174 INDUCTION. 



chance, but to unfairness in the dice, is unquestionably true. 

 But this arises from a totally different principle. We should 

 then he 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 referred 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 general cause operating through the structure 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 

 produce it, than to a cause which would be very unlikely to 

 produce it. According 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, unfair- 

 ness in the dice, would after a very few throws far outweigh 

 any antecedent probability 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 accounted for is not the occurrence itself, but the fact of 

 the witness's asserting 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 

 series of numbers, supposing him to be 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 



