The danger of analogy lies in the fact that we prefer naturally to depend on something already known, and that the preference is the greater in proportion to our feeling of the strangeness and ominousness of the particular intellectual or natural regions in which we find ourselves. I have already once demonstrated[141]how disquieting it is to notice, during the examination of the jury, that the jurymen who ask questions try to find some relation to their own trades even though this requires great effort, and seek to bring the case they are asking about under the light of their particular profession. So, however irrelevant the statement of a witness may be, the merchant juryman will use it to explain Saldo-Conti, the carpenter juryman to explain carpentry, the agriculturist to notice the farming of cattle, and then having set the problem in his own field construct the most daring analogies, for use in determining the guilt of the accused. And we lawyers are no better. The more difficult and newer a case is the more are we inclined to seek analogies. We want supports, for we do not find firm natural laws, and in our fear we reach out after analogies, not of course in law, because that is not permitted, but certainly in matters of fact. Witness X has given difficult testimony in a certain case. We seek an analogy in witness Y of an older case, and we observe the present issue thus analogically, without the least justification. We have never yet seen drops of blood on colored carpets, yet we believe in applyingour experience of blood stains on clothes and boots analogically. We have before us a perfectly novel deed rising from perverted sexual impulse—and we presuppose that the accused is to be treated altogether analogously to another in a different case, although indeed the whole event was different.
Moreover the procedure, where the analogy is justified, is complex. “With insight,” says Trendelenburg, “did the ancients regard analogy as important. The power of analogy lies in the construction and induction of a general term which binds the subconcept with regard to which a conclusion is desired, together with the individual object which is compared with the first, and which is to appear as a mediating concept but can not. This new general term is not, however, the highest concept among the three termini of the conclusion; it is the middle one and is nothing else than the terminus medius of the first figure.” This clear statement shows not only how circumstantial every conclusion from analogy is, but also how little it achieves. There is hardly any doubt of the well-known fact that science has much to thank analogy for, since analogy is the simplest and easiest means for progress in thought. If anything is established in any one direction but progress is desired in another, then the attempt is made to adapt what is known to the proximate unknown and to draw the possible inference by analogy. Thousands upon thousands of analogies have been attempted and have failed,—but no matter; one successful one became a hypothesis and finally an important natural law. In our work, however, the case is altogether different, for we are not concerned with the construction of hypotheses, we are concerned with the discovering of truth, or with the recognition that it cannot be discovered.
The only place where our problems permit of the use of analogy is in the making of so-called constructions, i.e., when we aim to clarify or to begin the explanation of a case which is at present unintelligible, by making some assumption. The construction then proceeds in analogy to some already well known earlier case. We say: “Suppose the case to have been so and so,” and then we begin to test the assumption by applying it to the material before us, eliminating and constructing progressively until we get a consistent result. There is no doubt that success is frequently attained in this way and that it is often the only way in which a work may be begun. At the same time, it must be recognized how dangerous this is, for in the eagerness of the work it is easy to forget that so far, one is working only according to analogy by means of an assumptionstill to be proved. This assumption is in such cases suddenly considered as something already proved and is counted as such with the consequence that the result must be false. If you add the variability in value of analogy, a variability not often immediately recognized, the case becomes still worse. We have never been on the moon, have therefore apparently no right to judge the conditions there—and still we know—only by way of analogy—that if we jumped into the air there we should fall back to the ground. But still further: we conclude again, by analogy, that there are intelligent beings on Mars; if, however, we were to say how these people might look, whether like us or like cubes or like threads, whether they are as large as bees or ten elephants, we should have to give up because we have not the slightest basis for analogy.
In the last analysis, analogy depends upon the recurrence of similar conditions. Therefore we tacitly assume when we judge by analogy that the similarity of conditions contains an equivalence of ultimately valid circumstance. The certainty of analogy is as great as the certainty of this postulate, and its right as great as the right of this postulate.
If, then, the postulate is little certain, we have gained nothing and reach out into the dark; if its certainty is great we no longer have an analogy, we have a natural law. Hence, Whately uses the term analogy as an expression for the similarity of relation, and in this regard the use of analogy for our real work has no special significance. Concerning so-called false analogies and their importance cf. J. Schiel’s Die Methode der induktiven Forschung (Braunschweig 1865).
Inasmuch as the work of the criminal judge depends upon the proof of evidence, it is conceivable that the thing for him most important is that which has evidential character or force.[142]A sufficient definition of evidence or proof does not exist because no bounds have been set to the meaning of “Proved.” All disciplines furnish examples of the fact that things for a long time had probable validity, later indubitable validity; that again some things were considered proved and were later shown to be incorrect, and that many things at one time wobbly are in various places, and even among particular persons, supposed to be at the limits of probability and proof. Especiallyremarkable is the fact that the concept ofthe provedis very various in various sciences, and it would be absorbing to establish the difference between what is called proved and what only probable in a number of given examples by the mathematician, the physicist, the chemist, the physician, the naturalist, the philologist, the historian, the philosopher, the lawyer, the theologian, etc. But this is no task for us and nobody is called upon to determine who knows what “Proved” means. It is enough to observe that the differences are great and to understand why we criminalists have such various answers to the question: Is this proved or only probable? The varieties may be easily divided into groups according to the mathematical, philosophic, historical or naturalistic inclinations of the answerer. Indeed, if the individual is known, what he means by “proved” can be determined beforehand. Only those minds that have no especial information remain confused in this regard, both to others, and to themselves.
Sharply to define the notion of “proved” would require at least to establish its relation to usage and to say: What we desire leads us to anassumption, what is possible gives usprobability, what appears certain, we callproved. In this regard the second is always, in some degree, the standard for the first (desires, e.g., cause us to act; one becomes predominant and is fixed as an assumption which later on becomes clothed with a certain amount of reliability by means of this fixation).
The first two fixations, the assumption and the probability, have in contrast to their position among other sciences only a heuristic interest to us criminalists. Even assumptions, when they become hypotheses, have in various disciplines a various value, and the greatest lucidity and the best work occur mainly in the quarrel about an acutely constructed hypothesis.
