GROUNDS OF DISBELIEF. 195 



If, says Laplace, there are one thousand tickets in 

 a box, and one only has been drawn out ; then if an 

 eye-witness affirms that the number drawn was 79, 

 this, though the chances were 999 in 1000 against it, 

 is not incredible, because the chances were equally 

 great against every other number. But (he continues) 

 if there are in the box 999 black balls and only one 

 white, and the witness affirms that the white ball was 

 drawn, this is incredible ; because there was but one 

 chance in favour of white, and 999 in favour of some 

 black ball. 



This appears to me entirely fallacious. It is evi- 

 dent, both from general reasoning and specific experi- 

 ence, that the white ball will be drawn out exactly as 

 often, in any large number of trials, as the ticket No. 

 79 will ; the two assertions, therefore, are precisely 

 on the same level in point of credibility. There is 

 one way of putting the case which, I think, must 

 carry conviction to every one. Suppose that the 

 thousand balls are numbered, and that the white ball 

 happens to be ticketed 79. Then the drawing of the 

 white ball, and the drawing of No. 79, are the very 

 same event ; how then can the one be credible, the 

 other absolutely incredible ? A witness sees it drawn, 

 and makes his report to us : if he says that No. 79 was 

 drawn, according to Laplace he may be believed ; if he 

 says a white ball was drawn, we are bound to disbe- 

 lieve him. Is this rational ? Is it not clear, on the 

 contrary, that the only difference there could be in the 

 credit due to him would arise from moral causes, 

 namely, from the influence which (if the witness knew 

 that there was but one white ball in a thousand) might 

 be assigned to the greater apparent wonder in the 

 latter case ? which to one kind of person would be a 

 temptation to deceive, or to take up a hasty impres- 



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