282 Probability before and after the event [CHAP. xn. 



remark that, however satisfactory such a view of the matter 

 might be to some theologians, no antagonist of miracles 

 would for a moment accept it. He would naturally object 

 that, instead of the miraculous element being (as Butler 

 considers) &quot;a small additional presumption&quot; against the 

 narrative, it involved the events in a totally distinct class of 

 incredibility ; that it multiplied, rather than merely added 

 to, the difficulties and objections in the way of accepting 

 the account. 



Mill s remarks (Logic, Bk. in. ch. xxv. 4) are of a dif 

 ferent character. Discussing the grounds of disbelief he 

 speaks of people making the mistake of &quot; overlooking the 

 distinction between (what may be called) improbability 

 before the fact, and improbability after it, two different 

 properties, the latter of which is always a ground of dis 

 belief, the former not always.&quot; He instances the throwing 

 of a die. It is improbable beforehand that it should turn 

 up ace, and yet afterwards, &quot; there is no reason for disbe 

 lieving it if any credible witness asserts it.&quot; So again, &quot; the 

 chances are greatly against A. B. s dying, yet if any one tells 

 us that he died yesterday we believe it.&quot; 



5. That there is some difficulty about such problems 

 as these must be admitted. The fact that so many people 

 find them a source of perplexity, and that such various 

 explanations are offered to solve the perplexity, are a suf 

 ficient proof of this 1 . The considerations of the last chapter, 



1 For instance, Sir J. F. Stephen babilities and chances. The proba 



explains it by drawing a distinction bility of an event is its capability of 



between chances and probabilities, being proved. Its chance is the 



which he says that Butler has con- numerical proportion between the 



fused together; &quot;the objection that number of possible cases supposed 



very ordinary proof will overcome a to be equally favourable favourable 



presumption of millions to one is to its occurrence; and the number 



based upon a confusion between pro- of possible cases unfavourable to its 