Probabilityhas a similar position in the sciences. The scholar who has discovered a new thought, a new order, explanation or solution, etc., will find it indifferent whether he has made it only highly probable or certain. He is concerned only with the idea, and a scholar who is dealing with the idea for its own sake will perhaps prefer to bring it to a great probability rather than to indubitable certainty, for where conclusive proof is presented there is no longer much interest in further research, while probability permits and requires further study. But our aim is certainty and proof only, and even a high degree of probability is no better than untruth and can not count. In passing judgment and for the purpose of judgmenta high degree of probability can have only corroborative weight, and then it is probability only when taken in itself, and proof when taken with regard to the thing it corroborates. If, for example, it is most probable that X was recognized at the place of a crime, and if at the same time his evidence of alibi has failed, his footmarks are corroborative; so are the stolen goods which have been seen in his possession, and something he had lost at the place of the crime which is recognized as his property, etc. In short, when all these indices are in themselves established only as highly probable, they give under certain circumstances, when taken together, complete certainty, because the coincidence of so many high probabilities must be declared impossible if X were not the criminal.
In all other cases, as we have already pointed out,assumptionand probability have only a heuristic value for us lawyers. With the assumption, we must of course count; many cases can not be begun without the assistance of assumption. Every only half-confused case, the process of which is unknown, requires first of all and as early as possible the application of some assumption to its material. As soon as the account is inconsistent the assumption must be abandoned and a fresh one and yet again a fresh one assumed, until finally one holds its own and may be established as probable. It then remains the center of operation, until it becomes of itself a proof or, as we have explained, until so many high probabilities in various directions have been gathered, that, taken in their order, they serve evidentially. A very high degree of probability is sufficient in making complaints; but sentencing requires “certainty,” and in most cases the struggle between the prosecution and the defense, and the doubt of the judge, turns upon the question of probability as against proof.[143]
That probability is in this way and in a number of relations, of great value to the criminalist can not appear doubtful. Mittermaier defines its significance briefly: “Probability naturally can never lead to sentence. It is, however, important as a guide for the conduct of the examiner, as authorizing him to take certain measures; it shows how to attach certain legal processes in various directions.”
Suppose that we review the history of the development of the theory of probability. The first to have attempted a sharp distinction between demonstrable and probable knowledge was Locke. Leibnitz was the first to recognize the importance of the theoryof probability for inductive logic. He was succeeded by the mathematician Bernoulli and the revolutionist Condorcet. The theory in its modern form was studied by Laplace, Quetelet, Herschel, von Kirchmann, J. von Kries, Venn, Cournot, Fick, von Bortkiewicz, etc. The concept that is called probability varies with different authorities. Locke[144]divides all fundamentals into demonstrative and probable. According to this classification it is probable that “all men are mortal,” and that “the sun will rise to-morrow.” But to be consistent with ordinary speech the fundamentals must be classified as evidence, certainties, and probabilities. By certainties I understand such fundamentals as are supported by experience and leave no room for doubt or consideration—everything else, especially as it permits of further proof, is more or less probable.
Laplace[145]spoke move definitely—“Probability depends in part on our ignorance, in part on our knowledge....
“The theory of probability consists in the reduction of doubts of the same class of a definite number of equally possible cases in such a way that we are equally undetermined with regard to their existence, and it further consists in the determination of the number of those cases which are favorable to the result the probability of which is sought. The relation of this number to the number of all possible cases is the measure of the probability. It is therefore a fraction the numerator of which is derived from the number of cases favorable to the result and the denominator from the number of all possible cases.” Laplace, therefore, with J. S. Mill, takes probability to be a low degree of certainty, while Venn[146]gives it an objective support like truth. The last view has a great deal of plausibility inasmuch as there is considerable doubt whether an appearance is to be taken as certain or as only probable. If this question is explained, the assertor of certainty has assumed some objective foundation which is indubitable at least subjectively. Fick represents the establishment of probability as a fraction as follows: “The probability of an incompletely expressed hypothetical judgment is a real fraction proved as a part of the whole universe of conditions upon which the realization of the required result necessarily depends.
“According to this it is hardly proper to speak of the probability of any result. Every individual event is either absolutely necessaryor impossible. The probability is a quality which can pertain only to a hypothetical judgment.”[147]
That it is improper to speak of the probability of a result admits of no doubt, nor will anybody assert that the circumstance of to-morrow’s rain is in itself probable or improbable—the form of expression is only a matter of usage. It is, however, necessary to distinguish between conditioned and unconditioned probability. If I to-day consider the conditions which are attached to the ensuing change of weather, if I study the temperature, the barometer, the cloud formation, the amount of sunlight, etc., as conditions which are related to to-morrow’s weather as its forerunners, then I must say that to-morrow’s rain is probable to such or such a degree. And the correctness of my statement depends upon whether I know the conditions under which rain must appear, more or less accurately and completely, and whether I relate those conditions properly. With regard to unconditioned probabilities which have nothing to do with the conditions of to-day’s weather as affecting to-morrow’s, but are simply observations statistically made concerning the number of rainy days, the case is quite different. The distinction between these two cases is of importance to the criminalist because the substitution of one for the other, or the confusion of one with the other, will cause him to confuse and falsely to interpret the probability before him. Suppose, e.g., that a murder has happened in Vienna, and suppose that I declare immediately after the crime and in full knowledge of the facts, that according to the facts, i.e., according to the conditions which lead to the discovery of the criminal, there is such and such a degree of probability for this discovery. Such a declaration means that I have calculated a conditioned probability. Suppose that on the other hand, I declare that of the murders occurring in Vienna in the course of ten years, so and so many are unexplained with regard to the personality of the criminal, so and so many were explained within such and such a time,—and consequently the probability of a discovery in the case before us is so and so great. In the latter case I have spoken of unconditioned probability. Unconditioned probability may be studied by itself and the event compared with it, but it must never be counted on, for the positive cases have already been reckoned with in the unconditioned percentage, and therefore should not be counted another time. Naturally, in practice, neither form of probability is frequently calculated in figures; only an approximateinterpretation of both is made. Suppose that I hear of a certain crime and the fact that a footprint has been found. If without knowing further details, I cry out: “Oh! Footprints bring little to light!” I have thereby asserted that the statistical verdict in such cases shows an unfavorable percentage of unconditional probability with regard to positive results. But suppose that I have examined the footprint and have tested it with regard to the other circumstances, and then declared: “Under the conditions before us it is to be expected that the footprint will lead to results”—then I have declared, “According to the conditions the conditioned probability of a positive result is great.” Both assertions may be correct, but it would be false to unite them and to say, “The conditions for results are very favorable in the case before us, but generally hardly anything is gained by means of footprints, and hence the probability in this case is small.” This would be false because the few favorable results as against the many unfavorable ones have already been considered, and have already determined the percentage, so that they should not again be used.
