RATIOCINATION, OR SYLLOGISM. 231 



Or if more significant symbols are preferred, 



To prove an affirmative, the argument must admit 

 of being stated in this form : 



All animals are mortal ; 



All men j 



Some men 1 are animals; 



Socrates 



therefore 

 All men 



Some men 

 Socrates 



are mortal. 



To prove a negative, the argument must be capable 

 of being expressed in this form: 



No one who is capable of self-control is necessarily 

 vicious ; 



All negroes j 



Some negroes > are capable of self-control ; 



Mr. A's negro J 



therefore 



No negroes are j 



Some negroes are not I necessarily vicious. 

 Mr. A's negro is not J 



Although all ratiocination admits of being thrown 

 into one or the other of these forms, and sometimes 

 gains considerably by the transformation, both in 

 clearness and in the obviousness of its consequence ; 

 there are, no doubt, cases in which the argument falls 

 more naturally into one of the other three figures, and 

 in which its conclusiveness is more apparent at the 

 first glance in those figures, than when reduced into 

 the first. Thus, if the proposition were that pagans 

 may be virtuous, and the evidence to prove it were 



