INDUCTION IN ITS VARIOUS SENSES 51 



It is not b or c or d . . . or z 

 .: It is*&quot; 1 



where a, b, c, . . . z are supposed alternative causes of the 

 phenomenon x. This reasoning is, as Mr. Joseph observes, 2 &quot; in 

 form very simple ; but the discovery of proper premisses is very 

 hard &quot;. How is the investigator to determine the extent of the 

 major premiss, the field of pertinent alternative hypotheses? 

 since he cannot realize Bacon s ideal of cataloguing all the 

 causes in the universe (209). Obviously, it is to be defined by 

 prudence rather than by inference. Then he must verify the 

 minor premiss &quot; piecemeal by hypothetical arguments that rest 

 upon one or other of the [usual] grounds of elimination &quot;. 3 



Finally, when, having verified our hypothesis, we apply it to 

 the explanation of facts, or when we explain itself by the appli 

 cation to it of wider laws, our reasoning is obviously syllogistic 

 and deductive. 



Is any of the forms of inference outlined above, so characteristic of the 

 inductive method as to merit the title of &quot; inductive reasoning &quot; ? It matters 

 little whether we so describe any of them, provided we bear in mind that 

 &quot; Induction &quot; is much more than any of them : that it involves many pro 

 cesses other than mere inference. And, indeed, the same may be said of the 

 title &quot; Deduction &quot; as applied to forms of inference rather than to method. We 

 have already seen (192) that there is no uniformity of usage in the application 

 of the titles &quot; deductive &quot; and &quot; syllogistic &quot; to forms of inference. A &quot; de 

 ductive &quot; inference is perhaps most commonly understood to signify an infer 

 ence in which it is sought to subordinate some special cases (or classes of 

 cases) under some wider principle or law. This would be chiefly characteristic 

 of syllogisms in the first figure, whether categorical or hypothetical. But then, 

 syllogisms in the second or third figures would not be deductive in this sense ; 

 for in them there is not usually any subordination of instances to a rule. 

 Mathematical reasoning, too, proceeds in large part from known principles not 

 to subordinate cases, but to other co-ordinate and coextensive principles : in 

 these sciences the cognate truths are so related that very often either of a 

 pair, a and b, can be used equally well to prove the other : the related truths 

 are reciprocal ; and yet mathematical reasoning is universally regarded as 

 deductive. 4 Hence, the subordination or subsumption of a case under a rule is 

 hardly a satisfactory criterion of &quot; deductive &quot; inference. 



Mr. Joseph s treatment of the contrast between deduction and induction 

 is instructive. &quot; Inductive Logic,&quot; he rightly remarks, &quot; has not really laid bare 

 any new forms of reasoning ; we have already seen that Bacon s Induction is 

 a disjunctive argument ... Or if anyone likes ... to call inference deductive 

 when it proceeds from conditions to their consequences, and inductive when it 

 proceeds from facts to the conditions that account for them, he will find 



JOSEPH, op. cit,, p. 406. *ibid. s ibid. 



4 C/. JOSEPH, op. cit., p. 368, 369 n. 2 : also pp. 503 sqq. 



4* 