Such mistakes are made particularly when determining the complicity of the accused. Suppose we say that the manner of the crime makes it highly probable that the criminal should be a skilful, frequently-punished thief, i.e., our probability is conditioned. Now we proceed to unconditioned probability by saying: “It is a well-known fact that frequently-punished thieves often steal again, and we have therefore two reasons for the assumption that X, of whom both circumstances are true, was the criminal.” But as a matter of fact we are dealing with only one identical probability which has merely been counted in two ways. Such inferences are not altogether dangerous because their incorrectness is open to view; but where they are more concealed great harm may be done in this way.
A further subdivision of probability is made by Kirchmann.[148]He distinguished:
(1) General probability, which depends upon the causes or consequences of some single uncertain result, and derives its character from them. An example of the dependence on causes is the collective weather prophecy, and of dependence on consequences is Aristotle’s dictum, that because we see the stars turn the earth must stand still. Two sciences especially depend upon such probabilities: history and law, more properly the practice and use of criminallaw. Information imparted by men is used in both sciences; this information is made up of effects and hence the occurrence is inferred from as cause.
(2) Inductive probability. Single events which must be true, form the foundation, and the result passes to a valid universal. (Especially made use of in the natural sciences, e.g., in diseases caused by bacilli; in case X we find the appearance A and in diseases of like cause Y and Z, we also find the appearance A. It is therefore probable that all diseases caused by bacilli will manifest the symptom A.)
(3) Mathematical Probability. This infers that A is connected either with B or C or D, and asks the degree of probability. I. e.: A woman is brought to bed either with a boy or a girl: therefore the probability that a boy will be born is one-half.
Of these forms of probability the first two are of equal importance to us, the third rarely of value, because we lack arithmetical cases and because probability of that kind is only of transitory worth and has always to be so studied as to lead to an actual counting of cases. It is of this form of probability that Mill advises to know, before applying a calculation of probability, the necessary facts, i.e., the relative frequency with which the various events occur, and to understand clearly the causes of these events. If statistical tables show that five of every hundred men reach, on an average, seventy years, the inference is valid because it expresses the existent relation between the causes which prolong or shorten life.
A further comparatively self-evident division is made by Cournot, who separates subjective probability from the possible probability pertaining to the events as such. The latter is objectively defined by Kries[149]in the following example:
“The throw of a regular die will reveal, in the great majority of cases, the same relation, and that will lead the mind to suppose it objectively valid. It hence follows, that the relation is changed if the shape of the die is changed.” But how “this objectively valid relation,” i.e., substantiation of probability, is to be thought of, remains as unclear as the regular results of statistics do anyway. It is hence a question whether anything is gained when the form of calculation is known.
Kries says, “Mathematicians, in determining the laws of probability, have subordinated every series of similar cases which takeone course or another as if the constancy of general conditions, the independence and chance equivalence of single events, were identical throughout. Hence, we find there are certain simple rules according to which the probability of a case may be calculated from the number of successes in cases observed until this one and from which, therefore, the probability for the appearance of all similar cases may be derived. These rules are established without any exception whatever.” This statement is not inaccurate because the general applicability of the rules is brought forward and its use defended in cases where the presuppositions do not agree. Hence, there are delusory results, e.g., in the calculation of mortality, of the statements of witnesses and judicial deliverances. These do not proceed according to the schema of the ordinary play of accident. The application, therefore, can be valid only if the constancy of general conditions may be reliably assumed.
But this evidently is valid only with regard to unconditioned probability which only at great intervals and transiently may influence our practical work. For, however well I may know that according to statistics every xth witness is punished for perjury, I will not be frightened at the approach of my xth witness though he is likely, according to statistics, to lie. In such cases we are not fooled, but where events are confused we still are likely to forget that probabilities may be counted only from great series of figures in which the experiences of individuals are quite lost.
Nevertheless figures and the conditions of figures with regard to probability exercise great influence upon everybody; so great indeed, that we really must beware of going too far in the use of figures. Mill cites a case of a wounded Frenchman. Suppose a regiment made up of 999 Englishmen and one Frenchman is attacked and one man is wounded. No one would believe the account that this one Frenchman was the one wounded. Kant says significantly: “If anybody sends his doctor 9 ducats by his servant, the doctor certainly supposes that the servant has either lost or otherwise disposed of one ducat.” These are merely probabilities which depend upon habits. So, it may be supposed that a handkerchief has been lost if only eleven are found, or people may wonder at the doctor’s ordering a tablespoonful every five quarters of an hour, or if a job is announced with $2487 a year as salary.
But just as we presuppose that wherever the human will played any part, regular forms will come to light, so we begin to doubt that such forms will occur where we find that accident, naturallaw, or the unplanned coöperation of men were determining factors. If I permit anybody to count up accidentally concurrent things and he announces that their number is one hundred, I shall probably have him count over again. I shall be surprised to hear that somebody’s collection contains exactly 1000 pieces, and when any one cites a distance of 300 steps I will suppose that he had made an approximate estimation but had not counted the steps. This fact is well known to people who do not care about accuracy, or who want to give their statements the greatest possible appearance of correctness; hence, in citing figures, they make use of especially irregular numbers, e.g. 1739, 7/8, 3.25%, etc. I know a case of a vote of jurymen in which even the proportion of votes had to be rendered probable. The same jury had to pass that day on three small cases. In the first case the proportion was 8 for, 4 against, the second case showed the same proportion and the third case the same. But when the foreman observed the proportion he announced that one juryman must change his vote because the same proportion three times running would appear too improbable! If we want to know the reason for our superior trust in irregularity in such cases, it is to be found in the fact that experience shows nature, in spite of all her marvelous orderliness in the large, to be completely free, and hence irregular in little things. Hence, as Mill shows in more detail, we expect no identity of form in nature. We do not expect next year to have the same order of days as this year, and we never wonder when some suggestive regularity is broken by a new event. Once it was supposed that all men were either black or white, and then red men were discovered in America. Now just exactly such suppositions cause the greatest difficulties, because we do not know the limits of natural law. For example, we do not doubt that all bodies on earth have weight. And we expect to find no exception to this rule on reaching some undiscovered island on our planet; all bodies will have weight there as well as everywhere else. But the possibility of the existence of red men had to be granted even before the discovery of America. Now where is the difference between the propositions: All bodies have weight, and, All men are either white or black? It may be said circularly the first is a natural law and the second is not. But why not? Might not the human body be so organized that according to the natural law it would be impossible for red men to exist? And what accurate knowledge have we of pigmentation? Has anybody ever seen a green horse? And is the accident that nobody has ever seen one to prevent thediscovery of green horses in the heart of Africa? May, perhaps, somebody not breed green horses by crossings or other experiments? Or is the existence of green horses contrary to some unknown but invincible natural law? Perhaps somebody may have a green horse to-morrow; perhaps it is as impossible as water running up hill.
