SECT. 3.] The Rule of Succession. 193 



that which (as was explained in Chap, vi.) measures our 

 belief of the individual case as deduced from the general 

 proposition. Granted that nine men out of ten of the kind 

 to which A. B. belongs do live another year, it obviously 

 does not follow at all necessarily that he will. We describe 

 this state of things by saying, that our belief of his surviving 

 is diminished from certainty in the ratio of 10 to 9, or, in 

 other words, is measured by the fraction -f^. 



(II) But are we certain that nine men out of ten like 

 him will live another year ? we know that they have so sur 

 vived in time past, but will they continue to do so? Since 

 A. B. is still alive it is plain that this proposition is to a 

 certain extent assumed, or rather obtained by Induction. 

 We cannot however be as certain of the inductive inference 

 as we are of the data from which it was inferred. Here, 

 therefore, is a second cause which tends to diminish our 

 belief; in practice these two causes always accompany each 

 other, but in thought they can be separated. 



The two distinct causes described above are very liable 

 to be confused together, and the class of cases from which 

 examples are necessarily for the most part drawn increases 

 this liability. The step from the statement all men have 

 died in a certain proportion to the inference they will con 

 tinue to die in that proportion is so slight a step that it is 

 unnoticed, and the diminution of conviction that should 

 accompany it is unsuspected. In what are called a priori 

 examples the step is still slighter. We feel so certain about 

 the permanence of the laws of mechanics, that few people 

 would think of regarding it as an inference when they 

 believe that a die will in the long run turn up all its faces 

 equally often, because other dice have done so in time 

 Bast. 

 al &quot; 4. It has been already pointed out (in Chapter vi.) 



v. 13 



