SECT. 8.] The Rules of Inference in Probability. 177 



the chance of the occurrence of the particular event. The 

 question may therefore now be raised, Can those writers who 

 (as described in the last chapter) take as the primary subject 

 of the science not the degree of statistical frequency, but the 

 quantity of belief, with equal consistency make this the basis 

 of their rules, and so also regard the fraction expressive of 

 the chance as a merely synonymous expression ? De Morgan 

 maintains that whereas in ordinary logic we suppose the 

 premises to be absolutely true, the province of Probability is 

 to study the effect which partial belief of the premises pro 

 duces with respect to the conclusion. It would appear 

 therefore as if in strictness we ought on this view to be able 

 to determine this consequent diminution at first hand, from 

 introspection of the mind, that is of the conceptions and 

 beliefs which it entertains; instead of making any recourse 

 to statistics to tell us how much we ought to believe the 

 conclusion. 



Any readers who have concurred with me in the general 

 results of the last chapter, will naturally agree in the conclu 

 sion that nothing deserving the name of logical science can 

 be extracted from any results of appeal to our consciousness 

 as to the quantity of belief we entertain of this or that pro 

 position. Suppose, for example, that one person in 100 dies 

 on the sea passage out to India, and that one in 9 dies dur 

 ing a 5 years residence there. It would commonly be said 

 that the chance that any one, who is now going out, has of 

 living to start homewards 5 years hence, is -^ ; for his chance 

 of getting there is T 9 ^ ; and of his surviving, if he gets 

 there, f ; hence the result or dependent event is got by 

 multiplying these fractions together, which gives -fijfo. Here 

 the real basis of the reasoning is statistical, and the processes 

 or results are merely translated afterwards into fractions. 

 But can we say the same when we look at the belief side of 

 v. 12 



