150 INDUCTION. 



If the premisses are known to be true not of a 

 bare majority, but of nearly the whole, of their respec- 

 tive subjects, we may go on joining one such pro- 

 position to another for several steps, before we reach 

 a conclusion not presumably true even of a majority. 

 The error of the conclusion will amount to the aggre- 

 gate of the errors of all the premisses. Let the pro- 

 position, Most A are B, be true of nine in ten; Most 

 B are C, of eight in nine: then not only will one A 

 in ten not be C, because not B, but even of the nine- 

 tenths which are B, only eight-ninths will be C : that 

 is, the cases of A which are C will be only f of -^, 

 or four-fifths. Let us now add Most C are D, and 

 suppose this to be true of seven cases out of eight ; 

 the proportion of A which is D will be only of & 

 of A, or -fo. Thus the probability progressively 

 dwindles. The experience, however, on which our 

 approximate generalizations are grounded, has so 

 rarely been subjected to, or admits of, accurate nume- 

 rical estimation, that we cannot in general apply any 

 measurement to the diminution of probability which 

 takes place at each illation ; but must be content with 

 remembering that it does diminish at every step, and 

 that unless the premisses approach very nearly indeed 

 to being universal truths, the conclusion after a very 

 few steps is worth nothing. A hearsay of a hearsay, 

 or an argument from presumptive evidence depend- 

 ing not upon immediate marks but upon marks of 

 marks, is worthless at a very few removes from the 

 first stage, 



7. There are, however, two cases in which 

 reasonings depending upon approximate generaliza- 

 tions may be carried to any length we please with 

 as much assurance, and are as strictly scientific, as if 



