188 



REASONING. 



them. Every valid ratiocination, therefore, may be stated in 

 the first figure, that is, in one of the following forms : 



Every B is C No B is C 



AHA ) TJ AHA ) 



isB, isB, 



Borne A ) Some A j 



therefore therefore 



All A is C&amp;gt; No A is 



&amp;gt; 

 Some A j Some A is not 



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 \ 



Some men j- are animals ; 



Socrates ) 



therefore 

 All men \ 



Some men i- are mortal. 

 Socrates ) 



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 



Some negroes 



are capable of self-control; 



Mr. A s negro 



therefore 



No negroes are \ 



Some negroes are not J- necessarily vicious. 



Mr. A s negro is not ) 



Though all ratiocination admits of being thrown into one 

 or the other of these forms, and sometimes gains consider 

 ably 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 



