136 INDUCTION. 



Let the proposition, 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 he 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 |- of T 9 ^, 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 J of 4 of T 9 o-, or ^. Thus the probability progressively 

 dwindles. The experience, however, on which our approxi- 

 mate generalizations are grounded, has so rarely been subjected 

 -to, or admits of, accurate numerical estimation, that we cannot 

 in general apply any measurement to the diminution of proba- 

 bility which takes place at each illation ; but must be content 

 with remembering that it does diminish at every step, and 

 that unless the premises approach very nearly indeed to being 

 universally true, the conclusion after a very few steps is worth 

 nothing. A hearsay of a hearsay, or an argument from pre- 

 sumptive evidence depending not on immediate marks but on 

 marks of marks, is worthless at a very few removes from the 

 first stage. 



7. There are, however, two cases in which reasonings 

 depending on approximate generalizations may be carried to 

 any length we please with as much assurance, and are as 

 strictly scientific, as if they were composed of universal laws 

 of nature. But these cases are exceptions of the sort which 

 are currently said to prove the rule. The approximate generali- 

 zations are as suitable, in the cases in question, for purposes of 

 ratiocination, as if they were complete generalizations, because 

 they are capable of being transformed into complete generali- 

 zations exactly equivalent. 



First: If the approximate generalization is of the class 

 in which our reason for stopping at the approximation is 

 not the impossibility, but only the inconvenience, of going 

 further; if we are cognizant of the character which distin- 

 guishes the cases that accord with the generalization from 

 those which are exceptions to it ; we may then substitute for 

 the approximate proposition, an universal proposition with a 