To know whether anything is natural law or not always depends upon the grade and standing of our immediate experience—and hence we shall never be able honestly to make any universal proposition. The only thing possible is the greatest possible accurate observation of probability in all known possible cases, and of the probability of the discovery of exceptions. Bacon called the establishment of reliable assumptions, counting up without meeting any contradictory case. But what gives us the law is the manner of counting. The untrained mind accepts facts as they occur without taking the trouble to seek others; the trained mind seeks the facts he needs for the premises of his inference. As Mill says, whatever has shown itself to be true without exception may be held universal so long as no doubtful exception is presented, and when the case is of such a nature that a real exception could not escape our observation.
This indicates how we are to interpret information given by others. We hear, “Inasmuch as this is always so it may be assumed to be so in the present case.” Immediate acceptance of this proposition would be as foolhardy as doubt in the face of all the facts. The proper procedure is to examine and establish the determining conditions, i.e., who has counted up this “always,” and what caution was used to avoid the overlooking of any exception. The real work of interpretation lies in such testing. We do not want to reach the truth with one blow, we aim only to approach it. But the step must be taken and we must know how large it is to be, and know how much closer it has brought us to the truth. And this is learned only through knowing who made the step and how it was made. Goethe’s immortal statement, “Man was not born to solve the riddle of the universe, but to seek out what the problem leads to in order to keep himself within the limits of the conceivable,” is valid for us too.
Our great mistake in examining and judging often lies in our setting too much value upon individual circumstances, and trying to solve the problem with those alone, or in not daring to use any given circumstance sufficiently. The latter represents that stupidity which is of use to scientific spirits when they lack complete proofof their points, but is dangerous in practical affairs. As a rule, it is also the consequence of the failure to evaluate what is given, simply because one forgets or is too lazy to do so. Proper action in this regard is especially necessary where certain legal proceedings have to occur which are entitled to a definite degree of probability without requiring certainty, i.e., preliminary examinations, arrests, investigations of the premises, etc. No law says how much probability is in such cases required. To say how much is impossible, but it is not unwise to stick to the notion that the event must appear true, if not be proved true, i.e., nothing must be present to destroy the appearance of truth. As Hume says, “Whenever we have reason to trust earlier experiences and to take them as standards of judgment of future experiences, these reasons may have probability.”
The place of probability in the positive determination of the order of modern criminal procedure is not insignificant. When the law determines upon a definite number of jurymen or judges, it is probable that this number is sufficient for the discovery of the truth. The system of prosecution establishes as a probability that the accused is the criminal. The idea of time-lapse assumes the probability that after the passage of a certain time punishment becomes illusory, and prosecution uncertain and difficult. The institution of experts depends on the probability that the latter make no mistakes. The warrant for arrest depends on the probability that the accused behaved suspiciously or spoke of his crime, etc. The oath of the witness depends on the probability that the witness will be more likely to tell the truth under oath, etc.
Modern criminal procedure involves not only probabilities but also various types of possibility. Every appeal has for its foundation the possibility of an incorrect judgment; the exclusion of certain court officials is based on the possibility of prejudice, or at least on the suspicion of prejudice; the publicity of the trial is meant to prevent the possibility of incorrectness; the revision of a trial depends on the possibility that even legal sentences may be false, and the institution of the defendant lawyer depends upon the possibility that a person without defense may receive injustice. All the formalities of the action of the court assume the possibility that without them improprieties may occur, and the institution of seizing letters and messages for evidence, asserts only the possibility that the latter contain things of importance, etc.
When the positive dicta of the law deal with possibility and probabilityin questions of great importance the latter become especially significant.
We have yet to ask what is meant by “rule” and what its relation is to probability. Scientifically “rule” means law subjectively taken and is of equal significance with the guiding line for one’s own conduct, whence it follows that there are only rules of art and morality, but no rules of nature. Usage does not imply this interpretation. We say that as a rule it hails only in the daytime; by way of exception, in the night also; the rule for the appearance of whales indicates that they live in the Arctic Ocean; a general rule indicates that bodies that are especially soluble in water should dissolve more easily in warm than in cold water, but salt dissolves equally well in both. Again we say: As a rule the murderer is an unpunished criminal; it is a rule that the brawler is no thief and vice versa; the gambler is as a rule a man of parts, etc. We may say therefore, that regularity is equivalent to customary recurrence and that whatever serves as rule may be expected as probable. If, i.e., it be said, that this or that happens as a rule, we may suppose that it will repeat itself this time. It is not permissible to expect more, but it frequently happens that we mistake rules permitting exceptions for natural laws permitting none. This occurs frequently when we have lost ourselves in the regular occurrences for which we are ourselves responsible and suppose that because things have been seen a dozen times they must always appear in the same way. It happens especially often when we have heard some phenomenon described in other sciences as frequent and regular and then consider it to be a law of nature. In the latter case we have probably not heard the whole story, nor heard general validity assigned to it. Or again, the whole matter has long since altered. Lotze wrote almost half a century ago, that he had some time before made the statistical observation that the great positive discoveries of exact physiology have an average life of about four years. This noteworthy statement indicates that great positive discoveries are set up as natural laws only to show themselves as at most regular phenomena which have no right to general validity. And what is true of physiology is true of many other sciences, even of the great discoveries of medicine, even legal medicine. This, therefore, should warn against too much confidence in things that are called “rules.” False usage and comfortable dependence upon a rule have very frequently led us too far. Its unreliability is shown by such maxims as “Three misses make a rule” or “Many stupiditiestaken together give a golden rule of life,” or “To-day’s exception is to-morrow’s rule,” or the classical perversion: “The rule that there are no rules without exception is a rule without exception, hence, there is one rule without exception.”
The unreliability of rules is further explained by their rise from generalization. We must not generalize, as Schiel says, until we have shown that if there are cases which contradict our generalizations we know those contradictions. In practice approximate generalizations are often our only guides. Natural law is too much conditioned, cases of it too much involved, distinctions between them too hard to make, to allow us to determine the existence of a natural phenomenon in terms of its natural characteristics as a part of the business of our daily life. Our own age generalizes altogether too much, observes too little, and abstracts too rapidly. Events come quickly, examples appear in masses, and if they are similar they tend to be generalized, to develop into a rule, while the exceptions which are infinitely more important are unobserved, and the rule, once made, leads to innumerable mistakes.
