felt, in the first instance, as not very powerful blows. Blows on the extremities are not felt as such, but rather as pain, and blows on the head are regularly estimated in terms of pain, and falsely with regard to their strength. If they were powerful enough to cause unconsciousness they are said to have been very ma.s.sive, but if they have not had that effect, they will be described by the most honest of witnesses as much more powerful than they actually were. Concerning the location of a wound in the back, in the side, even in the upper arm, the wounded person can give only general indications, and if he correctly indicates the seat of the wound, he has learned it later but did not know it when it occurred. According to Helmholtz,

practically all abdominal sensations are attributed to the anterior abdominal wall. Now such matters become of importance when an individual has suffered several wounds in a brawl or an a.s.sault and wants to say certainly that he got wound A when X appeared, wound B when Y struck at him, etc. These a.s.sertions are almost all false because the victim is likely to identify the pain of the moment of receiving the wound with its later painfulness. If, for example, an individual has received a rather long but shallow knife wound and a deep stab in the back, the first will cause him very considerable burning sensation, the latter only the feeling of a heavy blow. Later on, at the examination, the cut has healed and is no longer painful; the dangerous stab which may have reached the lung, causes pain and great difficulty in breathing, so that the wounded man a.s.signs the incidence of the stab to the painful sensation of the cut, and conversely.

Various perceptions of victims on receiving a wound are remarkable, and I have persuaded a police surgeon of considerable learning and originality to collect and interpret his great ma.s.s of material. It is best done by means of tabulation, accurate description of wounds according to their place, size, form, and significance, the statement of the victim concerning his feeling at the moment of receiving the wound, the consequences of healing, and at the end explanatory observations concerning the reasons for true or incorrect sensations of the victim. As this work is to have only psychological value it is indifferent whether the victim is veracious or not. What we want to know is what people say about their perception. The true and the false will distinguish themselves automatically, the material being so rich, and the object will be to compare true subjective feelings with true subjective deeds. Perhaps it may even be possible to draw generalizations and to abstract certain rules.

There are many examples of the fact that uncontrolled touch leads to false perceptions. Modern psychophysics has pointed to a large group of false perceptions due to illusions of pressure, stabs, or other contact with the skin. The best known, and criminalistically most important experiments, are those with open compa.s.ses. Pressed on the less sensitive parts of the body, the back, the thigh, etc., they are always felt as one, although they are quite far apart. The experiments of Flournoy, again, show how difficult it is to judge weights which are not helped by the eye's appreciation of their form and appearance. Ten objects of various forms were judged by fifty

people for their weight; only one discovered that they all had the same weight.

Similarly, mere touch can not give us proper control over the organs of the body. Sully says that in bed we may voluntarily imagine that a leg has a position quite different from that it really has. Let me cite some similar examples from my "Manual for Investigating Judges." If we take a pea between the thumb and the index finger, we feel the pea simply, although its tactile image comes to us through two fingers, i. e., double. If now we cross the third finger over the fourth and hold the pea between the ends of these two fingers, we feel it to be double because the fingers are not in their customary positions and hence give double results. From one point of view this double feeling is correct, but when we touch the pea naturally, experience helps us to feel only one pea. Another example consists in crossing the hands and turning them inward and upward, so that the left fingers turn to the left and the right fingers to the right. Here the localization of the fingers is totally lost, and if a second person points to one of the fingers without touching it, asking you to lift it, you regularly lift the a.n.a.logous finger of the other hand. This shows that the tactile sense is not in a very high stage of development, since it needs, when unhelped by long experience, the a.s.sistance of the sense of sight. Perceptions through touch alone, therefore, are of small importance; inferences are made on the basis of few and more coa.r.s.e characteristic impressions.

