162 Measurement of Belief. [CHAP. vi. 



said, that our belief of many events rests upon a very com 

 plicated and extensive basis. My belief may be the product 

 of many conflicting arguments, and many analogies more or 

 less remote ; these proofs themselves may have mostly faded 

 from my mind, but they will leave their effect behind them 

 in a weak or strong conviction. At the time, therefore, I 

 may still be able to say, with some degree of accuracy, 

 though a very slight degree, what amount of belief I enter 

 tain upon the subject. Now we cannot compare things that 

 are heterogeneous: if, therefore, we are to decide between 

 this and an event determined naturally and properly by 

 Probability, it is impossible to appeal to chances or frequency 

 of occurrence. The measure of belief is the only common 

 ground, and we must therefore compare this quantity in each 

 case. The test afforded will be an exceedingly rough one, 

 for the reasons mentioned above, but it will be better than 

 none ; in some cases it will be found to furnish all we want. 



Suppose, for example, that one letter in a million is lost 

 in the Post Office, and that in any given instance I wish to 

 know which is more likely, that a letter has been so lost, or 

 that my servant has stolen it? If the latter alternative 

 could, like the former, be stated in a numerical form, the 

 comparison would be simple. But it cannot be reduced to 

 this form, at least not consciously and directly. Still, if we 

 could feel that our belief in the man s dishonesty was greater 

 than one-millionth, we should then have homogeneous things 

 before us, and therefore comparison would be possible. 



35. We are now in a position to give a tolerably accu 

 rate definition of a phrase which we have frequently been 

 obliged to employ, or incidentally to suggest, and of which 

 the reader may have looked for a definition already, viz. the 

 probability of an event, or what is equivalent to this, the 

 chance of any given event happening. I consider that these 



