76 THE PRINCIPLES OF SCIENCE. 



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

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

 occur in these premises, namely A, 6, 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 holds true. 

 Fallacy is impossible. 



It would be a mistake to suppose that the mere 

 occurrence of negative terms in both premises render 

 them incapable of yielding a conclusion. The old rules 

 of logic 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 con- 

 clusion (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 yield a conclusion. To show this let 

 A = carbon, B = metallic, 

 C = capable of powerful magnetic influence. 

 The premises readily take the form 



b = be (i) 



A = A6 f . (2) 



and substitution for b in (2) by means of (i), gives the 

 conclusion 



A = Kbc (3) 



