146 INDUCTION. 



the proposition, Nine out of every ten A are B, in 

 cases of which we know nothing except that they fall 

 within the class A. For if we know, of any particu- 

 lar instance i, not only that it falls under A, but to 

 what species or variety of A it belongs, we shall gene- 

 rally err in applying to i the average struck for the 

 whole genus, from which the average corresponding 

 to that species alone would, in all probability, mate- 

 rially differ. And so if i, instead of being a particu- 

 lar sort of instance, is an instance known to be under 

 the influence of a particular set of circumstances. 

 The presumption drawn from the numerical propor- 

 tions in the whole genus would probably, in such a 

 case, only mislead. A general average should only be 

 applied to a case which is neither known, nor can be 

 presumed, to be other than an average case. Such 

 averages, therefore, are commonly of little use for the 

 practical guidance of any affairs but those which con- 

 cern large numbers. Tables of the chances of life are 

 useful to insurance offices, but they go a very little 

 way towards informing any one of the chances of his 

 own life, or any other life in which he is interested, 

 since almost every life is either better or worse than 

 the average. Such averages can only be considered 

 as supplying the first term in a series of approxima- 

 tions ; the subsequent terms proceeding upon an 

 appreciation of the circumstances belonging to the 

 particular case. 



6. From the application of a single approximate 

 generalization to individual cases, we proceed to the 

 application of two or more of them together to the 

 same case. 



When a judgment applied to an individual instance 

 is grounded upon two approximate generalizations 