This is shown by a youthful game we used to play. It consisted of stretching certain harmless things under the table-a soft piece of dough, a peeled, damp potato stuck on a bit of wood, a wet glove filled with sand, the spirally cut rind of a beet, etc. Whoever got one of these objects without seeing it thought he was holding some disgusting thing and threw it away. His sense of touch could present only the dampness, the coldness, and the motion, i. e., the coa.r.s.est traits of reptilian life, and the imagination built these up into a reptile and caused the consequent action. Foolish as this game seems, it is criminalistically instructive. It indicates what unbelievable illusions the sense of touch is capable of causing. To this inadequacy of the tactile imagination may be added a sort of transferability of certain touch sensations. For example, if ants are busy near my seat I immediately feel that ants are running about under my clothes, and if I see a wound or hear it described, I often feel pain in the a.n.a.logous place on my own body. That this may lead to considerable illusion in excitable witnesses is obvious.

Finally, this dependence of the sense of touch may be supplemented by the fact that it is counted only relatively, and its value varies with the individual. We find the cellar warm in winter and cold in summer, because we only feel the difference with the outer air, and when we put one hand in hot, and the other in cold water, and then put both in tepid water one finds the tepid water cold, the other warm. The record of tactile sensations is frequent in our protocols and requires constant consideration of the sense's unreliability.

Diseased conditions are of course to be referred to the physician. I need only mention that slight poisonings by means of chloroform, morphine, atropine, daturine, decrease, and that strychnine increases the sensitivity of the touch organ.

Section 102. (5) Illusions of the Sense of Taste.

Illusions of taste are of importance for us only in cases of poisoning in which we want the a.s.sistance of the victim, or desire to taste the poison in question in order to determine its nature. That taste and odor are particularly difficult to get any unanimity about is an old story, and it follows that it is still more difficult clearly to understand possible illusions of these senses. That disease can cause mistaken gustatory impressions is well known. But precedent poisoning may also create illusions. Thus, observation shows that poisoning by rose-santonin (that well-known worm remedy to which children are so abnormally sensitive) causes a long-enduring, bitter taste; sub-cutaneous morphine poisoning causes illusory bitter and sour tastes. Intermittent fevers tend to cause, when there is no attack and the patient feels comparatively well, a large number of metallic, particularly coppery tastes. If this is true it may lead to unjustified suspicions of poisoning, inasmuch as the phenomena of intermittent fever are so various that they can not all be identified.

Imagination makes considerable difference here. Taine tells somewhere of a novelist, who so graphically described the poisoning of his heroine that he felt the taste of a.r.s.enic and got indigestion. This may be possible, for perhaps everybody has already learned the great influence of the false idea of the nature of a food. If some salt meat is taken to be a sweet pastry, the taste becomes disgusting because the imaginary and the actual tastes seem to be mixed. The eye has especial influence, and the story cited and denied a hundred times, that in the dark, red wine and white wine, chicken and goose,

can not be distinguished, that the going out of a cigar is not noted, etc., is true. With your eyes closed it may be possible to eat an onion instead of an apple.

Prior tastes may cause significant gustatory illusions. Hence, when a.s.sertions are made about tastes, it is always necessary to inquire at the outset what had been eaten or drunk before. Experienced housewives take this fact into consideration in setting their tables and arranging their wines. The values of the wines are considerably raised by complete illusions of taste. All in all, it must not be forgotten that the reliability of the sense of taste can not be estimated too low. The illusions are greatest especially when a thing has been tasted with a preconceived notion of its taste.

Section 103. (6) The Illusions of the Olfactory Sense.

Olfactory illusions are very rare in healthy people and are hence of small importance. They are frequent among the mentally diseased, are connected in most cases with s.e.xual conditions and then are so vivid that the judge can hardly doubt the need of calling in the physician. Certain poisons tend to debauch the olfactory sense. Strychnine, e. g., tends to make it finer, morphine duller. People with weak lungs try, in most cases, to set their difficulty of breathing outside themselves and believe that they are inhaling poisoned air, coal-gas, etc. If one considers in this connection the suspiciousness which many people suffering from lung trouble often exhibit, we may explain many groundless accusations of attempted murder by stifling with poisonous or unbreathable gas. If this typical illusion is unknown to the judge he may find no reason for calling in the physician and then-injustice.

