8/OLOGICAL 



vi.] THE INDIRECT METHOD OF INFERENCE. 101 



Fourth Example. 



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 forms 



A = AB, (i) 



C = CD, (2) 



B = Ik/. (3) 



On examining the series of sixteen combinations, only 

 five are found to be consistent with the above conditions 

 namely, 



AEcd 

 aBcd 

 abCD 

 abcD 

 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 Croom Rolxtrtson has 

 pointed out to me, the second and third premises ra>y be thrown 

 into a single proposition, D = DeBO ( PE6r, 



