APPROXIMATE GENERALIZATIONS. 149 



tion, or even wholly, in the third section ; in which 

 last case the probability arising from A and C toge- 

 ther would be no greater than that arising from A 

 alone. 



When approximate generalizations are joined toge- 

 ther in the other mode, that of deduction, the degree 

 of probability of the inference, instead of increasing, 

 diminishes at each step. From two such premisses 

 as Most A are B, Most B are C, we cannot with cer- 

 tainty conclude that even a single A is C; for the 

 whole 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, pro- 

 vided the average, on which the second proposition is 

 grounded, was taken fairly with reference to the first; 

 provided the proposition Most B are C 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 although 

 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 proposi- 

 tions 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; although it is rigorously possible (how- 

 ever improbable) that the whole Swedish population 

 of Stockholm may belong to that tenth section of the 

 people of Sweden who are an exception to the rest. 



