130 REASONING. 



Every B is C No B is C 



AHA ). -R AHA ). ^ 



Some A P^ ^' Some A ^^ ^' 



therefore therefore 



AHA ). ^ No A is l^ 



Some A f 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 : 



AH animals are mortal ; 

 All men ) 



Some men V are animals; 

 Socrates ) 



therefore 

 All men ) 

 Some men v 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 v are capable of self-control ; 



Mr. A's negro ) 



therefore 

 No negroes are ) 



Some negroes are not V 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 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 to the first. Thus, if the proposition 

 were that pagans may be virtuous, and the evidence to prove it were the 

 example of Aristides ; a syllogism in the third figure, 



Aristides was virtuous, 

 Aristides was a pagan, 



therefore 

 Some pagan was virtuous, 



would be a more natural mode of stating the argument, and would carry 

 conviction more instantly home, than the same ratiocination strained into 

 the first figure, thus — 



Aristides was virtuous, 



Some pagan was Aristides, 

 therefore 



Some pagan was virtuous. 



A German phHosopher, Lambert, whose JVeues Organon (published in 

 the year 1764) contains among other things one of the most elaborate and 

 complete expositions which had ever been made of the syllogistic doctrine, 

 has expressly examined what sort of arguments fall most naturally and suit- 

 ably into each of the four figures; and his investigation is characterized by 



