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our profession, indeed its most important object, the human being itself, constitute an integrating part of our studies. And the question may be still further raised whether mathematics is really so exempt from skepticism. The work of Gauss, Lobatschewski, Bolyai, Lambert, would make the answer negative.

Let us, for once, consider what significance mathematical postulates have. When Pythagoras discovered his proposition in such a way that he first drew a right-angled triangle and then built a square on each of the sides, and finally measured the area of each and compared them, he must at first have got the notion that that also might be merely accidental. If he had made the construction 10 or 100 times with various triangles and these had resulted always identically, only then might he have been justified in saying that he had apparently discovered a theorem. But then his process was just as thoroughly experiential as that of a scientist who says that a bird has never yet been observed to give birth to living young, and that hence all birds lay eggs.

But Pythagoras did not proceed in this experiential manner in the discovery of his theorem. He constructed and he counted, and when he did that he acted on postulates: β€œIf this is a right-angled triangle and if that be a square, so,”—and this is just what is done in every science. The general propositions are, β€œIf the relations remain the same as formerly the moon must rise to-morrow at such and such a time.” β€œIf this step in a deduction is not false, if it is well grounded at this point, if it really refers to x, it follows....” In his procedures the criminalist does exactly the same thing. What he must be skeptical about is the postulates from which he starts.

Section 26. (d) The Empirical Method in the Study of Cases.

Properly to bound our discussion of Humian skepticism, a few words have to be said concerning the empirical method of the sciences. We will call those laws purely empirical which, in the study of nature, yield regularities that are demonstrated by observation and experiment, but upon which little or no reliance is placed with regard to cases which differ considerably from the observed. The latter is done because no reason is seen for the existence of such laws. The empirical rule is, therefore, no final law, but is capable of explaining, especially when true, e.g., the succession of a certain condition of weather from certain meteorological signs, the improvement of species through crossing, the fact that some alloys are harder than their components, and so on. Or, to choose examples from our own field, jurisprudence may assert as empirical law that a murderer is a criminal who has gone unpunished for his earlier crimes; that all gamblers show such significant resemblances; that the criminal who has soiled his hands with blood in some violent crime was accustomed to wipe them on the underside of a table; that the slyest person generally perpetrates some gross stupidity after committing a serious crime, and so renders discovery simpler; that lust and cruelty have a certain relation; that superstition plays a great rΓ΄le in crime, etc.

It is of exceeding importance to establish such purely empiric laws in our science, which has done little with such matters because, owing to scanty research into most of them, we need these laws. We know approximately that this and that have come to light so and so often, but we have not reduced to order and studied systematically the cases before us, and we dare not call this knowledge natural law because we have subjected it to no inductive procedure. β€œThe reference of any fact discovered by experience to general laws or rules we call induction. It embraces both observation and deduction.” Again, it may be defined as β€œthe generalization or universalization of our experiences; and inference that a phenomenon occurring x times will invariably occur when the essential circumstances remain identical. The earliest investigators started with the simplest inductions,β€”that fire burns, that water flows downward,β€”so that new, simple truths were continually discovered. This is the type of scientific induction and it requires further, the addition of certainty and accuracy.”[138]

