RATIOCINATION, OR SYLLOGISM. 187 



being an universal negative, admits of simple conversion, and 

 may be changed into No B is C, which, as we showed, is the 

 very same assertion in other words the same fact differently 

 expressed. This transformation having been effected, the 

 argument assumes the following form : 



No B is C 



All A is B 



therefore 



No A is C, 



which is a good syllogism in the second mood of the first 

 figure. Again, an argument in the first mood of the third 

 figure must resemble the following : 



All B is C 

 All B is A 

 therefore 

 Some A is C, 



where the minor premise, All B is A, conformably to what 

 was laid down in the last chapter respecting universal affirma- 

 tives, does not admit of simple conversion, but may be 

 converted per accidens, thus, Some A is B ; which, though it 

 does not express the whole of what is asserted in the propo- 

 sition All B is A, expresses, as was formerly shown, part 

 of it, and must therefore be true if the whole is true. We 

 have, then, as the result of the reduction, the following syllo- 

 gism in the third mood of the first figure : 



All B is C 

 Some A is B, 



from which it obviously follows, that 



Some A is C. 



In the same manner, or in a manner on which after these 

 examples it is not necessary to enlarge, every mood of the 

 second, third, and fourth figures may be reduced to some one 

 of the four moods of the first. In other words, every conclu- 

 sion which can be proved in any of the last three figures, 

 may be proved in the first figure from the same premises, 

 with a slight alteration in the mere manner of expressing 



