SECT. 23.] Measurement of Belief. 145 



Now it will be obvious, on a moment s consideration, that 

 our conduct is capable of being slightly varied: of being 

 varied, that is, in form, whilst it remains identical in respect 

 of its results. It is clear that to pay 1 every time we lose, 

 and to get 1 every time we gain, comes to precisely the same 

 thing, in the case under consideration, as to pay ten shillings 

 every time without exception, and to receive 1 every time 

 that head occurs. It is so, because heads occur, on the 

 average, every other time. In the long run the two results 

 coincide ; but there is a marked difference between the two 

 cases, considered individually. The difference is two-fold. 

 In the first place we depart from the notion of a payment 

 every other time, and come to that of one made every time. 

 In the second place, what we pay every time is half of what 

 we get in the cases in which we do get anything. The dif 

 ference may seem slight ; but mark the effect when our con 

 duct is translated back again into the subjective condition 

 upon which it depends, viz. into our belief. It is in conse 

 quence of such a translation, as it appears to me, that the 

 notion has been acquired that we have an accurately deter- 

 minable amount of belief as to every such proposition. To 

 have losses and gains of equal amount, and to incur them 

 equally often, was the experience connected with our belief 

 that the two events, head and tail, would occur equally often. 

 This was quite intelligible, for it referred to the long run. 

 To find that this could be commuted for a payment made 

 every time without exception, a payment, observe, of half the 

 amount of what we occasionally receive, has very naturally 

 been interpreted to mean that there must be a state of half- 

 belief which refers to each individual throw. 



23. One such example, of course, does not go far to 

 wards establishing a theory. But the reader will bear in 

 mind that almost all our conduct tends towards the same 

 v - 10 



