382 INDUCTION. 



It is obvious, too, that even when the probabilities are derived from ob- 

 servation and experiment, a very slight improvement in the data, by better 

 observations, or by taking into fuller consideration the special circumstances 

 of the case, is of more use than the most elaborate application of the cal- 

 culus to probabilities founded on the data in their previous state of inferi- 

 ority. The neglect of this obvious reflection has given rise to misapplica- 

 tions of the calculus of probabilities which have made it the real oppro- 

 brium of mathematics. It is sufficient to refer to the applications made of 

 it to the credibility of witnesses, and to the correctness of the verdicts of 

 juries. In regard to the first, common sense would dictate that it is im- 

 possible to strike a general average of the veracity and other qualifications 

 for true testimony of mankind, or of any class of them ; and even if it were 

 possible, the employment of it for such a purpose implies a misapprehen- 

 sion of the use of averages, which serve, indeed, to protect those whose in- 

 terest is at stake, against mistaking the general result of large masses of 

 instances, but are of extremely small value as grounds of expectation in any 

 one individual instance, unless the case be one of those in which the great 

 majority of individual instances do not differ much from the average. In 

 the case of a witness, persons of common sense would draw their conclu- 

 sions from the degree of consistency of his statements, his conduct under 

 cross-examination, and the relation of the case itself to his interests, his 

 partialities, and his mental capacity, instead of applying so rude a standard 

 (even if it were capable of being verified) as the ratio between the num- 

 ber of true and the number of erroneous statements which he may be sup- 

 posed to make in the course of his life. 



Again, on the subject of juries or other tribunals, some mathematicians 

 have set out from the proposition that the judgment of any one judge or 

 juryman is, at least in some small degree, more likely to be right than 

 wrong, and have concluded that the chance of a number of persons concur- 

 ring in a wrong vei'dict is diminished the more the number is increased; 

 so that if the judges are only made sufficiently numerous, the correctness 

 of the judgment may be reduced almost to certainty. I say nothing of the 

 disregard shown to the effect produced on the moral position of the judges 

 by multiplying their numbers, the virtual destruction of their individual 

 responsibility, and weakening of the application of their minds to the sub- 

 ject. I remark only the fallacy of reasoning from a wide average to cases 

 necessarily differing greatly from any average. It may be true that, taking 

 all causes one with another, the opinion of any one of the judges would be 

 oftener right than wrong; but the argument forgets that in all but the 

 more simple cases, in all cases in which it is really of much consequence 

 what the tribunal is, the proposition might probably be reversed ; besides 

 which, the cause of error, whether arising from the intricacy of the case or 

 from some common prejudice or mental infirmity, if it acted upon one 

 judge, would be extremely likely to affect all the others in the same man- 

 suppose a case more analogous to those which occur in natui'e : instead of three colors, let 

 there be in the box all possible colors, we being supposed ignorant of the comparative fre- 

 quency with which different colors occur in nature, or in the productions of art. How is the 

 list of cases to be made out ? Is every distinct shade to count as a color ? If so, is the test 

 to be a common eye, or an educated eye — a painter's, for instance ? On the answer to these 

 questions would depend whether the chances against some particular color would be esti- 

 mated at ten, twenty, or perhaps five hundred to one. While if we knew from experience 

 that the particular color occurs on an average a certain number of times in every hundred or 

 thousand, we should not require to know any thing either of the frequency or of the number 

 of the other possibilities. 



