116 THE PRINCIPLES OF SCIENCE. 



those which are inconsistent with the premises, there 

 remain only 



ABcd 

 AbCd 

 AbcD 

 abcD 

 abed. 



The expression for not-opaque things consists of the 

 three combinations containing d, thus 



d = KBcd \- AbCd { abed, 

 or d = Ad (Be -|- bC) [ abed. 



In ordinary language, what is not-opaque is either 

 metal which is gold, and then not-silver, or silver and then 

 not gold, or else it is not-metal and neither gold nor silver. 

 A good example for the illustration of the Indirect 

 Method is to be found in De Morgan's Formal Logic (p. 

 123), the premises being substantially as follows : 



From A follows B, and from C follows D ; but B and 

 D are inconsistent with each other ; therefore A and C 

 are inconsistent. 



The meaning no doubt is that where A is, B will be 

 found, or that every A is a B, and similarly every C is a D ; 

 but B and D cannot occur together. The premises there- 

 fore appear to be of the form 



A = AB, (i) 



C = CD, (2) 



B = Ed. (3) 



On examining the series of sixteen combinations, but five 

 are found to be consistent with the above conditions, 

 namely, 



ABcd 

 aBcd 

 abCD 

 abcD 

 abed. 



