SECT. 29.] Measurement of Belief. 153 



often the case, to import other sentiments besides pure belief, 

 and to find a justification for them also in the results of our 

 science, the confusion becomes far worse. The following 

 extract from Archbishop Thomson s Laws of Thought ( 122, 

 Ed. n.) will show what kind of applications of the science are 

 contemplated here : &quot; In applying the doctrine of chances to 

 that subject in connexion with which it was invented games 

 of chance, the principles of what has been happily termed 

 moral arithmetic must not be forgotten. Not only would 

 it be difficult for a gamester to find an antagonist on terms, 

 as to fortune and needs, precisely equal, but also it is im 

 possible that with such an equality the advantage of a 

 considerable gain should balance the harm of a serious loss. 

 * If two men, says Buffon, were to determine to play for 

 their whole property, what would be the effect of this agree 

 ment? The one would only double his fortune, and the 

 other reduce his to naught. What proportion is there be 

 tween the loss and the gain? The same that there is between 

 all and nothing. The gain of the one is but a moderate 

 sum, the loss of the other is numerically infinite, and 

 morally so great that the labour of his whole life may not 

 perhaps suffice to restore his property. &quot; 



As moral advice this is all very true and good. But if it 

 be regarded as a contribution to the science of the subject it 

 is quite inappropriate, and seems calculated to cause con 

 fusion. The doctrine of chances pronounces upon certain 

 kinds of events in respect of number and magnitude ; it has 

 absolutely nothing to do with any particular person s feelings 

 about these relations. We might as well append a corollary 

 to the rules of arithmetic, to point out that although it is 

 very true that twice two are four it does not follow that four 

 horses will give twice as much pleasure to the owner as two 

 will. If two men play on equal terms their chances are 



