GROUNDS OF DISBELIEF 



41S 



flifferent principle. We should then 

 be considering, not the probability of 

 the fact in itself, but the comparative 

 probability with which, when it is 

 known to have happened, it may be re- 

 ferred to one or to another cause. The 

 regular series is not at all less likely 

 than the irregular one to be brought 

 about by chance, but it is much more 

 likely than the irregular one to be 

 produced by design, or by some gene- 

 ral cause operating through the struc- 

 ture of the dice. It is the nature of 

 casual combinations to produce a 

 repetition of the same event, as often 

 and no oftener than any other series 

 of events. But it is the nature of 

 general causes to reproduce, in the 

 same circumstances, always the same 

 event. Common sense and science 

 alike dictate that, all other things 

 being the same, we should rather 

 attribute the effect to a cause which, 

 if real, would be very likely to pro- 

 duce it, than to a cause which would 

 be very unlikely to produce it. Ac- 

 cording to Laplace's sixth theorem, 

 which we demonstrated in a former 

 chapter, the difference of probability 

 arising from the superior efficacy of 

 the constant cause, unfairness in the 

 dice, would after a very few throws 

 far outweigh any antecedent proba- 

 bility which there could be against its 

 existence. 



D'Alembert should have put the 

 question in another manner. He 

 should have supposed that we had 

 ourselves previously tried the dice, 

 and knew by ample experience that 

 they were fair. Another person then 

 tries them in our absence, and assures 

 us that he threw sixes ten times in 

 succession. Is the assertion credible 

 or not? Here the effect to be ac- 

 counted for is not the occurrence 

 itself, but the fact of the witness's as- 

 serting it. This may arise either 

 from its having really happened, or 

 from some other cause. What we 

 have to estimate is the comparative 

 probability of these two suppositions. 



If the witness affirmed that he had 

 thrown any other ieries of numbers, 



supposing him to he a person of 

 veracity and tolerable accuracy, and 

 to profess that he took particular 

 notice, we should believe him. But 

 the ten sixes are exactly as likely to 

 have been really thrown as the other 

 series. If, therefore, this assertion 

 is less credible than the other, the 

 reason must be, not that it is less 

 likely than the other to be made 

 truly, but that it is more likely than 

 the other to be made falsely. 



One reason obviously presents itself 

 why what is called a coincidence 

 should be oftener asserted falsely 

 than an ordinary combination. It 

 excites wonder. It gratifies the love 

 of the marvellous. The motives, 

 therefore, to falsehood, one of the 

 most frequent of which is the desire 

 to astonish, operate more strongly in 

 favour of this kind of assertion than 

 of the other kind. Thus far there is 

 evidently more reason for discrediting 

 an alleged coincidence, than a state- 

 ment in itself not more probable, but 

 which if made would not be thought 

 remarkable. There are cases, how- 

 ever, in which the presumption on 

 this ground would be the other way. 

 There arc some witnesses who, the 

 more extraordinary an occurrence 

 might appear, would be the more 

 anxious to verify it by the utmost 

 carefulness of observation before they 

 would venture to believe it, and still 

 more before they would assert it to 

 others. 



§ 6. Independently, however, of 

 any peculiar chances of mendacity 

 arising from the nature of the asser- 

 tion, Laplace contends, that merely 

 on the general ground of the falli- 

 bility of testimony, a coincidence is 

 not credible on the same amount of 

 testimony on which we should be 

 warranted in believing an ordinary 

 combination of events. In order to 

 do justice to his argument, it is neces- 

 sary to illustrate it by the example 

 chosen by himself. 



If, says Laplace, there were one 

 thousand tickets in a box, and one 



