420 INDUCTION. 



not, we find, for instance, the following : the witness's being ah honest per- 

 son or not ; his being an accurate observer or not ; his having an interest 

 to serve in the matter or not. Now, not only may we be able to obtain 

 other approximate generalizations respecting the degree of frequency of 

 these various possibilities, but we may know which of them is positively 

 realized in the individual case. That the witness has or has not an inter- 

 est to serve, we perhaps know directly ; and the other two points indirect- 

 ly, by means of marks ; as, for example, from his conduct on some former 

 occasion ; or from his reputation, which, though a very uncertain mark, af- 

 fords an approximate generalization (as, for instance. Most persons who 

 are believed to be honest by those with whom they have had frequent deal- 

 ings, are really so), which approaches nearer to a universal truth than the 

 approximate general proposition with which we set out, viz., Most persons 

 on most occasions spe^k truth. 



As it seems unnecessary to dwell further on the question of the evidence 

 of approximate generalizations, we shall proceed to a not less important 

 topic, that of the cautions to be observed in arguing from these incomplete- 

 ly universal propositions to particular cases. 



§ 5. So far as regards the direct application of an approximate generali- 

 zation to an individual instance, this question presents no difficulty. If the 

 proposition, Most A are B, has been established, by a sufficient induction, 

 as an empirical law, we may conclude that any particular A is B with a 

 probability proportioned to the preponderance of the number of affirmative 

 instances over the number of exceptions. If it has been found practicable 

 to attain numerical precision in the data, a corresponding degree of precis- 

 ion may be given to the evaluation of the chances of error in the conclu- 

 sion. 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 knowm 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 can not be counted on for any sub-class or variety of A (or 

 for A in any set of external circumstances) which were not included in the 

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

 Nine out of every ten A are B, only in cases of which we know nothing ex- 

 cept that they fall within the class A. For if we know, of any particular 

 instances i, not only that it falls under A, but to what species or variety of 

 A it belongs, 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 be- 

 ing a particular sort of instance, is an instance known to be under the in- 

 fluence 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 commonly of little use for the practical guid- 

 ance 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 

 toward 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 case. 



