THE INDIRECT METHOD OF INFERENCE. 115 



we can substitute in ( i ) obtaining the conclusion 



A = Ac. 



But the same result may be obtained by taking the 

 eight combinations of A, B, C, of the abecedarium ; it will 

 be found that only three combinations, namely 



aBC 



abc, 

 are consistent with the premises, whence it results that 



A = Abe, 

 or by the process of Ellipsis before described (p. 69) 



A = Ac. 



As a somewhat more complex example I take the 

 argument thus stated, one which could not be thrown 

 into the syllogistic form. 



* All metals except gold and silver are opaque ; there- 

 fore what is not opaque is either gold or silver 

 or is not-metal/ 



There is more implied in this statement than is dis- 

 tinctly asserted, the full meaning being as follows : 



All metals not gold or silver are opaque, (i) 

 Gold is not opaque but is a metal. (2) 



Silver is not opaque but is a metal, (3) 



Gold and silver are distinct substances. (4) 



Taking our letters thus 



A metal C = silver 



B = gold D = opaque, 



we may state the premises in the form 



A&c = AfoD (i) 



B = ABeJ (2) 



C = ACd (3) 



B = Be. (4) 



To obtain a complete solution of the question we take 

 the sixteen combinations of A, B, C, D, and striking out 



i 2 



