THE LOGICAL ABACUS. 119 



must be either granite or not, and vice versd, 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 (pp. 75-77). 



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. 77) 



All planets are subject to gravity, (i) 



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. (a) 



The combinations which remain uncontradicted on com- 

 parison with these premises are 



aBC abG 



abc. 



For fixed star we have the description 

 B = aBC -I- aBc, 



that is, ' a fixed star is not a planet, but is either subject 

 or not, as the case may be, to gravity/ 



The Logical Abacus. 



The Indirect Method of Inference has now been suffi- 

 ciently described, and a careful examination of its powers 

 will show that it is capable of giving a full analysis and 

 solution of every question involving any simply logical 

 relations. The chief difficulty of the method consists in 

 the great number of combinations which may have to 



