METHOD OF DISCOVERING CAUSAL LAWS 199 



thing to remark is, that they take for granted the very thing 

 which is most difficult to discover, the reduction of the phenomena 

 to formulae such as are here presented to us (Phil, of Discovery, 

 P- 263).&quot;! 



The symbolizing of the methods by employing the letters of the alphabet 

 to represent the various elements that enter into a process of inductive analysis 

 has its advantages and its disadvantages. Its chief advantage is, perhaps, 

 that it helps us to realize more clearly what we are aiming at in each of the 

 methods. But, on the other hand, it is liable to create false impressions about 

 the nature of the analysis symbolized : the impression that the work of 

 analysis is simpler than it really is ; the impression, too, that the elements 

 with which we are dealing are distinct, isolated, independent, individual 

 entities, like the symbols themselves. The system of symbols employed by 

 Mill has an additional drawback : by employing corresponding capitals and 

 small letters for the antecedents and consequents, he conveys the impression 

 that nature presents us with corresponding connexions between the elements 

 of our experience ; whereas in reality these connexions have to be discovered 

 by ourselves. The following are his formulae for the various methods : 

 Method of Agreement : 



ABC followed by a b c, 

 A D E ade, 



.. A and a are causally connected. 

 Method of Difference : 



ABC followed by a b c, 

 B C b c, 

 .-. A and a are causally connected. 



Joint Method of Agreement and Differences. Mill himself gives no 

 formula, but, following the lines of those just given, we arrive at some such 

 scheme as the following : 



A B C a b c \ 



A D E a d e \ positive instances ; 

 A F G a fg &amp;gt; 

 B M N b m n \ 



D O P d o p \ negative instances ; 

 F Q R-/ q r J 



.-. A and a are causally connected. 

 Method of Concomitant Variations : 

 A 1 B C a 1 b c, 

 A 3 B Ca 2 b c, 

 A 3 B C a 3 b c, 



.. A and a are causally connected. 

 Method of Residues : 



A B C D is the known cause of a b c d 

 A a 



B b 



C c 



.-. D and d are causally connected. 



1 WELTON, ibid., pp. 148-9. 



