,-i.] THE INDIRECT METHOD OF INFERENCE. 101 



Fourth Example. 



A good example for the illustration of tlie 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 I) 

 are inconsistent with each other ; therefore A and G 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 forms 



A = AB, (i) 



C = CD, (2) 



B = BdL (3) 



On examining the series of sixteen combinations, only 

 five are found to be consistent with the above conditions, 

 namely, 



ABcd 

 aEcd 

 dbCD 

 dbcD 

 abed. 



In these combinations the only A which appears is joined 

 to c, and similarly C is joined to a, or A is inconsistent 

 with C. 



Fifth Example. 



A more complex argument, also given by De Morgan, 1 

 contains five terms, and is as stated below, except that 

 the letters are altered. 



Every A is one only of the two B or C ; D is both B 

 and C, except when B is E, and then it is 

 neither ; therefore no A is D. 



The meaning of the above premises is difficult to 

 interpret, but seems to be capable of expression in the 

 following symbolic forms 



1 Formal Logic, p. 124. As Professor Groom Robertson has 

 pointed out to me, the second and third premises may be thrown 

 into a single proposition, D = DeBG ] DE6c. 



