244 THE SCIENCE OF LOGIC 



We have already compared deduction and induction as methods, or lines 

 of direction, according to which progress in knowledge may be made (213). 

 Let us now compare them briefly from the standpoint of their material contents, 

 inquiring how truth is discovered and proved in each. 



The problem of discovering and proving a general truth or law by induction 

 may be stated in this way : Given that in a particular case (or cases), S, is 

 observed to be connected with P, find whether and why &quot; All S s are P,&quot; or, 

 discover and prove that All S s are P &quot;. And the problem should be re 

 garded as fully solved only when we can assert that &quot; All .S s will be and must 

 be P, because, or provided that, or as long as (a) they will be M, and (b} M 

 will be P ; and in no other conditions or circumstances &quot;. This solution sup 

 poses that in M we have reached the ground or reason which not only neces 

 sitates the connexion between 6&quot; and P, but which alone can necessitate this 

 connexion on the assumption that the course of nature is not miraculously 

 interfered with. It supposes that we are able to overcome and remove all 

 indefiniteness from the conditions, to eliminate &quot;plurality of antecedents (140) 

 or causes&quot; (221) by discovering among all the possible groups (each of which 

 was regarded as a distinct and separate &quot; antecedent &quot;), the one necessitating 

 and indispensable factor which was common to, and operative in, all of them, 

 and in virtue of which all of them necessitated, though no one of them was in 

 dispensable to, the given consequent. 



Let us see, in the next place, how the problem of discovering and proving 

 a truth, whether general or particular, by deduction, may be stated. What 

 exactly is the nature of the mental process by which truths are discovered and 

 proved &quot; deductively,&quot; in geometry, for example ? It would certainly be an 

 inadequate and misleading statement of the deductive method to represent 

 the problem of deduction as : &quot; Given a certain antecedent, or certain pre 

 misses, find the consequent or conclusion.&quot; In discussing the nature and 

 characteristics of inference (197, 198) we saw that the real difficulty of dis 

 covering and proving new truths deductively lay rather in discovering proper 

 antecedents fresh and fruitful combinations of old truths for the formation of 

 new sets of premisses, than in the comparatively simple task of detecting 

 the new consequent or conclusion in the newly formed premisses, and formally 

 inferring it therefrom. If the general inductive problem might be stated : 

 &quot; Given one of the multitudinous facts of sense experience, which make up the 

 physical universe, discover the causes and laws by which it happens,&quot; the 

 general deductive problem might be stated : &quot; Given a knowledge of certain, 

 necessary, self-evident principles, discover all the truths involved in them &quot;. 



&quot; Deduction and Induction,&quot; writes Dr. Mellone, 1 &quot; are not two different 

 and independent kinds of reasoning. The real process of thinking is the same in 

 ooth i.e. to find a place for some fact as a detail within a system \cf. 212, 

 213]. In the case of syllogistic deductive reasoning our system is partly 

 known beforehand, in the form of a general law under which the fact or detail 

 is brought. We start, having in our hands the common thread which unites 

 the various facts. But in Inductive reasoning we have to find the common 

 thread. We [a] start with certain kinds of facts which occur together in our 

 experience. We \b~\ assume that there is some principle which unites them ; 

 and our object is to read out of these particular details the general law of 



1 op. cit., p. 383. 



