390 



iNDtrCTlON 



law ; at other times, the frequency of 

 the causes, or of some collateral in- 

 dications. It commonly happens that 

 neither is susceptible of so satisfactory 

 an induction as could be desired, and 

 that the grounds on which the con- 

 clusion is received ai-e compounded of 

 both. Thus a person may believe 

 that most Scotchmen can read, i)e- 

 cause, so far as his information ex- 

 tends, most Scotchmen have been 

 sent to school, and most Scotch 

 schools teach reading effectually ; and 

 also because most of the Scotchmen 

 whom he has known or heard of 

 could read ; though neither of these 

 two sets of observations may by 

 itself fulfil the necessary conditions 

 of extent and variety. 



Although the approximate gene- 

 ralisation may in most cases be indis- 

 pensable for our guidance, even when 

 we know the cause, or some certain 

 mark, of the attribute predicated ; 

 it needs hardly be observed that we 

 may always replace the uncertain in- 

 dication by a certain one, in any case 

 in which we can actually recognise 

 the existence of the cause or mark. 

 For example, an assertion is made by 

 a witness, and the question is whether 

 to believe it. If we do not look to 

 any of the individual circumstances 

 of the case, we have nothing to direct 

 us but the approximate generalisa- 

 tion that truth is more common than 

 falsehood, or, in other words, that 

 most persons, on most occasions, speak 

 truth. But if we consider in what 

 circumstances the cases where truth 

 is spoken differ from those in which 

 it is not, we find, for instance, the 

 following : the witness's being an 

 honest person 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 gene- 

 ralisations respecting the degree of 

 frequency of these various possibili- 

 ties, but we may know which of them 

 is positively realised in the individual 

 case. That the witness has or has 

 not an interest to serve, we perhaps 



know directly, and the other two 

 points indirectly, by means of marks ; 

 as, for example, from his conduct on 

 some former occasion, or from his re- 

 putation, which, though a very un- 

 certain mark, affords an approximate 

 generalisation, (as, for instance. Most 

 persons who are believed to be 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 

 further on the question of the evi- 

 dence of approximate generalisations, 

 we shall proceed to a not less im- 

 portant topic, that df 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 gene- 

 ralisation to an individual instance, 

 this question presents no difficulty. 

 If the proposition. Most A are B, has 

 been established, by a sufficient induc- 

 tion, 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 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 estab- 

 lished 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 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 



