APPROXIMATE GENERALIZATIONS. 



there will be one chance in ten of error in assuming that any 

 A, not individually known to us, is a 13 : hut this of course 

 holds only within the limits of time, place, and circumstance 

 embraced in the observations, and therefore cannot be counted 

 on for any sub-class or variety of A (or for A in any set of 

 3xternal circumstances) which were not included in the 

 average. It must be added, that we can guide ourselves by 

 the proposition, Xine out of every ten A are 13, only in cases 

 of which we know nothing except that they fall within the 

 class A. For if we know, of any particular instance i, not only 

 that it falls under A, but to what species or variety of A it be 

 longs, we shall generally 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, materially differ. 

 And so if i, instead of being a particular sort of instance, is an 

 instance known to be under the influence of a particular set of 

 circumstances. The presumption drawn from the numerical 

 proportions in the whole genus would probably, in such a 

 case, only mislead. A general average should only be applied 

 to cases which are neither known, nor can be presumed, to be 

 other than average cases. Such averages, therefore, are com 

 monly of little use for the practical guidance of any affairs 

 but those which concern 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 approximations; the subsequent terms proceeding on an 

 appreciation of the circumstances belonging to the particular 



1 1 



case. 



^ 0. From the application of a single approximate gene 

 ralization to individual cases, we proceed to the application of 

 two or more of them together to the same case. 



\\hen a judgment applied to an individual instance is 

 grounded on two approximate generalisations taken in con 

 junction, the propositions may co-operate towards the result 



92 



