190 INDUCTION. 



sion, while to another, the same thing would be a 

 motive for assuring himself more positively of the fact, 

 and would therefore actually increase the credit due 

 to his testimony. 



The mathematical reasoning which misled Laplace 

 into this logical error, is too long to be here quoted. 

 It is found in the section of his Essai Philosophique 

 sur les Probabilites entitled De la Probabilite des 

 Temoignages, and is founded upon a misapplication, 

 noticed by us in a former place, of his own sixth theorem 

 of the doctrine of chances ; a theorem which he himself 

 describes as that by which we determine the proba- 

 bility that a given effect was produced by one or by 

 another of several causes capable of producing it. 

 The substance of his argument may be briefly stated 

 as follows: Treating the assertion of the witness as 

 the effect, he considers as its two possible causes, the 

 veracity or mendacity of the witness on the particular 

 occasion, that is, the truth or falsity of the fact. Ac- 

 cording to the theorem, the probability that the effect 

 was produced by a particular cause, is as the antece- 

 dent probability of the cause, multiplied by the pro- 

 bability that the cause, if it existed, would produce the 

 given effect. Accordingly (says Laplace) in the case of 

 the thousand tickets, the cause mendacity might pro- 

 duce any one of 999 untrue statements, while in the 

 case of the balls, there being only two statements to 

 make, viz., white or black, and one of these being 

 true, the cause mendacity could only produce one 

 untrue statement: and consequently (the antecedent 

 probability of mendacity from the character of the 

 witness being supposed the same in both cases) men- 

 dacity was 999 times less likely to have produced the 

 particular assertion made, and is therefore 999 times 

 less likely to have existed, in the former case than in 

 the latter. 



