356 INDUCTION. 



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

 geneialization to an individual instance, this question presents no diffi- 

 culty. 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 preponder- 

 ance of the number of affirmative instances over the number of excep- 

 tions. If it has been found practicable to attain numerical precision 

 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 eiTor 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 observa- 

 tions, and therefore cannot be counted upon for any sub-class or variety 

 of A (or for A in any set of external circumstances) which were not 

 included in the avei'age. It must be added, that we can only guide 

 ourselves by 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 particular instance i, not only that it falls 

 under A, but to what species or variety of A it belongs, we shall 

 generally eiT in applying to i the average struck for the whole genus, 

 from which the average corresj^onding to that species alone would, in 

 all probability, materially differ. And so if /, instead of being a par- 

 ticular 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 prcbably, 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 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 teiTn in a series of ap- 

 proximations ; the subsequent tenns 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 taken in conjunction, the prop- 

 ositions may cooperate towards the result in two different ways. In 

 the one, each proposition is separately applicable to the case in hand, 

 and our object in combining them is to give to the conclusion in that 

 particular case the double probability arising from the two propositions 

 separately. This may be called joining two probabilities by way of 

 Addition; and the result is a probability gi-eater than either. ^ The 

 other mode is, when only one of the propositions is directly applicable 

 to the case, the second being only applicable to it by virtue of the 

 application of the first. This is joining two probabilities by way of 

 Deduction ; the result of which is a less probability than either. The 



