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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.[1]

He distinguished:

 

[1] <U:>ber die Wahrscheinlicbkeit, Leipzig 1875.

 

(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 criminal <p 153>

law. 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[1] in the following example: [1] J. v. Kries: <U:>ber die Wahrseheinlichkeit Il. M<o:>glichkeit u. ihre Bedeutung in Strafrecht. Zeitschrift f. d. ges. St. R. W. Vol. IX, 1889.

 

“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 take <p 154>

one 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 $2437 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, natural <p 155>

law, or the unplanned co<o:>peration 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 the <p 156>

discovery 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

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