The psychological significance of what we call chance depends upon the concept of chance and the degree of influence that we allow it to possess in our thinking. What is generally called chance, and what is called chance in particular cases, will depend to a significant degree upon the nature of the case. In progressive sciences the laws increase and the chance-happenings decrease; the latter indeed are valid only in particular cases of the daily life and in the general business of it. We speak of chance or accident when events cross which are determined in themselves by necessary law, but the law of the crossing of which is unknown. If, e.g., it is observed that where there is much snow the animals are white, the event must not be attributed to accident, for the formation of snow in high mountains or in the north, and its long stay on the surface of the earth develop according to special natural laws, and the colors of animals do so no less—but that these two orderly series of facts should meet requires a third law, or still better, a third group of laws, which though unknown some time ago, are now known to every educated person.
For us lawyers chance and the interpretation of it are of immense importance not only in bringing together evidence, but in every case of suspicion, for the problem always arises whether a causalrelation may be established between the crime and the suspect, or whether the relation is only accidental. “Unfortunate coincidence”—“closely related connection of facts”—“extraordinary accumulation of reason for suspicion,”—all these terms are really chance mistaken for causation. On the knowledge of the difference between the one and the other depends the fate of most evidence and trials. Whoever is fortunate enough in rightly perceiving what chance is, is fortunate in the conduct of his trial.
Is there really a theory of chance? I believe that a direct treatment of the subject is impossible. The problem of chance can be only approximately explained when all conceivable chance-happenings of a given discipline are brought together and their number reduced by careful search for definite laws. Besides, the problem demands the knowledge of an extremely rich casuistry, by means of which, on the one hand, to bring together the manifoldness of chance events, and on the other to discover order. Enough has been written about chance, but a systematic treatment of it must be entirely theoretical. So Windelband’s[150]excellent and well-ordered book deals with relations (chance and cause, chance and law, chance and purpose, chance and concept) the greatest value of which is to indicate critically the various definitions of the concept of chance. Even though there is no definition which presents the concept of chance in a completely satisfactory manner, the making of such definitions is still of value because one side of chance is explained and the other is thereby seen more closely. Let us consider a few of these and other definitions. Aristotle says that the accidental occurs, παρἁ φὑσν, according to nature. Epicurus, who sees the creation of the world as a pure accident, holds it to occur τἁ μἑν ἁπὁ τὑχης, τἁ δἑ παρ’ἡμὡν. Spinoza believes nothing to be contingent save only according to the limitations of knowledge; Kant says that conditioned existence as such, is called accidental; the unconditioned, necessary. Humboldt: “Man sees those things as accident which he can not explain genetically.” Schiel: “Whatever may not be reduced back to law is called accidental.” Quetelet: “The word chance serves officiously to hide our ignorance.” Buckle derives the idea of chance from the life of nomadic tribes, which contains nothing firm and regulated. According to Trendelenburg chance is that which could not be otherwise. Rosenkranz says: Chance is a reality which has only the value of possibility, while Fischer calls chance the individualized fact, and Lotze identifies itwith everything that is not valid as a natural purpose. For Windelband “chance consists, according to usage, in the merely factual but not necessary transition from a possibility to an actuality. Chance is the negation of necessity. It is a contradiction to say: ‘This happened by accident,’ for the word ‘by’ expressed a cause.”
A. Höfler[151]says most intelligently, that the contradiction of the idea of chance by the causal law may be easily solved by indicating the especial relativity of the concept. (Accidental with regard to one, but otherwise appearing as a possible causal series).
The lesson of these definitions is obvious. What we call chance plays a great role in our legal work. On our recognizing a combination of circumstances as accidental the result of the trial in most cases depends, and the distinction between accident and law depends upon the amount of knowledge concerning the events of the daily life especially. Now the use of this knowledge in particular cases consists in seeking out the causal relation in a series of events which are adduced as proof, and in turning accident into order. Or, in cases where the law which unites or separates the events can not be discovered, it may consist in the very cautious interpretation of the combination of events on the principlesimul cum hoc non est propter hoc.
How in the course of trial are people convinced? The criminalist has as presiding officer not only to provide the truth which convinces; it is his business as state official to convince the defendant of the correctness of the arguments adduced, the witness of his duty to tell the truth. But he again is often himself convinced by a witness or an accused person—correctly or incorrectly. Mittermaier[152]calls conviction a condition in which our belief-it-is-true depends on full satisfactory grounds of which we are aware. But this state of conviction is a goal to be reached and our work is not done until the convincing material has been provided. Seeking the truth is not enough. Karl Gerock assures us that no philosophical system offers us the full and finished truth, but there is a truth for the idealist, and to ask Pilate’s blasé question is, as Lessing suggests, rendering the answer impossible. But this shows the difference between scientific and practical work; science may be satisfied with seeking truth, but we must possess truth. If it were true that truth aloneis convincing, there would not be much difficulty, and one might be content that one is convinced only by what is correct. But this is not the case. Statistically numbers are supposed to prove, but actually numbers prove according to their uses. So in the daily life we say facts are proofs when it would be more cautious to say: facts are proofs according to their uses. It is for this reason that sophistical dialectic is possible. Arrange the facts in one way and you reach one result, arrange the facts another way and you may reach the opposite. Or again, if you study the facts in doubtful cases honestly and without prejudice you find how many possible conclusions may be drawn, according to their arrangement. We must, of course, not have in mind that conviction and persuasion which is brought about by the use of many words. We have to consider only that adduction of facts and explanation, simple or complex, in a more or less skilful, intentional or unintentional manner, by means of which we are convinced at least for a moment. The variety of such conviction is well known to experience.
“The naïveté of the first glance often takes the prize from scholarship. All hasty, decisive judgment betrays, when it becomes habitual, superficiality of observation and impiety against the essential character of particular facts. Children know as completely determined and certain a great deal which is doubtful to the mature man” (V. Volkmar).
So, frequently, the simplest thing we are told gets its value from the manner of telling, or from the person of the narrator. And inasmuch as we ourselves are much more experienced and skilful in arranging and grouping facts than are our witnesses and the accused, it often happens that we persuade these people and that is the matter which wants consideration.
Nobody will assert that it will occur to any judge to persuade a witness to anything which he does not thoroughly believe, but we know how often we persuade ourselves to some matter, and nothing is more conceivable than that we might like to see other people agree with us about it. I believe that the criminalist, because, let us say, of his power, as a rule takes his point of view too lightly. Every one of us, no doubt, has often begun his work in a small and inefficient manner, has brought it along with mistakes and scantiness and when finally he has reached a somewhat firm ground, he has been convinced by his failures and mistakes of his ignorance and inadequacy. Then he expected that this conviction would be obvious also to other people whom he was examining. But this obviousnessis remarkably absent, and all the mistakes, cruelties, and miscarriages of justice, have not succeeded in robbing it of the dignity it possesses in the eyes of the nation. Perhaps the goodwill which may be presupposed ought to be substituted for the result, but it is a fact that the layman presupposes much more knowledge, acuteness, and power in the criminalist than he really possesses. Then again, it is conceivable that a single word spoken by the judge has more weight than it should have, and then when a real persuasion—evidently in the best sense of the word—is made use of, itmustbe influential. I am certain that every one of us has made the frightful observation that by the end of the examination the witness has simply taken the point of view of the examiner, and the worst thing about this is that the witness still thinks that he is thinking in his own way.