The largest number of olfactory illusions are due to imagination. Carpenter's frequently cited case of the officials who smelled a corpse while a coffin was being dug up, until finally the coffin was found to be empty, has many fellows. I once was making an examination of a case of arson, and on approaching the village noted a characteristic odor which is spread by burned animals or men. When we learned: that the consumed farm lay still an hour's ride from the village, the odor immediately disappeared. Again, on returning home, I thought I heard the voice of a visitor and immediately smelled her characteristic perfume, but she had not been there that day.

Such illusions are to be explained by the fact that many odors are in the air, that they are not very powerfully differentiated and

may hence be turned by means of the imagination into that one which is likely to be most obvious.

The stories told of hyper-sensitives who think they are able to smell the pole of a magnet or the chemicals melted into a gla.s.s, belong to this cla.s.s. That they do so in good faith may be a.s.sumed, but to smell through melted gla.s.s is impossible. Hence it must be believed that such people have really smelled something somewhere and have given this odor this or that particular location. Something like this occurs when an odor, otherwise found pleasant, suddenly becomes disgusting and unbearable when its source is unknown. However gladly a man may eat sardines in oil he is likely to turn aside when his eyes are closed and an open can of sardines is held under his nose. Many delicate forms of cheese emit disgusting odors so long as it is not known that cheese is the source. The odor that issues from the hands after crabs have been eaten is unbearable; if, however, one bears in mind that the odor is the odor of crabs, it becomes not at all so unpleasant.

a.s.sociation has much influence. For a long time I disliked to go to a market where flowers, bouquets, wreaths, etc., were kept because I smelled dead human bodies. Finally, I discovered that the odor was due to the fact that I knew most of these flowers to be such as are laid on coffins-are smelled during interment. Again, many people find perfumes good or bad as they like or dislike the person who makes use of them, and the judgment concerning the pleasantness or unpleasantness of an odor is mainly dependent upon the pleasantness or unpleasantness of a.s.sociative memories. When my son, who is naturally a vegetarian and who could never be moved to eat meat, became a doctor, I thought that he could never be brought to endure the odor of the dissecting room. It did not disturb him in the least, however, and he explained it by saying: "I do not eat what smells like that, and I can not conceive how you can eat anything from the butcher shops where the odor is exactly like that of the dissecting room." What odor is called good or bad, ecstatic or disgusting, is purely a subjective matter and never to be the basis of a universal judgment. Statements by witnesses concerning perceptions of odor are valueless unless otherwise confirmed.

Section 104. (b) Hallucinations and Illusions.

The limits between illusions of sense and hallucinations and illusions proper can in no sense be definitely determined inasmuch

as any phenomena of the one may be applied to the other, and vice versa.[1] Most safely it may be held that the cause of illusions of sense lies in the nature of sense-organs, while the hallucinations and illusions are due to the activity of the brain. The latter are much more likely to fall within the scope of the physician than sense- illusions, but at the same time many of them have to be determined upon by the lawyer, inasmuch as they really occur to normal people or to such whose disease is just beginning so that the physician can not yet reach it. Nevertheless, whenever the lawyer finds himself face to face with a supposed illusion or hallucination he must absolutely call in the physician. For, as rarely as an ordinary illusion of sense is explicable by the rules of logic or psychology, or even by means of other knowledge or experience at the command of any educated man, so, frequently, do processes occur in cases of hallucination and illusion which require, at the very least, the physiological knowledge of the physician. Our activity must hence be limited to the perception of the presence of hallucination or illusion; the rest is matter for the psychiatrist. Small as our concern is, it is important and difficult, for on the one hand we must not appeal to the physician about every stupid fancy or every lie a prisoner utters, and on the other hand we a.s.sume a heavy responsibility if we interpret a real hallucination or illusion as a true and real observation. To acquire knowledge of the nature of these things, therefore, can not be rigorously enough recommended.

