136 Measurement of Belief. [CHAP. vi. 



sands of the Wash or Morecambe Bay, in a dense mist, when 

 the spring-tide is coming in; and knows therefore that to 

 be once caught by the tide would be fatal. He hears a 

 church-bell at a distance, but has no means of knowing 

 whether it is on the same side of the water with himself or 

 on the opposite side. He cannot tell therefore whether by 

 following its sound he will be led out into the mid-stream 

 and be lost, or led back to dry land and safety. Here there 

 can be no repetition of the event, and the cases are indis- 

 tinguishably alike, to him, in the only circumstances which 

 can affect the issue : is not then his prospect of death, it 

 will be said, necessarily equal to one-half? A proper analysis 

 of his state of mind would be a psychological rather than 

 a logical enquiry, and in any case, as above remarked, the 

 decision of this question does not touch our logical position. 

 But according to the best introspection I can give I should 

 say that what really passes through the mind in such a case 

 is something of this kind: In most doubtful positions and 

 circumstances we are accustomed to decide our conduct by 

 a consideration of the relative advantages and disadvantages 

 of each side, that is by the observed or inferred frequency 

 with which one or the other alternative has succeeded. In 

 proportion as these become more nearly balanced, we are 

 more frequently mistaken in the individual cases ; that is, it 

 becomes more and more nearly what would be called a 

 mere toss up whether we are right or wrong. The case 

 in question seems merely the limiting case, in which it has 



that there are volcanoes on the unseen seem good instances to illustrate the 



side of the moon larger than those position that we always entertain a 



on the side turned towards us; or, certain degree of belief on every 



with Jevons (Principles of Science, question which can be stated, and 



Ed. ii. p. 212) whether he considers that utter inability to give a reason 



that a Platythliptic Coefficient is in favour of either alternative cor- 



positive. These do not therefore responds to half belief. 



