APPROXIMATE GENERALIZATIONS. 145 



affords an approximate generalization (as, for instance, 

 Most persons who are reputed honest by those with 

 whom they have had frequent dealings, are really so,) 

 which approaches nearer to an universal truth than 

 the approximate general proposition with which we 

 set out, viz., Most persons on most occasions speak 

 truth. 



As it seems unnecessary to dwell any further upon 

 the question of the evidence of approximate generali- 

 zations, we shall proceed to a not less important topic, 

 that of the cautions to be observed in arguing from 

 these incompletely universal propositions to particular 

 cases. 



5. So far as regards the direct application of an 

 approximate generalization to an individual instance, 

 this question presents no difficulty. If the propo- 

 sition, Most A are B, has been established, by a suffi- 

 cient induction, as an empirical law, we may conclude 

 that any particular A is B, with a probability propor- 

 tioned to the preponderance of the number of affirma- 

 tive instances over the number of exceptions. If it 

 has been found practicable to attain numerical pre- 

 cision in the data,, a corresponding degree of precision 

 may be given to the evaluation of the chances of error 

 in the conclusion. If it can be established as an 

 empirical law that nine out of every ten A are B, 

 there will be one chance in ten of error in assuming 

 that any A, not individually known to us, is a B : but 

 this of course holds only within the limits of time, 

 place, and circumstance., embraced in the observations, 

 and therefore cannot be counted upon for any sub-class 

 or variety of A (or for A in any set of external cir- 

 cumstances) which were not included in the average. 

 It must be added, that we can only guide ourselves by 



VOL. II. I, 