Hallucination and illusion have been distinguished by the fact that hallucination implies no external object whatever, while in illusion objects are mistaken and misinterpreted. When one thing is taken for another, e. g., an oven for a man, the rustle of the wind for a human song, we have illusion. When no objective existence is perceived, e. g., when a man is seen to enter, a voice is heard, a touch is felt, although nothing whatever has happened, we have hallucination. Illusion is partial, hallucination complete, supplementation of an external object. There is not a correct and definite difference between illusion and hallucination inasmuch as what is present may be so remotely connected with what is perceived that it is no more than a stimulus, and thus illusion may be turned into real hallucination. One authority calls illusion the conception of an actually present external event which is perceived by the peripheral organs in the form of an idea that does not coincide with the

[1] C. Wernicke ber Halluzinationen, Ratlosigkeit, Desorientierung etc. Monatschrift f. Psychiatrie u. Neurologie, IX, 1 (1901).

event. The mistake does not lie in the defective activity of the senses so much as in the fact that an apperceptive idea is subst.i.tuted for the perceptive view. In hallucination every external event is absent, and hence, what is seen is due to a stimulation of the periphery. Some authorities believe hallucination to be caused by cramp of the sensory nerve. Others find illusions to be an externally stimulated sense-perception not corresponding to the stimulus, and still others believe it to be essentially normal. Most human beings are from time to time subject to illusions; indeed, n.o.body is always sober and intelligent in all his perceptions and convictions. The luminous center of our intelligent perceptions is wrapped in a cloudy half-shadow of illusion.

Sully[1] aims to distinguish the essential nature of illusion from that characterized by ordinary language. Illusion, according to him, is often used to denote mistakes which do not imply untrue perceptions. We say a man has an illusion who thinks too much of himself, or when he tells stories otherwise than as they happen because of a weakness of memory. Illusion is every form of mistake which subst.i.tutes any direct self-evident or intuitive knowledge, whether as sense-perception or as any other form.

Nowadays the cause of hallucination and illusion is sought in the over-excitement of the cerebro-spinal system. As this stimulation may be very various in its intensity and significance, from the momentary rush of blood to complete lunacy, so hallucinations and illusions may be insignificant or signs of very serious mental disturbances. When we seek the form of these phenomena, we find that all those psychical events belong to it which have not been *purposely performed or lied about. When Brutus sees C

[1] James Sully. Illusions.

[2] J, J. Hoppe. Erkl

man always was seeing a skeleton. 3. Pascal, after a heavy blow, saw a fiery abyss into which he was afraid he would fall. 4. A man who had seen an enormous fire, for a long time afterward saw flames continually. 5. Numerous cases in which criminals, especially murderers, always had their victims before their eyes. 6. Justus Mser saw well-known flowers and geometrical figures very distinctly. 7. Bonnet knows a "healthy" man who saw people, birds, etc., with open eyes. 8. A man got a wound in his left ear and for weeks afterward saw a cat. 9. A woman eighty-eight years old often saw everything covered with flowers,-otherwise she was quite "well."

A part of these stories seems considerably fict.i.tious, a part applies to indubitable pathological cases, and certain of them are confirmed elsewhere. That murderers, particularly women-murderers of children, often see their victims is well known to us criminalists. And for this reason the habit of confining prisoners in a dark cell for twenty-four hours on the anniversary of a crime must be pointed to as refined and thoroughly medi

Hoppe tells of a great group of hallucinations in conditions of waking and half-waking, and a.s.serts that everybody has them and can note them if he gives his attention thereto. This may be an exaggeration, but it is true that a healthy person in any way excited or afraid may hear all kinds of things in the crackling of a fire, etc., and may see all kinds of things, in smoke, in clouds, etc. The movement of portraits and statues is particularly characteristic, especially in dim light, and under unstable emotional conditions. I own a relief by Ghiberti called the "Rise of the Flesh," in which seven femurs dance around a corpse and sing. If, at night, I put out the lamp in my study and the moon falls on the work, the seven femurs dance as lively as may be during the time it takes my eyes to adapt themselves from the lamplight to the moonlight. Something similar

