RATIOCINATION, OR SYLLOGISM. 113 



be found in both premisses, since it is by means of it that the (tthcr 

 two terms are to be connected together. The predicate of the conchi- 

 sion is called the major tenn of the syllogism; the subject of the con- 

 clusion is called tlie minor term. As theie can be but three terms, 

 the major and minor terms must each be found in one, and only one, 

 of the premisses, together with the middleterm which is in them both. 

 The premiss which contains the middleterm and the mnjt)r term is 

 called the major premiss ; that w^hich contains the middleterm and the 

 niinor term is called the mmor premiss of the syllogism. 



Syllogisms are divided by some logicians into throe Jigures, by oth- 

 ers into four, according to the position of the middleterm, which may 

 either be the subject in both premisses, the predicate in both, or the 

 subject in one and the predicate in the other. Tlie most common 

 case is that in which the middleterm is the subject of the major prem- 

 iss and the predicate of the minor. This is reckoned as the first figure. 

 When the middleterm is the predicate in both premisse.s, the syllogism 

 belongs to the second figure ; when it is the subject in both, to the 

 third. In the fourth figure the middleterm is the subject of the minor 

 premiss and the predicate of the major. Those WTiters who reckon 

 no more than tluree figures, include this case in the first. 



Each figure is subdivided into modes, according to what are called 

 the quantity and qimlitij of the propositions, that is, according as they 

 are universal or particular, aflirmative or negative. The following are 

 examples of all the legitimate modes, that is, all those in which the. 

 conclusion coiTectly follows from the premisses; A is the minor term, 

 C the major, B the middleterm. 



' FiKST Figure. 



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



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



therefore therefore therefore therefore 



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



Second Figure. 



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



All A is B No A is B Some A is B Some A is not B 



therefore therefore therefore therefore 



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



Third Figure. 



All B is C NoBisC Some B is C All Bis C iSomeBisnotC No B is C 



All B is A All Bis A All Bis 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. 



, All C is B All C is B Some C is B No C is B No C is B 



All B, is A - No Bis A All Bis A All B is A Some Bis A 



therefore therefore therefore therefore therefore 



Some A i^C Some A i.s C Some A is C Some A is not C Some A is not C 



In these exemplars, or blank fonns for making syllogisms, no place 

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

 positions are not used in ratiocination, but because, their predicate 

 being affirmed or denied of the whole of the subject, they are ranked, 

 for the purposes of the syllogism, with universal propositions. Thus, 

 these two syllogisms — 



