394 



INDUCTION. 



§ 7. There are, however, two cases 

 in which reasonings depending on 

 approximate generalisations 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 generalisations are 

 as suitable, in the cases in question, 

 for purposes of ratiocination, as if 

 they were complete generalisations, 

 because they are capable of being 

 transformed into complete generalisa- 

 tions exactly equivalent. 

 - First : If the approximate gene- 

 ralisation is of the class in which our 

 reason for stopping at the approxima- 

 tion is not the impossibility, but only 

 the inconvenience, of going farther ; 

 if we are cognisant of the character 

 which distinguishes the cases that 

 accord with the generalisation from 

 those which are exceptions to it, we 

 may then substitute for the approxi- 

 mate proposition an universal pro- 

 position with a proviso. The pro- 

 position, Most persons who have un- 

 controlled power employ it ill, is a 

 generalisation of this class, and may 

 be transformed into the following : — 

 All persons who have uncontrolled 

 power employ it ill, provided they are 

 not persons of unusual strength of judg- 

 ment and rectitude of purpose. 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 reason- 

 ing may reach, the hjrpothesis, being 

 carried forward to the conclusion, will 

 exactly indicate how far that con- 

 clusion is from being applicable uni- 

 versally. If in the course of the argu- 

 ment other approximate generalisa- 

 tions 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 con- 

 clusion. Thus, to the proposition last 



cited let us add the following :— All 

 absolute monarchs have uncontrolled 

 power, unless their position is such that 

 they need the active support of their 

 subjects (as was the case with Queen 

 Elizabeth,. Frederick of Prussia, and 

 others). Combining these two pro- 

 positions, we can deduce from them 

 an universal conclusion, which will 

 be subject to both the hypotheses in 

 the premises ; All absolute monarchs 

 employ their power ill, unless their 

 position makes them need the active 

 support of their subjects, or unless 

 they are persons of unusual strength 

 of judgment and rectitude of purpose. 

 It is of no consequence how rapidly 

 the errors in our premises accumulate, 

 if we are able in this manner to record 

 each error, and keep an account of 

 the aggregate as it swells up. 



Secondly : There is a case in which 

 approximate propositions, even with- 

 out our taking note of the condi- 

 tions under which they are not true 

 of individual cases, are yet, for the 

 purposes of science, universal ones ; 

 namely, in the inquiries which relate 

 to the properties not of individuals, 

 but of multitudes. The principal of 

 these is the science of politics, or of 

 human society. This science is princi- 

 pally concerned with the actions not 

 of solitary individuals, but of masses ; 

 with the fortunes not of single per- 

 sons, but of communities. For the 

 statesman, therefore, it is generally 

 enough to know that most persons act 

 or are acted upon in a particular way, 

 since his speculations and his practi- 

 cal arrangements refer almost ex- 

 clusively to cases in which the whole 

 community, or some large portion of 

 it, is acted upon at once, and in which, 

 therefore, what is done or felt by most 

 persons determines the result pro- 

 duced by or upon the body at large. 

 He can get on well enough with ap- 

 proximate generalisations on human 

 nature, since what is true approxi- 

 mately of all individuals is true ab- 

 solutely of all masses. And even 

 when the operations of individual men 

 have a part to play in his deductions, 



