vr.] THE INDIRECT METHOD OF INFERENCE. 103 



the premises become A = Ab, (i) 



C = Cb. (2) 



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

 agree with these conditions, namely 



A&C aBe 



Abe abC 



abc. 



Selecting the combinations which contain A, we find the 

 description of granite to be 



A = AZ>C + Abc = Ab(G -|. c), 



that is, granite is nofc a sedimentary rock, and is either 

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

 answer is of like form 



C = AbC -I- abC = bC(A -I- a), 



that is basalt is not a sedimentary rock, and is either 

 granite or not-granite. As it is already perfectly evident 

 that basalt must be either granite or not, and vice versa, 

 the premises fail to give us any information on the point, 

 that is to say the Method of Indirect Inference saves us 

 from falling into any fallacious conclusions. This 

 example sufficiently illustrates both the fallacy of 

 Negative premises and that of Undistributed Middle of 

 the old logic. 



The fallacy called the Illicit Process of the Major Term 

 is also incapable of commission in following the rules of 

 the method. Our example was (p. 65) 



All planets are subject to gravity, (l) 



Fixed stars are not planets. (2) 



The false conclusion is that " fixed stars are not subject to 

 gravity." The terms are 



A = planet 

 B = fixed star 

 C = subject to gravity. 



And the premises are A = AC, (i) 



B = aB. (2) 



The combinations which remain uncontradicted on com- 

 parison with these premises are 



AbG aBc 



aBC abG 



abc. 



For fixed star we have the description 

 B = aBG -I- aBc, 



