SECT. 5.] Measurement of Belief. 123 



which in its nature admits of determination, though we may 

 practically find it difficult in any particular case to determine 

 it. He considers, in fact, that Probability is a sort of sister 

 science to Formal Logic 1 , speaking of it in the following 

 words : &quot; I cannot understand why the study of the effect,, 

 which partial belief of the premises produces with respect to- 

 the conclusion, should be separated from that of the con 

 sequences of supposing the former to be absolutely true 2 &quot;. 

 In other words, there is a science Formal Logic which in 

 vestigates the rules according to which one proposition can be 

 necessarily inferred from another ; in close correspondence 

 with this there is a science which investigates the rules ac 

 cording to which the amount of our belief of one proposition 

 varies with the amount of our belief of other propositions 

 with which it is connected. 



The same view is also supported by another high authority, 

 the late Prof. Donkin, who says (Phil. Mag. May, 1851), &quot;It 

 will, I suppose, be generally admitted, and has often been 

 more or less explicitly stated, that the subject-matter of 

 calculation in the mathematical theory of Probabilities is 

 quantity of belief.&quot; 



5. Before proceeding to criticise this opinion, one re 

 mark may be made upon it which has been too frequently 

 overlooked. It should be borne in mind that, even were this 

 view of the subject not actually incorrect, it might be objected 

 to as insufficient for the purpose of a definition, on the ground 

 that variation of belief is not confined to Probability. It is 

 a property with which that science is concerned, no doubt, 

 but it is a property which meets us in other directions a& 



1 In the ordinary signification of indicated in his title Formal Logic, 



this term. As De Morgan uses it or the Calculus of Inference, neces- 



he makes Formal Logic include Pro- sary and probable.&quot; 



bability, as one of its branches, as 2 Formal Logic. Preface, page v. 



