SECT. 3.] Measurement of Belief. 121 



that I shall select, and which belongs to the most favourite 

 class of examples in this subject, the substitution becomes 

 accidentally unnecessary. The things, as has been repeatedly 

 pointed out, may sometimes need no trimming, because in 

 the form in which they actually present themselves they are 

 almost idealized. In most cases a good deal of alteration is 

 necessary to bring the series into shape, but in some pro 

 minently in the case of games of chance we find the alter 

 ations, for all practical purposes, needless. 



3. We start then, from such a series as this, upon the 

 enquiry, What kind of inference can be made about it? It 

 may assist the logical reader to inform him that our first step 

 will be analogous to one class of what are commonly known 

 as immediate inferences, inferences, that is, of the type, 

 &quot; All men are mortal, therefore any particular man or men 

 are mortal. This case, simple and obvious as it is in Logic, 

 requires very careful consideration in Probability. 



It is obvious that we must be prepared to form an opinion 

 upon the propriety of taking the step involved ki making 

 such an inference. Hitherto we have had as little to do as 

 possible with the irregular individuals ; we have regarded 

 them simply as fragments of a regular series. But we cannot 

 long continue to neglect all consideration of them. Even if 

 these events in the gross be tolerably certain, it is not only 

 in the gross that we have to deal with them ; they con 

 stantly come before us a few at a time, or even as indivi 

 duals, and we have to form some opinion about them in this 

 state. An insurance office, for instance, deals with num 

 bers large enough to obviate most of the uncertainty, but 

 each of their transactions has another party interested in 

 it What has the man who insures to say to their proceed 

 ings ? for to him this question becomes an individual one. 

 And even the office itself receives its cases singly, and would 



