RATIOCINATION, OR SYLLOGISM. 



109 



Each figure is divided into moods, 

 according to what are called the 

 quantity and qualiti/ of the proposi- 

 tions, that is, according as they are 

 universal or particular, affirmative or 

 negati ve. The following are examples 



of all the legitimate moods, that is 

 all those in which the conclusion cor- 

 rectly follows from the premises. A 

 is the minor term, C the major, B the 

 middle term. 



First Figure. 

 All B is C No B is C All B is 



All A is B All A is B Some A is B 

 therefore therefore therefore 



All A is No A is C Some A is C 



Second Figure. 

 No C is B All C is B No C is B 

 All A is B No A is B Some A is B 

 therefore therefore therefore 



No A is C No A is C Some A is not C 



No B is C 



Some A is B 



therefore 

 Some A is not C 



AUG is B 

 Some A is not B 



therefore 

 Some A is not C 



Third Figure. 



AUBisC NoBisC Some B is C All B is C Some Bis not C No B is C 



All Bis A All Bis A All B is A Some B is A All B is A Some B is A 



therefore therefore therefore therefore therefore therefore 



Some A is C Some A is not C Some A is C Some A is C Some A is not C Some A is not C 



Fourth Figure. 



AH C is B All C is B Some C is B No C is B No C is B 



All B is A No B is A All B is A All B is A Some B is A 

 therefore therefore therefore therefore therefore 



Some A is C Some A is not C Some A is C Some A ia not C 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 propositions 

 are not used in ratiocination, but be- 

 cause, their predicate being affirmed 

 or denied of the whole of the subject, 

 they are ranked, for the purposes of 

 the syllogism, with universal proposi- 

 tions. Thus, these two syllogisms — 



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 ; 

 thnugh they come within the designation 

 which he himself proposes as an equivalent 

 for Universal, that of Total. He would 

 even, to use his own expression, banish 

 them entirely from the syllogism. He 

 takes as an example, 



The reasons why syllogisms in any 

 of the above forms are legitimate, that 

 is, why, if the premises are true, the 

 conclusion must inevitably be so, and 

 why this is not the case in any other 

 possible mood, (that is, in any other 

 combination of universal and parti- 

 cular, affirmative and negative pro- 

 positions, ) any person taking interest 

 in these inquiries may be presumed to 

 have either learned from the common 

 school-books of the syllogistic logic, or 

 to be capable of discovering for him- 

 self. The reader may, however, be 

 referred for every needful explanation 

 to Archbishop Whately's Elements of 

 Logic, where he will find stated with 



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 1 he 

 meaning of the word Socrates, there is 

 then no march of rea.«oning at all. We 

 have given in Soqrates, inter alia,, the facta 



