OF ARTS AND SCIENCES : APRIL 9, 1867. 273 



obtained by simple conversion. Ferison and its long reduction are 



Any S is not P, Any some-AS' is M, 



Some S is 3f; Some not-P is some-zS* ; 



(.*. Some M is not P.) .•. Some not-P is M. 



And from the conclusion of the reduction, the conclusion of Ferison 

 may be obtained by a substitution whose possibility is expressed syllo- 

 gistically thus : — 



Any not-P is not P, 

 Some not-P is M; 

 .'. Some M is not P. 

 Bocardo and its long reduction are 



Some S is not P, Any S is M, 



Any S' is M; Some not-P is S; 



(.'. Some 31 is not P.) .-. Some not-P is M. 



And the conclusion of Bocardo is obtained from that of its reduction 

 in the same way as the conclusion of Ferison. 



The ostensive reduction of the indirect or apagogical figures may 

 be considered as the exhibition of them under the general form of 

 syllogism, 



S is M; M is P: 



.-. ^ is P. 



But, in this sense, it is not truly a reduction if the substitutions made 

 in the process are inferences. But although the possibility of the con- 

 versions and contrapositions can be expressed syllogistically, yet this 

 can be done only by taking as one of the premises, 



"All N is N," 



" Any not-i\^ is not N," 



or " Some N is some-^." 

 VOL. VII. 35 



