LAWS OF THOUGHT. 393 



It would be more accurate in these examples to introduce 

 a symbol x or y to indicate that B is only one of the possible 

 sons of A, an individual ranged under the species sA. I shall 

 do that in the next example, in which the word son is replaced 

 by the more general term descendant denoted by d. The equa- 

 tions will now be 



videlicet a descendant not of the first generation. The result of 

 eliminating B now is 



C = ydxdA : 

 but by a principle about to be noticed 



dx = x'd ; 

 .'. C = yx'zdA, 

 or C is included in the class of descendants of A. 



The principle just used forms one of the recognized examples 

 of an inference not lying within the domain of Aristotelian logic. 

 It was called Transit io ex recto in obliquum. Whately, though 

 he says nothing of its nature, gives in his praxis of examples 

 one which depends upon it. A negro is a man, therefore he who 

 kills a negro kills a man ; let this derived notion killing be de- 

 noted by f, which may serve to indicate a general functional 

 dependence : then, M 9 N, denoting man and negro respectively, 

 we have the following equations : 



JV 



.-. /A r = x'fM, 



or the killing of a negro is a kind of homicide. The evidence 

 of the truth of the equation 



is the same as that in favour of the equation 



xy = yx, 

 when x and y both belong to the kind of symbols used in the 



