THE INDIRECT METHOD OF INFERENCE. 105 



class not-element or c. By the Law of Duality we can 

 develop c into four alternatives, thus 



c = ABc -I- Kbc -|- aBc -|- abc. 

 Now if we substitute for A and B as before, we get 



c = ABCc -I- AB&c -I- aBCc -|- abc, 



and striking out the terms which break the Law of Contra- 

 diction there remains 



c = abc, 



or what is not element is also not iron and not metal. 

 This Indirect Method of Inference thus furnishes a 

 complete solution of the following problem Given any 

 number of logical premises or conditions, required the 

 description of any class of objects, or any term,, as governed 

 by those conditions. 



The steps of the process of inference may thus be 

 concisely stated : 



1. By the Law of Duality develop the utmost number 

 of alternatives which may exist in the description of the 

 required class or term as regards the terms involved in 

 the premises. 



2. For each term in these alternatives substitute its 

 description as given in the premises. 



3. Strike out every alternative which is then found to 

 break the Law of Contradiction, 



4. The remaining terms may be equated to the term in 

 question as the desired description or inference. 



Abbreviation of the Process. 



Before proceeding to illustrations of the use of this 

 method, I must point out how much its practical em- 

 ployment can be simplified, and how much more easy it 

 is than would appear from the description. When we 

 want to effect at all a complete solution of a logical 





