SECT. 19.] Measurement of Belief. 141 



in itself; but it is sufficient for our present purpose, which is 

 merely that of determining what is meant by the correctness 

 of our belief, and by the test of its correctness. In all infer 

 ences about things, in which the amount of our belief is not 

 taken into account, such an explanation as the above is quite 

 sufficient ; it would be the ordinary one in any question of 

 science. It is moreover perfectly intelligible, whether the 

 conclusion is particular or universal. Whether we believe 

 that some men die 7 , or that all men die , our belief may with 

 equal ease be tested by the appropriate train of experience. 



19. But when we attempt to apply the same test to 

 partial belief, we shall find ourselves reduced to an awkward 

 perplexity. A difficulty now emerges which has been singu 

 larly overlooked by those who have treated of the subject. 

 As a simple example will serve our purpose, we will take the 

 case of a penny. I am about to toss one up, and I therefore 

 half believe, to adopt the current language, that it will give 

 head. Now it seems to be overlooked that if we appeal to 

 the event, as we did in the case last examined, our belief 

 must inevitably be wrong, and therefore the test above men 

 tioned will fail. For the thing must either happen or not 

 happen : i.e. in this case the penny must either give head, or 

 not give it; there is no third alternative. But whichever 

 way it occurs, our half-belief, so far as such a state of mind 

 admits of interpretation, must be wrong. If head does come, 

 I am wrong in not having expected it enough ; for I only half 

 believed in its occurrence. If it does not happen, I am 

 equally wrong in having expected it too much; for I half 

 believed in its occurrence, when in fact it did not occur at all. 



The same difficulty will occur in every case in which we 

 attempt to justify our state of partial belief in a single con 

 tingent event. Let us take another example, slightly differ 

 ing from the last. A man is to receive 1 if a die gives six, 



