338 Fallacies. [CHAP. xiv. 



chance selection with one which is more or less picked. 

 When we are dealing with familiar objects in a concrete 

 way, especially when the greater rarity corresponds to su 

 periority of quality, almost every one has learnt to recognize 

 the distinction. No one, for instance, on observing a fine 

 body of troops in a foreign town, but would be prompted to 

 ask whether they came from an average regiment or from 

 one that was picked. When however the distinction refers 

 to unfamiliar objects, and especially when only comparative 

 rarity seems to be involved, the fallacy may assume a rather 

 subtle and misleading form, and seems to deserve special 

 notice by the consideration of a few examples. 



Sometimes the result is not so much an actual fallacy as 

 a slight misreckoning of the order of probability of the event 

 under consideration. For instance, in the Pyramid question, 

 we saw that it made some difference whether we considered 

 that TT alone was to be taken into account or whether we 

 put this constant into a class with a small number of other 

 similar ones. Tn deciding, however, whether or not there is 

 anything remarkable in the actual falling short of the 

 representation of the number 7 in the evaluation of TT 

 (v. p. 248) the whole question turns upon considerations of 

 this kind. The only enquiry raised is whether there is any 

 thing remarkable in this departure from the mean, and the 

 answer depends upon whether we suppose that we are re 

 ferring to a predetermined digit, or to whatever digit of the 

 ten happens to be most above or below the average. Or, 

 take the case raised by Cournot (Exposition de la Theorie 

 des Chances, 102, 114), that a certain deviation from the 

 mean in the case of Departmental returns of the proportion 

 between male and female births is significant and indicative 

 of a difference in kind, provided that we select at random a 

 single French Department ; but that the same deviation may 



