14-6 Measurement of Belief. [CHAP. vi. 



result ; that it is not in betting only, but in every course of 

 action in which we have to count the events, that such a 

 numerical apportionment of our conduct is possible. Hence, 

 by the ordinary principles of association, it would appear 

 exceedingly likely that, not exactly a numerical condition of 

 mind, but rather numerical associations, become inseparably 

 connected with each particular event which we know to occur 

 in a certain proportion of times. Once in six times a die 

 gives ace ; a knowledge of this fact, taken in combination 

 with all the practical results to which it leads, produces, one 

 cannot doubt, an inseparable notion of one-sixth connected 

 with each single throw. But it surely cannot be called belief 

 to the amount of one-sixth ; at least it admits neither of 

 justification nor explanation in these single cases, to which 

 alone the fractional belief, if such existed, ought to apply. 



It is in consequence, I apprehend, of such association that 

 we act in such an unhesitating manner in reference to any 

 single contingent event, even when we have no expectation 

 of its being repeated. A die is going to be thrown up once, 

 and once only. I bet 5 to 1 against ace, not, as is commonly 

 asserted, because I feel one -sixth part of certainty in the 

 occurrence of ace; but because I know that such conduct 

 would be justified in the long run of such cases, and I apply 

 to the solitary individual the same rule that I should apply 

 to it if I knew it were one of a long series. This accounts 

 for my conduct being the same in the two cases ; by associa 

 tion, moreover, we probably experience very similar feelings 

 in regard to them both. 



24. And here, on the view of the subject adopted in 

 this Essay, we might stop. We are bound to explain the 

 * measure of our belief in the occurrence of a single event 

 when we judge solely from the statistical frequency with 

 which such events occur, for such a series of events was our 



