354 



INDUCTION. 



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 misappre- 

 hension of the use of averages : which 

 nerve indeed to protect those whose 

 interest 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 con- 

 clusions from the degree of consis- 

 tency of his statements, his conduct 

 under cross-examination, and the re- 

 lation of the case itself to his interests, 

 his partialities, and his mental capa- 

 city, instead of applying so rude a 

 standard (even if it were capable of 

 being verified) as the ratio between 

 the number of true and the number of 

 erroneous statements which he may 

 be supposed 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 con- 

 curring in a wrong verdict is dimi- 

 nished the more the number is in- 

 creased ; so that if the judges are only 

 made suflBciently numerous, the cor- 

 rectness 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 subject. 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 mudi 

 consequence what the tribunal is, the 

 proposition might probably be re- 

 versed ; besides which, the cause of 

 error, whether arising from the intri- 

 cacy of the case or from some common 

 prejudice or mental infirmity, if it 

 acted upon one judge, would be extre- 

 mely likely to affect all the others in 

 the same manner, or at least a majo- 

 rity, and thus render a wrong instead 

 of a right decision more probable, the 

 more the number was increased. 



These are but samples of the errors 

 frequently committed by men who, 

 having made themselves familiar with 

 the difficult formulae which algebra 

 affords for the estimation of chances 

 under suppositions of a complex cha- 

 racter, like better to employ those 

 formulae in computing what are the 

 probabilities to a person half informed 

 about a case, than to look out for means 

 of being better informed. Before 

 applying the doctrine of chances to 

 any scientific purpose, the foundation 

 must be laid for an evaluation of the 

 chances, by possessing ourselves of the 

 utmost attainable amount of positive 

 knowledge. The knowledge required 

 is that of the comparative frequency 

 with which the different events in fact 

 occur. For the purposes, therefore, 

 of the present work, it is allowable 

 to suppose that conclusions respecting 

 the probability of a fact of a particular 

 kind rest on our knowledge of the 

 proportion between the cases in which 

 facts of that kind occur and those in 

 which they do not occur : this know- 

 ledge being either derived from spe- 

 cific experiment, or deduced from our 

 knowledge of the causes in operation 

 which tend to produce, compared with 

 those which tend to prevent, the fact 

 in question. 



Such calculation of chances is 

 grounded on an induction ; and to 

 render the calculation legitimate, the 

 induction inust be 3, valid one, It 



