290 THE SCIENCE OF LOGIC 



instances. Necessity is only found when conditions are exactly 

 determined, and ex hypothesi that is just what is not done in the 

 case of an average. As Sigwart says: Such uniformities of 

 numbers and averages are primarily mere descriptions of facts, 

 which need explanation as much as the uniformity of the alterna 

 tion between day and night ; and the explanation can be found 

 only where the actual conditions . . . are forthcoming. But 

 these are the concrete conditions of the particular instances 

 counted, they are not directly causes of the numbers ; it is only 

 the nature of the concrete causes which can show it to be neces 

 sary for the effects to appear in certain numbers and numerical 

 relations (Logic, Eng. trans., vol. ii., p. 490).&quot; l 



Inferences from statistics about natural and social phenomena 

 can never, therefore, be more than probable approximations 

 not laws. Those phenomena result from the combination of 

 numerous unknown or partly unknown causes ; and we have 

 no guarantee that these will persist unchanged. No doubt, if the 

 future faithfully resemble the past, the tabulated averages will recur. 

 But who knows accurately what has been the past? Or what 

 guarantee have we for thinking that the future will be a repeti 

 tion of it ? Furthermore, we will have observed fluctuations of 

 more or less importance in the number and order of the past 

 events, and we must take warning from them not to expect any 

 greater regularity in the future. 



Careful and conscientious scientists, like Quetelet, recognize in what a 

 transferred sense the word &quot; law &quot; is applicable to the moral world. He pro 

 tested against the accusation that according to his theory every year should 

 necessarily produce its crop of crimes in the same number and order, and with 

 the same invariable distribution of each class of crime over the same regions. 

 He objected to the word &quot; invariable,&quot; and never used it himself in his 

 writings. On the contrary, he had written expressly : &quot; The laws relating to 

 the condition of the social body are not necessarily invariable : they can change 

 with the nature of the causes that give rise to them &quot;. a 



But hasty and unreflecting people have pushed to absurd extremes the 

 idea of seeking in statistics an explanation of the whole vast group of pheno 

 mena which constitute the subject-matter of the social, political, and economic 

 sciences, to erect statistical averages and uniformities into laws, and to estab 

 lish a new science which was to be a sort of social mathematics. It was 

 obviously under the influence of such preoccupations as these that Buckle 

 wrote paragraphs like the following : &quot; In a given state of society a certain 

 number of persons must put an end to their own life. This is the general 

 law, and the special question as to who shall commit the crime depends of course 



1 WELTON, op. cit., p. 199. *op. cit., p. 15. 



