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possession of all the determining factors of a phenomenon； and hence we must adhere to the only unexceptionable rule： _Be careful about making rules that admit of no exceptions_。 There is still another objection to discuss； i。 e。 the mathematical exception to Humian skepticism。 It might be held that inasmuch as the science of justice is closely related in many ways to mathematics； it may permit of propositions a priori。 Leibnitz already had said； ‘‘The mathematicians count with numbers； the lawyers with ideas；fundamentally both do the same thing。'' If the relationship were really so close； general skepticism about phenomenal sciences could not be applied to the legal disciplines。 But we nowadays deal not with concepts merely； and in spite of all obstruction； Leibnitz's time has passed and the realities of 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。
＇1＇ Liebman Zur Analysis der Wirklichkeit。 Strassburg 1888。
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： ‘‘If 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； ‘‘If the relations remain the same as formerly the moon must rise to…morrow at such and such a time。'' ‘‘If 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 rle 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。 ‘‘The 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 ‘‘the 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；that fire burns； that water flows downward；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。''＇1＇
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 ‘‘fire 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
＇1＇ ttingen： Die Moralstatistik。 Erlangen 1882。
rare。 The situation is different in other disciplines。 ‘‘Our experience；'' says James Sully；''＇1＇ enables 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 ad