DEDUCTIVE REASONING. 75 



readily and clearly explained on the single principle of 

 substitution. It is now desirable to show that the same 

 principle would prevent us falling into fallacies. So long 

 as we exactly observe the one rule of substitution of 

 equivalents it will be impossible to commit a paralogism, 

 or to break any one of the elaborate rules of the ancient 

 system. One rule is thus proved to be as powerful as 

 the six, eight, or more rules by which the correctness of 

 syUogistic reasoning was guarded. 



It was a fundamental rule, for instance, that two nega- 

 tive premises could give no conclusion. If we take the 

 propositions- 

 Granite is not a sedimentary rock, (i) 

 Basalt is not a sedimentary rock, (2) 

 we ought not to be able to draw any inference concerning 

 the relation of granite and basalt. Taking our letter- 

 terms thus 



A = granite 

 B = sedimentary rock 

 C basalt, 

 the premises may be expressed in the form 



A - B (i) 



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. 62). Thus our rule gives 

 us no power whatever of drawing any inference. 



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

 power of always turning a negative proposition into an 

 affirmative one ; and it might seem that the old rule of 

 negative premises would be thus circumvented. Let us 

 try. The premises (i) and (2) when affirmatively stated 

 (see p. 54), will take the form 



A = Kb (i) 



C = Cb. (2) 



