330 THE SCIENCE OF LOGIC 



(0 (2) (3) (4) (5) (6) 



MeP PeM MeP PeM PeM MeP 



S i M Si M Mi S M i S Ma S MaS 



SoP SoP SoP SoP SoP SoP 



(b) If the major premiss be O, P must be its predicate, and M, 

 to be distributed in the minor, must be subject of an A proposi 

 tion. Hence we have : 



(7) 



Mo P 

 Ma S 

 SoP 



(V) If the major premiss be A, P must be its subject, and M, 

 to be distributed in the minor (which must be negative), must be 

 predicate. The minor must therefore be O. Hence we have the 

 form : 



(8) 



P a M 

 S o M 

 SoP 



(d) The major premiss cannot be I, for this would involve 

 illicit major. 



There are, therefore, EIGHT possible ways (besides four sub 

 altern moods) of proving an O proposition. These are 

 E I O (Ferio) in the first figure ; 

 E I O, A O O (Festino and Baroco) in the second ; 

 E A O, O A O, E I O (Felapton, Bocardo, Ferison) in the third ; 

 E A O, E I O (Fesapo, Fresison) in the fourth. 

 Summing up our results we see that : 



(1) A can be proved in one way, E in four, I in six, and O in 

 eight ways : making nineteen valid and useful moods in all. 



(2) A can be proved in only one figure (the first), E in every 

 figure except the third (which proves only particulars), I in every 

 figure except the second (which proves only negatives), O in every 

 figure without exception. 



These results are interesting. The universal affirmative, 

 which is the most valuable proposition scientifically, is shown to 

 be hardest to prove there being only one way possible. It is 

 likewise easiest to disprove ; for it is disproved by establishing its 

 contradictory, O, and this is the easiest of the four propositions to 

 establish there being eight ways possible. The E proposition, 



