RATIOCINATION, OR SYLLOGISM. 



127 



the middle term is the subject of the major premise and the predicate of 

 the minor. This is reckoned as the first figure. When the middle term is 

 the predicate in both premises, the syllogism belongs to the second figure ; 

 when it is the subject in both, to the third. In the fourth figure the mid- 

 dle term is the subject of the minor premise and the predicate of the major. 

 Those writers who reckon no more than three figures, include this case in 

 the first. 



Each figure is divided into moods, according to what are called the quan- 

 tity and quality of the propositions, that is, according as they are universal 

 or particular, affirmative or negative. The following are examples of all 

 the legitimate moods, that is, all those in which the conclusion correctly 

 follows from the premises. A is the minor term, C the major, B the mid- 

 dle term. 



FIRST FIGURE. 



All B is C 

 All A is B 

 therefore 

 All A is C 



No C is B 



All A is B 



therefore 



No A is C 



No B is C 

 All A is B 

 therefore 

 No A is C 



All B is C 

 Some A is B 



therefore 

 Some A is C 



SECOND FIGURE. 



All C is B 



No A is B 



therefore 



No A is C 



No C is B 

 Some A is B 



therefore 

 Some A is not C 



No B is C 

 Some A is B 



therefore 

 Some A is not C 



All C is B 



Some A is not B 



therefore 

 Some A is not C 



All B is C 

 All B is A 



therefore 

 Some A is C 



No B is C 

 All B is A 



therefore 

 Some A is not C 



THIRD FIGURE. 



Some B is C All B is C 



All B is A Some B is A 



therefore therefore 



Some A is C Some A is C 



Some B is not C 

 All B is A 

 therefore 

 Some A is not C 



No B is C 



Seme B is A 



therefore 

 Some A is not C 



All C is B 

 All B is A 

 therefore 

 Some A is C 



All C is B 

 No B is A 



therefore 

 Some A is not C 



FOURTH FIGURE. 



Some C is B No C is B 



All B is A 

 therefore 

 Some A is C 



All B is A 

 therefore 

 Some A is not C 



No C is B 

 Some B is A 



therefore 

 Some A is not C 



In these exemplars, or blank forms for making syllogisms, no place is 

 assigned to singular propositions ; not, of course, because such proposi- 

 tions are not used in ratiocination, but because, their predicate being af- 

 firmed or denied of the whole of the subject, they are ranked, for the pur- 

 poses of the syllogism, with universal propositions. Thus, these two syllo- 

 gisms — 



All men are mortal, All men are mortal, 



All kings are men, Socrates is a man, 



therefore therefore 



All kings are mortal, Socrates is mortal, 



are arguments precisely similar, and are both ranked in the first mood of 

 the first figure.* 



* Professor Bain denies the claim of Singular Propositions to be classed, for the purposes 

 of ratiocination, with Universal ; though they come within the designation which he himself 

 proposes as an equivalent for Universal, that of Total. He would even, to use his own ex- 

 pression, banish them entirely from the syllogism. He takes as an example, 



Socrates is wise, 



Socrates is poor, therefore 

 ' Some poor men are wise, 

 or more properly (as he observes) "one poor man is wise." "Now, if wise, poor, and a 

 man, are attributes belonging to the meaning of the word Socrates, there is then no march of 



