APPROXIMATE GENERALIZATIONS. 151 



they were composed of universal laws of nature. 

 Both these cases are exceptions of the sort which are 

 currently said to prove the rule. The approximate 

 generalizations are as suitable, in the cases in ques- 

 tion, for purposes of ratiocination, as if they were 

 complete generalizations, because they are capable 

 of being transformed into complete generalizations 

 exactly equivalent. 



First: If the approximate generalization is of the 

 class in which our reason for stopping at the approxi- 

 mation is not the impossibility, but only the inconve- 

 nience, of going further; if we are cognizant of the 

 character which distinguishes the cases that accord 

 with the generalization from those which are excep- 

 tions to it; we may then substitute, for the approxi- 

 mate proposition, an universal proposition with a 

 proviso. The proposition, Most persons who have 

 uncontrolled power employ it ill, is a generalization 

 of this class, and may be transformed into the fol- 

 lowing: All persons who have uncontrolled power 

 employ it ill, provided they are not persons of unusual 

 strength of judgment and will, and confirmed habits 

 of virtue. The proposition, carrying the hypothesis 

 or proviso with it, may then be dealt with no longer 

 as an approximate, but as an universal proposition; 

 and to whatever number of steps the reasoning may 

 reach, the hypothesis, being carried forward to the 

 conclusion, will exactly indicate how far that con- 

 clusion is from being applicable universally. If in 

 the course of the argument other approximate gene- 

 ralizations are introduced, each of them being in like 

 manner expressed as an universal proposition with a 

 condition annexed, the sum of all the conditions will 

 appear at the end as the sum of all the errors which 

 affect the conclusion. Thus, to the proposition last 