The foregoing might have been written expressly for us lawyers, but we have to bear in mind that we have not proceeded in our own generalizations beyond β€œfire burns, water flows downward.” And such propositions we have only derived from other disciplines. Those derived from our own are very few indeed, and to get more we have very far to go. Moreover, the laws of experience are in no way so certain as they are supposed to be, even when mathematically conceived. The empirical law is established that the sum of the three angles of a triangle is equal to two right angles. And yet nobody, ever since the science of surveying has been invented, has succeeded in discovering 180 degrees in any triangle. Now then, when even such things, supposed ever since our youth to be valid, are not at all true, or true theoretically only, how much more careful must we be in making inferences from much less certain rules, even though we have succeeded in using them before in many analogous cases? The activity of a criminalist is of far too short duration to permit him to experience any more than a very small portion of the possibilities of life, and suggestions from foreign sources are very rare. The situation is different in other disciplines. β€œOur experience,” says James Sully,[139] β€œenables us to express a number of additional convictions. We can predict political changes and scientific developments, and can conceive of the geographical conditions at the north pole.” Other disciplines are justified to assert such additional propositions, but is ours? A man may have dealt for years with thieves and swindlers, but is he justified in deducing from the inductions made in his experience, the situation of the first murderer he deals with? Is he right in translating things learned by dealing with educated people to cases where only peasants appear? In all these cases what is needed in making deductions is great caution and continual reminder to be very careful, for our work here still lacks the proper material. In addition we have to bear in mind that induction is intimately related to analogy. According to Lipps[140] the ground of one is the ground of the other; they both rest on the same foundation. β€œIf I am still in doubt whether the fact on which a moment ago I depended as the sufficient condition for a judgment may still be so regarded, the induction is uncertain. It is unjustified when I take for sufficiently valid something that as a matter of fact ought not to be so taken.” If we bear in mind how much we are warned against the use of analogy, how it is expressly excluded in the application of certain criminal laws, and how dangerous the use of every analogy is, we must be convinced that the use for our cases of both induction and analogy, is always menace. We have at the same time to bear in mind how much use we actually make of both; even our general rulesβ€”e.g., concerning false testimony,β€”bias, revertibility, special inclinations, etc.β€”and our doctrines concerning the composition and indirection of testimony, even our rules concerning the value of witnesses and confessions, all these depend upon induction and analogy. We pass by their use in every trial from case to case. A means so frequently and universally used must, however, be altogether reliable, or be handled with the greatest care. As it is not the first it must be handled in the second way.

We have yet to indicate the various ways in which induction may be used. Fick has already called attention to the astounding question concluding Mill’s system of logic: Why, in many cases, is a single example sufficient to complete induction, while in other cases myriads of unanimous instances admitting of no single known or suspected exception, make only a small step toward the establishment of a generally valid judgment?

This question is of enormous significance in criminal cases because it is not easy to determine in any particular trial whether we have to deal with a situation of the first sort where a single example is evidential, or a situation of the second sort where a great many examples fail to be evidential. On this difficulty great mistakes depend, particularly mistakes of substitution of the first for the second. We are satisfied in such cases with a few examples and suppose ourselves to have proved the case although nothing whatever has been established.

We must see first of all if it is of any use to refer the difficulty of the matter to the form in which the question is put, and to say: The difficulty results from the question itself. If it be asked, β€œAre any of the thousand marbles in the bag white marbles?” the question is determined by the first handful, if the latter brings to light a single white marble. If, however, the problem is phrased so: Does the bag contain white marbles only? then, although 999 marbles might already have been drawn from the receptacle, it can not be determined that the last marble of the 1000 is white. In the same way, if people assert that the form of the question determines the answer, it does not follow that the form of the question is itself determined or distinguished inasmuch as the object belongs to the first or the second of the above named categories.

A safe method of distinction consists in calling the first form of the question positive and the second negative. The positive refers to a single unit; the negative to a boundless unit. If then I ask: Are there any white marbles whatever in the bag? the answer is rendered affirmative by the discovery of a single white marble. But if the question is phrased: Are there only white marbles in the bag? merely its form is positive but its intent is negative. To conform the manner of the question to its intent, it would be necessary to ask: Are there no other colors than white among the marbles in the bag? And inasmuch as the negative under given circumstances is in many ways boundless, the question admits of no answer until the last marble has been brought to light. If the total number of marbles is unlimited the question can receive no complete inductive answer in mathematical form; it can be solved only approximately. So again, if one asks: Are there any purely blue birds? the answer is affirmative as soon as a single completely blue bird is brought to light. But if the question is: Do not also striped birds exist? no answer is possible until the very last bird on earth is exhibited. In that way only could the possibility be excluded that not one of the terrestrial fowls is striped. As a matter of fact we are satisfied with a much less complete induction. So we say: Almost the whole earth has been covered by naturalists and not one of them reports having observed a striped bird; hence there would be none such even in the unexplored parts of the earth. This is an inductive inference and its justification is quite another question.

The above mentioned distinction may be made still clearer if instead of looking back to the form of the question, we study only the answer. We have then to say that positive statements are justified by the existence of a single instance, negative assertions only by the complete enumeration of all possible instances and never at all if the instances be boundless. That the negative proof always requires a series of demonstrations is

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