The examiner knows the matter in its relation much better, knows how to express it more beautifully, and sets pretty theories going. The witness, to whom the questions are suggestive, becomes conceited, likes to think that he himself has brought the matter out so excellently, and therefore is pleased to adopt the point of view and the theories of the examiner who has, in reality, gone too far in his eagerness. There is less danger of this when educated people are examined for these are better able to express themselves; or again when women are examined for these are too obstinate to be persuaded, but with the great majority the danger is great, and therefore the criminalist can not be told too often how necessary it is that he shall meet his witness with the least conceivable use of eloquence.
Forensic persuasion is of especial importance and has been considered so since classical days, whether rightly, is another question. The orations of state prosecutors and lawyers for the defense, when made before scholarly judges, need not be held important. If individuals are ever asked whether they were persuaded or made doubtful by the prosecutor or his opponent they indicate very few instances. A scholarly and experienced judge who has not drawn any conclusions about the case until the evidence was all in need hardly pay much attention to the pleaders. It may indeed be that the prosecution or defense may belittle or intensify one or another bit of evidence which the bench might not have thought of; or they may call attention to some reason for severity or mercy. But on the one hand if this is important it will already have been touched in the adduction of evidence, and on the other hand such points aregenerally banal and indifferent to the real issue in the case. If this be not so it would only indicate that either we need a larger number of judges, or even when there are many judges that one thing or another may be overlooked.
But with regard to the jury the case is quite different; it is easily influenced and more than makes up for the indifference of the bench. Whoever takes the trouble to study the faces of the jury during trial, comes to the conclusion that the speeches of the prosecution and defense are the most important things in the trial, that they absorb most of the attention of the jury, and that the question of guilt or innocence does not depend upon the number and weight of the testimony but upon the more or less skilful interpretation of it. This is a reproach not to the jury but to those who demand from it a service it can not render. It is first necessary to understand how difficult the conduct of a trial is. In itself the conduct of a jury trial is no art, and when compared with other tasks demanded of the criminalist may be third or fourth in difficulty. What is difficult is the determination of the chronological order in which to present evidence, i.e., the drawing of the brief. If the brief is well drawn, everything develops logically and psychologically in a good way and the case goes on well; but it is a great and really artistic task to draw this brief properly. There are only two possibilities. If the thing is not done, or the brief is of no use, the case goes on irrelevantly, illogically and unintelligibly and the jury can not understand what is happening. If the trick is turned, however, then like every art it requires preparation and intelligence. And the jury do not possess these, so that the most beautiful work of art passes by them without effect. They therefore must turn their attention, to save what can be saved, upon the orations of the prosecution and defense. These reproduce the evidence for them in some intelligible fashion and the verdict will be innocence or guilt according to the greater intelligence of one or the other of the contending parties. Persuasiveness at its height, Hume tells us, leaves little room for intelligence and consideration. It addresses itself entirely to the imagination and the affections, captures the well-inclined auditors, and dominates their understanding. Fortunately this height is rarely reached. In any event, this height, which also dominates those who know the subject, will always be rare, yet the jury are not people of knowledge and hence dominations ensue, even through attempts at persuasiveness which have attained no height whatever. Hence the great danger.
The only help against this is in the study by the presiding justice, not as lawyer but as psychologist, of the faces of the jury while the contending lawyers make their addresses. He must observe very narrowly and carefully every influence exercised by the speeches, which is irrelevant to the real problem, and then in summing up call it to the attention of the jury and bring them back to the proper point of view. The ability to do this is very marvelous, but it again is an exceedingly difficult performance.
Nowadays persuadability is hardly more studied but anybody who has empirically attained some proficiency in it has acquired the same tricks that are taught by theory. But these must be known if they are to be met effectively. Hence the study of the proper authors can not be too much recommended. Without considering the great authors of the classical period, especially Aristotle and Cicero, there are many modern ones who might be named.
The judgment to be discussed in the following section is not the judgment of the court but the more general judgment which occurs in any perception. If we pursue our tasks earnestly we draw from the simplest cases innumerable inferences and we receive as many inferences from those we examine. The correctness of our work depends upon the truth of both. I have already indicated how very much of the daily life passes as simple and invincible sense-perception even into the determination of a sentence, although it is often no more than a very complicated series of inferences each of which may involve a mistake even if the perception itself has been correct. The frequency with which an inference is made from sense-perception is the more astonishing inasmuch as it exceeds all that the general and otherwise valid law of laziness permits. In fact, it contradicts that law, though perhaps it may not do so, for a hasty inference from insufficient premises may be much more comfortable than more careful observation and study. Such hasty inference is made even with regard to the most insignificant things. In the course of an investigation we discover that we have been dealing only with inferences and that our work therefore has been for nothing. Then again, we miss that fact, and our results are false and their falsehood is rarely sought in these petty mistakes. So the witness may have “seen” a watch in such and such a place when in reality he has only heard a noise that he took for the ticking of a watch and henceinferredthat there had really been a watch, that he hadseen it, and finallybelievedthat he had seen it. Another witness asserts that X has many chickens; as a matter of fact he has heard two chickens cluck and infers a large number. Still another has seen footprints of cattle and speaks of a herd, or he knows the exact time of a murder because at a given time he heard somebody sigh, etc. There would be little difficulty if people told us how they had inferred, for then a test by means of careful questions would be easy enough—but they do not tell, and when we examine ourselves we discover that we do exactly the same thing and often believe and assert that we have seen or heard or smelt or felt although we have only inferred these things.[153]Here belong all cases of correct or partly correct inference and of false inference from false sense-perception. I recall the oft-cited story in which a whole judicial commission smelt a disgusting odor while a coffin was being exhumed only to discover that it was empty. If the coffin, for one reason or another, had not been opened all those present would have taken oath that they had an indubitable perception although the latter was only inferred from its precedent condition.