I see on an old carved dresser. The carving is so delicate that in dim light it shows tiny heads and flames after the fashion of the Catholic church pictures of "poor souls," in purgatory. Under certain conditions of illumination the flames flicker, the heads move, and out of the fire the arms raise themselves to the clouds floating above. Now this requires no unusual excitement, simply the weary sensing of evening, when the eyes turn from prolonged uniform reading or writing to something else.[1] It has happened to me from my earliest childhood. High bodily temperature may easily cause hallucinations. Thus, marching soldiers are led to shoot at non- existing animals and apparently-approaching enemies. Uniform and fatiguing mental activity is also a source of hallucination. Fechner says that one day having performed a long experiment with the help of a stop-watch, he heard its beats through the whole evening after. So again when he was studying long series of figures he used to see them at night in the dark so distinctly that he could read them off.

Then there are illusions of touch which may be criminalistically important. A movement of air may be taken for an approaching man. A tight collar or cravat may excite the image of being stifled! Old people frequently have a sandy taste while eating,-when this is told the thought occurs that it may be due to coa.r.s.ely powdered a.r.s.enic, yet it may be merely illusion.

The slightest abnormality makes hallucinations and illusions very easy. Persons who are in great danger have all kinds of hallucinations, particularly of people. In the court of law, when witnesses who have been a.s.saulted testify to having seen people, hallucination may often be the basis of their evidence. Hunger again, or loss of blood, gives rise to the most various hallucinations. Menstruation and h

It might seem that in this matter, also, the results are destructive and that the statements of witnesses are untrue and unreliable. I do not a.s.sert that our valuation of these statements shall be checked from all possible directions, but I do say that much of what we have considered as true depends only on illusions in the broad sense of the word and that it is our duty before all things rigorously to test everything that underlies our researches.

[1] Cf. A. Mosso: Die Ermdung. Leipzig 1892.

Section 105. (C) Imaginative Ideas.

Illusions of sense, hallucinations, and illusions proper taken as a group, differ from imaginative representations because the individual who has them is more or less pa.s.sive and subject to the thing from which they arise, while with the latter the individual is more active and creates new images by the *combination of existing or only imagined conditions. It does not matter whether these consist of the idea only, or whether they are the product of word, ma.n.u.script, picture, sculpture, music, etc. We have to deal only with their occurrence and their results. Of course there is no sharp boundary between imaginative ideas and sense-perception, etc. Many phenomena are difficult to cla.s.sify and even language is uncertain in its usage. The notion "illusion" has indicated many a false ideal, many a product of incoherent fancy.

The activity of the imagination, taken in the ordinary sense, requires a.n.a.lysis first of all. According to Meinong[1] there are two kinds of imaginative images-a generative, and a constructive kind. The first exhibits elements, the second unites them. Thus: I imagine some familiar house, then I reproduce the idea of fire (generative), now I unite these two elements, and imagine the house in question in flames (constructive). This involves several conditions.

The conditions of generation offer no difficulties. The difficulty lies in the constructive aspect of the activity, for we can imagine astonishingly little. We can not imagine ourselves in the fourth dimension, and although we have always had to make use of such quant.i.ties, we all have the idea that the quant.i.ty A represents, e. g,, a line, A<2s>, a square, A<3s>, a cube, but as soon as we have to say what image A<5s>, A<6s>, etc., represents, our mathematical language is at an end. Even twelve men or a green flame seen through red gla.s.s or two people speaking different things can barely be imagined with any clearness. We have the elements but we can not construct their compounds. This difficulty occurs also in the consideration of certain objects. Suppose we are looking at an artistically complete angel; we are always bothered by the idea that his wings are much too small to enable him to fly. If an angel constructed like a man is to be borne by his wings, they must be so gigantic as to be unreproducible by an artist. Indeed a person slightly more grubby,

[1] Phantasie u. Phantasienvorstellung. Zeitsehrift f. Philosophie u. philosophische Kritik. Vol. 95.