VI.] THE INDIRECT METHOD OF INFERENCE. loi 



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 jiremises 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 = Bd (3) 



On examining the series of sLxteen combinations, only 

 five are found to be consistent Math the above conditions, 

 namely, 



ABc(^ 



a^cd 



«&CD 



ahcD 



ahcd. 



In these combinations the only A which appears is joined 



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



M-ith C. 



Fifth Example. 



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

 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 li 



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 — 



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

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

 into a tingle prupoeition, D = DcHO -J- DE'.'C. 