Exner[154]cites the excellent example in which a mother becomes frightened while her child cries, not because the cry as such sounds so terrible as because of its combination with the consciousness that it comes from her own child and that something might have happened to it. It is asserted, and I think rightly, that verbal associations have a considerable share in such cases. As Stricker[155]expresses it, the form of any conceptual complex whatever, brings out its appropriate word. If we see thethingwatch, we get thewordwatch. If we see a man with a definite symptom of consumption the word tuberculosis occurs at once. The last example is rather more significant because when the whole complex appears mistakes are more remote than when merely one or another “safe” symptom permits the appearance of the word in question. What is safe to one mind need not be so to another, and the notion as to the certainty of any symptom changes with time and place and person. Mistakes are especially possible when people are so certain of their “safe” symptoms that they do not examine how they inferred from them. This inference, however, is directly related to the appearance of the word. Return to the example mentioned above, and suppose that A has discovered a “safe” symptom of consumption in B and theword tuberculosis occurs to him. But the occurrence does not leave him with the word merely, there is a direct inference “B has tuberculosis.” We never begin anything with the word alone, we attach it immediately to some fact and in the present case it has become, as usual, a judgment. The thought-movement of him who has heard this judgment, however, turns backward and he supposes that the judge has had a long series of sense-perceptions from which he has derived his inference. And in fact he has had only one perception, the reliability of which is often questionable.
Then there is the additional difficulty that in every inference there are leaps made by each inferer according to his character and training. And the maker does not consider whether the other fellow can make similar leaps or whether his route is different. E. g., when an English philosopher says, “We really ought not to expect that the manufacture of woolens shall be perfected by a nation which knows no astronomy,”—we are likely to say that the sentence is silly; another might say that it is paradoxical and a third that it is quite correct, for what is missing is merely the proposition that the grade of culture made possible by astronomy is such as to require textile proficiency also. “In conversation the simplest case of skipping is where the conclusion is drawn directly from the minor premise. But many other inferences are omitted, as in the case of real thinking. In giving information there is review of the thinking of other people; women and untrained people do not do this, and hence the disconnectedness of their conversation.”[156]In this fact is the danger in examining witnesses, inasmuch as we involuntarily interpolate the missing details in the skipping inferences, but do it according to our own knowledge of the facts. Hence, a test of the correctness of the other man’s inference becomes either quite impossible or is developed coarsely. In the careful observation of leaping inferences made by witnesses—and not merely by women and the uneducated—it will be seen that the inference one might oneself make might either have been different or have proceeded in a different way. If, then, all the premises are tested a different result from that of the witness is obtained. It is well known how identical premises permit of different conclusions by different people.
In such inferences certain remarkable things occur which, as a rule, have a given relation to the occupation of the witness. So, e.g., people inclined to mathematics make the greatest leaps, and though these may be comparatively and frequently correct, thedanger of mistake is not insignificant when the mathematician deals in his mathematical fashion with unmathematical things.
Another danger lies in the testimony of witnesses who have a certain sense of form in representation and whose inferential leaps consists in their omitting the detailed expression and in inserting the notion of form instead. I learned of this notable psychosis from a bookkeeper of a large factory, who had to provide for the test of numberless additions. It was his notion that if we were to add two and three are five, and six are eleven, and seven are eighteen we should never finish adding, and since the avoidance of mistakes requires such adding we must so contrive that the image of two and three shall immediately call forth the image of five. Now this mental image of five is added with the actual six and gives eleven, etc. According to this we do not add, we see only a series of images, and so rapidly that we can follow with a pencil but slowly. And the images are so certain that mistake is impossible. “You know how 9 looks? Well, just as certainly we know what the image of 27 and 4 is like; the image of 31 occurs without change.”
This, as it happens, is a procedure possible only to a limited type, but this type occurs not only among bookkeepers. When any one of such persons unites two events he does not consider what may result from such a union; he sees, if I may say so, only a resulting image. This image, however, is not so indubitably certain as in the case of numbers; and it may take all kinds of forms, the correctness of which is not altogether probable. E. g., the witness sees two forms in the dark and the flash of a knife and hears a cry. If he belongs to the type under discussion he does not consider that he might have been so frightened by the flashing knife as to have cried out, or that he had himself proceeded to attack with a stick and that the other fellow did the yelling, or that a stab or cut had preceded the cry—no, he saw the image of the two forms and the knife and he heard the cry and these leap together into an image, i.e., one of the forms has a cut above his brow. And these leaps occur so swiftly and with such assurance that the witness in question often believes himself to have seen what he infers and swears to it.
There are a great many similar processes at the bottom of impressions that depend only upon swift and unconscious inference. Suppose, e.g., that I am shown the photograph of a small section of a garden, through which a team is passing. Although I observe the image of only a small portion of the garden and therefore have no notion of its extent, still, in speaking of it, I shall probablyspeak of a very big garden. I have inferred swiftly and unconsciously that in the fact that a wagon and horses were present in the pictured portion of the garden, is implied great width of road, for even gardens of average size do not have such wide roads as to admit wagons; the latter occurring only in parks and great gardens. Hence my conclusion: the garden must be very big. Such inferences[157]are frequent, whence the question as to the source and the probability of the witness’s information, whether it is positive or only an impression. Evidently such an impression may be correct. It will be correct often, inasmuch as impressions occur only when inferences have been made and tested repeatedly. But it is necessary in any case to review the sequence of inferences which led to this impression and to examine their correctness. Unfortunately the witness is rarely aware whether he has perceived or merely inferred.
Examination is especially important when the impression has been made after the observation of a few marks or only a single one and not very essential one at that. In the example of the team the impression may have been attained by inference, but frequently it will have been attained through some unessential, purely personal, determinative characteristic. “Just as the ancient guest recognizes his friend by fitting halves of the ring, so we recognize the object and its constitution from one single characteristic, and hence the whole vision of it is vivified by that characteristic.”[158]
All this is very well if no mistakes are made. When Tertullian said, “Credo quia impossibile est,” we will allow honesty of statement to this great scholar, especially as he was speaking about matters of religion, but when Socrates said of the works of Heraclitus the Obscure: “What I understand of it is good; I think that what I do not understand is also good”—he was not in earnest. Now the case of many people who are not as wise as Tertullian and Socrates is identical with theirs. Numerous examinations of witnesses made me think of Tertullian’s maxim, for the testimonies presented the most improbable things as facts. And when they even explained the most unintelligible things I thought: “And what you do not understand is also good.”
