118 THE PRINCIPLES OF SCIENCE. 



Fallacies analysed by the Indirect Method. 



It has been sufficiently shown, perhaps, that we can by 

 the Indirect Method of Inference extract the whole truth 

 from any series of propositions, and exhibit it anew in any 

 required form of conclusion. But it may also need to be 

 shown by examples that so long as we follow correctly 

 the almost mechanical rules of the method, we cannot fall 

 into any of the common fallacies or paralogisms which are 

 not seldom committed in ordinary discussion. Let us 

 take the example of a fallacious argument, previously 

 treated by the Method of Direct Inference (p. 75), 



Granite is not a sedimentary rock, ( i ) 



Basalt is not a sedimentary rock, (2) 



and let us ascertain whether any precise conclusion can be 

 drawn concerning the relation of granite and basalt. 



Taking as before 



A = granite, 



B = sedimentary rock, 

 C = basalt, 



the premises become A = Ab, (i) 



C = Cb. (2) 



Of the eight conceivable combinations of A, B, C, five agree 

 with these conditions, namely 



A6C aBc 



Abc a&C 



abc ; 

 the description of granite is found to be 



A - A&C I Abc = Ab(G | c), 



that is, granite is not a sedimentary rock but is either 

 basalt or not-basalt. If we want a description of basalt 

 the answer is of like form 



C = A&C! a&C = bC (A | a). 



Basalt is a sedimentary rock, and either granite or not- 

 granite. As it is already perfectly evident that basalt 



