APPROXIMATE GENERALIZATIONS. 135 



have a greater chance of doing so. Otherwise the uot-Bs which 

 are Cs may be, most or even all of them, identical with the not- 

 Bs which are As ; in which last case the probability arising 

 from A and C together will be no greater than that arising 

 from A alone. 



When approximate generalizations are joined together in 

 the other mode, that of deduction, the degree of probability of 

 the inference, instead of increasing, diminishes at each step. 

 From two such premises as Most A. are B, Most B are C, we 

 cannot with certainty conclude that even a single A is C ; for 

 the wiiole of the portion of A which in any way falls under B, 

 may perhaps be comprised in the exceptional part of it. 

 Still, the two propositions in question afford an appreciable 

 probability that any given A is C, provided the average on 

 which the second proposition is grounded, was taken fairly with 

 reference to the first; provided the proposition, Most B are 0, 

 was arrived at in a manner leaving no suspicion that the 

 probability arising from it is otherwise than fairly distributed 

 over the section of B which belongs to A. For though the 

 instances which are A may be all in the minority, they may, 

 also, be all in the majority ; and the one possibility is to be set 

 against the other. On the whole, the probability arising from 

 the two propositions taken together, will be correctly measured 

 by the probability arising from the one, abated in the ratio of 

 that arising from the other. If nine out of ten Swedes have 

 light hair, and eight out of nine inhabitants of Stockholm are 

 Swedes, the probability arising from these two propositions, 

 that any given inhabitant of Stockholm is light-haired, will 

 amount to eight in ten ; though it is rigorously possible 

 that the whole Swedish population of Stockholm might belong 

 to that tenth section of the people of Sweden who are an 

 exception to the rest. 



If the premises are known to be true not of a bare 

 majority, but of nearly the whole, of their respective subjects, 

 we may go on joining one such proposition 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 aggregate of the errors of all the premises. 