This belief of uncultured people in their own intelligence has been most excellently portrayed by Wieland in his immortal “Abderites.” The fourth philosopher says: “What you call the worldis essentially an infinite series of worlds which envelop one another like the skin of an onion.” “Very clear,” said the Abderites, and thought they understood the philosopher because they knew perfectly well what an onion looked like. The inference which is drawn from the comprehension of one term in a comparison to the comprehension of the other is one of the most important reasons for the occurrence of so many misunderstandings. The example, as such, is understood, but its application to the assertion and the question whether the latter is also made clear by the example are forgotten. This explains the well known and supreme power of examples and comparisons, and hence the wise of all times have used comparisons in speaking to the poor in spirit. Hence, too, the great effect of comparisons, and also the numerous and coarse misunderstandings and the effort of the untrained and unintelligent to clarify those things they do not understand by means of comparisons. Fortunately they have, in trying to explain the thing to other people, the habit of making use of these difficultly discovered comparisons so that the others, if they are only sufficiently observant, may succeed in testing the correctness of the inference from one term in a comparison to the other. We do this frequently in examining witnesses, and we discover that the witness has made use of a figure to clarify some unintelligible point and that he necessarily understands it since it lies within the field of his instruments of thought. But what is compared remains as confused to him as before. The test of it, therefore, is very tiring and mainly without results, because one rarely succeeds in liberating a man from some figure discovered with difficulty. He always returns to it because he understands it, though really not what he compares. But what is gained in such a case is not little, for the certainty that, so revealed, the witness does not understand the matter in hand, easily determines the value of his testimony.
The fullness of the possibilities under which anything may be asserted is also of importance in this matter. The inference that a thing is impossible is generally made by most people in such wise that they first consider the details of the eventualities they already know, or immediately present. Then, when these are before them, they infer that the matter is quite impossible—and whether one or more different eventualities have missed of consideration, is not studied at all. Our kindly professor of physics once told us: “To-day I intended to show you the beautiful experiments in the interference of light—but it can not be observed in daylight and whenI draw the curtains you raise rough-house. The demonstration is therefore impossible and I take the instruments away.” The good man did not consider the other eventuality, that we might be depended upon to behave decently even if the curtains were drawn.
Hence the rule that a witness’s assertion that a thing is impossible must never be trusted. Take the simplest example. The witness assures us that it is impossible for a theft to have been committed by some stranger from outside. If you ask him why, he will probably tell you: “Because the door was bolted and the windows barred.” The eventuality that the thief might have entered by way of the chimney, or have sent a child between the bars of the window, or have made use of some peculiar instrument, etc., are not considered, and would not be if the question concerning the ground of the inference had not been put.
We must especially remember that we criminalists “must not dally with mathematical truth but must seek historical truth. We start with a mass of details, unite them, and succeed by means of this union and test in attaining a result which permits us to judge the existence and the characteristics of past events.” The material of our work lies in the mass of details, and the manner and reliability of its presentation determines the certainty of our inferences.
Seen more closely the winning of this material may be described as Hume describes it:[159]“If we would satisfy ourselves, therefore, concerning the nature of that evidence which assures us of matters of fact, we must inquire how we arrive at the knowledge of cause and effect. I shall venture to affirm as a general proposition which admits of no exception, that the knowledge of this relation is not, in any instance, attained by reasonings a priori; but arises entirely from experience, when we find that any particular objects are constantly conjoined with each other; ... nor can our reason, unassisted by experience, ever draw any inference concerning real existence and matter of fact.”
In the course of his explanation Hume presents two propositions,
(1) I have found that such an object has always been attended with such an effect.
(2) I foresee that other objects which are in appearance similar, will be attended with similar effects.
He goes on: “I shall allow, if you please, that the one proposition may justly be inferred from the other; I know in fact that it alwaysis inferred. But if you insist that the inference is made by a chain of reasoning, I desire you to produce that chain of reasoning. The connection between these propositions is not intuitive. There is required a medium which may enable the mind to draw such an inference, if, indeed, it be drawn by reasoning and argument. What the medium is, I must confess, passes my comprehension; and it is incumbent on those to produce it who assert that it exists, and is the origin of all our conclusions concerning matters of fact.”
If we regard the matter more closely we may say with certainty: This medium exists not as a substance but as a transition. When I speak in the proposition of “such an object,” I already have “similar” in mind, inasmuch as there is nothing absolutely like anything else, and when I say in the first proposition, “such an object,” I have already passed into the assertion made in the second proposition.
Suppose that we take these propositions concretely:
(1) I have discovered that bread made of corn has a nourishing effect.
(2) I foresee that other apparently similar objects, e.g., wheat, will have a like effect.
I could not make various experiments with the same corn in case (1). I could handle corn taken as such from one point of view, or considered as such from another, i.e., I could only experiment with very similar objects. I can therefore make these experiments with corn from progressively remoter starting points, or soils, and finally with corn from Barbary and East Africa, so that there can no longer be any question of identity but only of similarity. And finally I can compare two harvests of corn which have less similarity than certain species of corn and certain species of wheat. I am therefore entitled to speak of identical or similar in the first proposition as much as in the second. One proposition has led into another and the connection between them has been discovered.
The criminological importance of this “connection” lies in the fact that the correctness of our inferences depends upon its discovery. We work continuously with these two Humian propositions, and we always make our assertion, first, that some things are related as cause and effect, and we join the present case to that because we consider it similar. If it is really similar, and the connection of the first and the second proposition are actually correct, the truth of the inference is attained. We need not count the unexplained wonders of numerical relations in the result. D’Alembertasserts: “It seems as if there were some law of nature which more frequently prevents the occurrence of regular than irregular combinations; those of the first kind are mathematically, but not physically, more probable. When we see that high numbers are thrown with some one die, we are immediately inclined to call that die false.” And John Stuart Mill adds, that d’Alembert should have set the problem in the form of asking whether he would believe in the die if, after having examined it and found it right, somebody announced that ten sixes had been cast with it.
We may go still further and assert that we are generally inclined to consider an inference wrong which indicates that accidental matters have occurred in regular numerical relation. Who believes the hunter’s story that he has shot 100 hares in the past week, or the gambler’s that he has won 1000 dollars; or the sick man’s, that he was sick ten times? It will be supposed at the very least that each is merely indicating an approximately round sum. Ninety-six hares, 987 dollars, and eleven illnesses will sound more probable. And this goes so far that during examinations, witnesses are shy of naming such “improbable ratios,” if they at all care to have their testimony believed. Then again, many judges are in no wise slow to jump at such a number and to demand an “accurate statement,” or even immediately to decide that the witness is talking only “about.” How deep-rooted such views are is indicated by the circumstance that bankers and other merchants of lottery tickets find that tickets with “pretty numbers” are difficult to sell. A ticket of series 1000, number 100 is altogether unsalable, for such a number “can not possibly be sold.” Then again, if one has to count up a column of accidental figures and the sum is 1000, the correctness of the sum is always doubted.