134 Measurement of Belief. [CHAP. vi. 



it was exercised, or would suppose that the former had any 

 thing else to do than to follow the lead of the latter. Hence 

 it results that that separation of the subjective necessity from 

 the objective, and that determination to treat the former 

 as a science apart by itself, for which a plausible defence 

 could be made in the case of pure logic, is entirely inad 

 missible in the case of probability. However we might 

 contrive to think aright without appeal to facts, we can 

 not believe aright without incessantly checking our pro 

 ceedings by such appeals. Whatever then may be the 

 claims of Formal Logic to rank as a separate science, it 

 does not appear that it can furnish any support to the 

 theory of Probability at present under examination. 



14. The point in question is sometimes urged as 

 follows. Suppose a man with two, and only two, alterna 

 tives before him, one of which he knows must involve 

 success and the other failure. He knows nothing more 

 about them than this, and he is forced to act. Would he 

 not regard them with absolutely similar and equal feelings 

 of confidence, without the necessity of referring them to any 

 real or imaginary series ? If so, is not this equivalent to 

 saying that his belief of either, since one of them must 

 come to pass, is equal to that of the other, and therefore that 

 his belief of each is one-half of full confidence ? Similarly 

 if there are more than two alternatives : let it be supposed 

 that there are any number of them, amongst which no 

 distinctions whatever can be discerned except in such par 

 ticulars as we know for certain will not affect the result ; 

 should we not feel equally confident in respect of each of 

 them ? and so here again should we not have a fractional 

 estimate of our absolute amount of belief? It is thus 

 attempted to lay the basis of a pure science of Probability, 

 determining the distribution and combination of our belief 



