DEDUCTIVE REASONING. 



A - B, (1) 



C ~ B. (2) 



We have in this form two statements of difference ; but 

 the principle of inference can only work with a statement 

 of agreement or identity (p. 63). Thus our rule gives 

 us no power whatever of drawing any inference ; this is 

 exactly in accordance with the fifth rule of the syllogism. 

 It is to be remembered, indeed, that we claim the 

 power of always turning a negative proposition into an 

 affirmative one (p. 45) ; and it might seem that the old rule 

 against negative premises would thus be circumvented. 

 Let us try. The premises (i) and (2) when affirmatively 

 stated take the forms 



A = Ab (I) 



C = 06. (2) 



The reader will find it impossible by the rule of substitu- 

 tion to discover a relation between A and C. Three terms 

 occur in the above premises, namely A, b, and C ; but they 

 are so combined that no term occurring in one has its 

 exact equivalent stated in the other. No substitution 

 can therefore be made, and the principle of the fifth rule of 

 the syllogism holds true. Fallacy is impossible. 



It would be a mistake, however, to suppose that the 

 mere occurrence of negative terms in both premises of a 

 syllogism renders them incapable of yielding a conclusion. 

 The old rule informed us that from two negative premises 

 no conclusion could be drawn, but it is a fact that the rule 

 in this bare form does not hold universally true ; and I 

 am not aware that any precise explanation has been given 

 of the conditions under which it is or is not imperative. 

 Consider the following example : 



Whatever is not metallic is not capable of power- 

 ful magnetic influence, (i) 

 Carbon is not metallic, (2) 

 Therefore, carbon is not capable of powerful mag- 

 netic influence. (3) 

 Here we have two distinctly negative premises (i) and 

 (2), and yet they yield a perfectly valid negative conclu- 

 sion (3). The syllogistic rule is actually falsified in its bare 

 and general statement. In this and many other cases we 

 can convert the propositions into affirmative ones which will 

 yield a conclusion by substitution without any difficulty 



