138 Measurement of Belief. [CHAP. vi. 



of a double loss; alternatives which the common mathe 

 matical statement of their chances has a decided tendency 

 to make us regard as indistinguishable from one another. 

 But clearly the decision must be grounded on the desires, 

 feelings, and conscience of the agents. Probability cannot 

 say a word upon this question. As I have pointed out else 

 where, there has been much confusion on this matter in 

 applications of the science to betting, and in the discussion 

 of the Petersburg problem. 



We have thus examined the doctrine in question with 

 a minuteness which may seem tedious, but in consequence of 

 the eminence of its supporters it would have been presump 

 tuous to have rejected it without the strongest grounds. The 

 objections which have been urged might be summarised as 

 follows : the amount of our belief of any given proposition, 

 supposing it to be in its nature capable of accurate determi 

 nation (which does not seem to be the case), depends upon a 

 great variety of causes, of which statistical frequency the 

 subject of Probability is but one. That even if we confine 

 our attention to this one cause, the natural amount of our 

 belief is not necessarily what theory would assign, but has to 

 be checked by appeal to experience. The subjective side of 

 Probability therefore, though very interesting and well de 

 serving of examination, seems a mere appendage of the objec 

 tive, and affords in itself no safe ground for a science of 

 inference. 



17. The conception then of the science of Probability 

 as a science of the laws of belief seems to break down at 

 every point. We must not however rest content with such 

 merely negative criticism. The degree of belief we enter 

 tain of a proposition may be hard to get at accurately, and 

 when obtained may be often wrong, and may need therefore 

 to be checked by an appeal to the objects of belief. Still in 



