GROUNDS OF DISBELIEF. 177 



To make this argument valid it must of course be supposed, 

 that the announcements made by the witness are average 

 specimens of his general veracity and accuracy ; or, at least, 

 that they are neither more nor less so in the case of the black 

 and white balls, than in the case of the thousand tickets. 

 This assumption, however, is not warranted. A person is far 

 less likely to mistake, who has only one form of error to guard 

 against, than if he had 999 different errors to avoid. For 

 instance, in the example chosen, a messenger who_might make 

 a mistake once in ten times in reporting the number drawn in 

 a lottery, might not err once in a thousand times if sent simply 

 to observe whether a ball was black or white. Laplace s 

 argument therefore is faulty even as applied to his own case. 

 Still less can that case be received as completely representing 

 all cases of coincidence. Laplace has so contrived his example, 

 that though black answers to 999 distinct possibilities, and 

 white only to one, the witness has nevertheless no bias which 

 can make him prefer black to white. The witness did not 

 know that there were 999 black balls in the box and only one 

 white ; or if he did, Laplace has taken care to make all the 

 999 cases so undistinguishably alike, that there is hardly a 

 possibility of any cause of falsehood or error operating in favour 

 of any of them, which would not operate in the same manner 

 if there were only one. Alter this supposition, and the whole 

 argument falls to the ground. Let the balls, for instance, be 

 numbered, and let the white ball be No. 79. Considered in 

 respect of their colour, there are but two things which the 

 witness can be interested in asserting, or can have dreamt or 

 hallucinated, or has to choose from if he answers at random, 

 viz. black and white : but considered in respect of the numbers 

 attached to them, there are a thousand : and if his interest or 

 error happens to be connected with the numbers, though the 

 only assertion he makes is about the colour, the case becomes 

 precisely assimilated to that of the thousand tickets. Or 

 instead of the balls suppose a lottery, with 1000 tickets and 

 but one prize, and that I hold No. 79, and being interested 

 only in that, ask the witness not what was the number drawn, 

 but whether it was 79 or some other. There are now only 

 VOL. u. 12 



