198 THE SCIENCE OF LOGIC 



then find, their application, one or other or all of them, in exclud 

 ing successively a, and b, and c , . . . until m alone is left : that is, 

 in establishing minor premisses for our alternative major, &quot; The 

 cause of x is not a&quot; &quot; The cause of x is not b&quot; etc., until we are 

 thus enabled indirectly to prove that &quot; The cause of x is m &quot;. In 

 proving each minor premiss, by the application of the &quot; methods,&quot; 

 there is deductive reasoning from the hypothesis that is being 

 tested. It is a mistake, therefore, to contrast the principles in 

 volved in these methods with the various principles or axioms of 

 deductive inference, by describing those as &quot; material &quot; and these 

 as &quot; formal &quot;. Nor can the rules for elimination be called &quot; in 

 ductive &quot; in the sense that they enable us to generalize directly 

 from the individual data of our experience, independently of hypo 

 thesis and deductive reasoning: for they do not enable us to general 

 ize in this way. It was Mill s mistake to think that they do ; 

 though he seems to have felt the difficulty of such a position : 

 for he admits the utility of hypothesis and deductive reasoning 

 in what he calls the &quot;deductive method&quot; j 1 and although he re 

 stricts the application of the latter to the more complex sort of 

 phenomena, he is forced to admit that it is to this method &quot; the 

 human mind is indebted for its most conspicuous triumphs in the 

 investigation of nature &quot; 2 . Indeed, even the simplest phenomena 

 of concrete nature are far too complex to admit of the direct appli 

 cation of any one of the &quot;methods&quot; to them. &quot;The only true 

 function of the methods is, indeed, given by Mill himself when, in 

 speaking of cases in which there is an interference of causes with 

 one another, he says : The instrument of Deduction alone is 

 adequate to unravel the complexities proceeding from this source ; 

 and the four methods have little more in their power than to 

 supply premises for, and a verification of, our deductions (III., x., 



3)&quot;- 3 



Attention has already been called (240) to the fact that the 

 application of the so-called &quot; inductive canons &quot; supposes the 

 materials already analysed and prepared, &quot; that limited groups 

 of antecedents and consequents, known to be causally connected, 

 have been separated out for the purpose of inductive inquiry, 

 whose task is only to obtain simple causal connexions by elimin 

 ating some of the elements still left. . . . Whewell is, indeed, 

 quite justified when he says : Upon these methods, the obvious 



1 Logic, III., xi., 93. Cf. supra, p. 45. 



2 ibid. ; cf. WELTQN, op. cit., ii., pp. 59, 83. 3 WELTON, ibid., pp. 158-9, 



