334 Fallacies. [CHAP..XIV. 



thing to be unlikely to guess an event rightly without 

 specific evidence; it is another and very different thing to 

 appreciate the truth of a story which is founded partly or 

 entirely upon evidence. But it is a great mistake to transfer 

 tc one of these ways of viewing the matter the mental im 

 pressions which properly belong to the other. It is like 

 drawing the target afterwards, and then being surprised to 

 find that the shot lies in the centre of it. 



3. One aspect of this fallacy has been already dis 

 cussed, but it will serve to clear up difficulties which are 

 often felt upon the subject if we reexamine the question 

 under a somewhat more general form. 



In the class of examples under discussion we are generally 

 presented with an individual which is not indeed definitely 

 referred to a class, but in regard to which we have no great 

 difficulty in choosing the appropriate class. Now suppose 

 we were contemplating such an event as the throwing of 

 jdxes with a pair of dice four times running. Such a throw 

 would be termed a very unlikely event, as the odds against 

 its happening would be 36 x 36 x 36 x 36 - 1 to 1 or 1679615 

 to 1. The meaning of these phrases, as has been abundantly 

 pointed out, is simply that the event in question occurs very 

 rarely; that, stated with numerical accuracy, it occurs once in 

 1679616 times. 



4. But now let us make the assumption that the 

 throw has actually occurred; let us put ourselves into the 

 position of contemplating sixes four times running when it is 

 known or reported that this throw has happened. The same 

 phrase, namely that the event is a very unlikely one, will 

 often be used in relation to it, but we shall find that this 

 phrase may be employed to indicate, on one occasion or 

 another, extremely different meanings. 



(1) There is, firstly, the most correct meaning. The 



