LOGIC 297 



The four forms of categorical propositions (uni- 

 versal and particular as both affirmative and nega- 

 tive) we have* symbolised by the letters A, E, I, 0, 

 as denoting the; quantity and quality of propo- 

 sitions. 



Syllogisms are said to differ in mood when they differ 

 with respect to the quantity and quality of their com- 

 ponent propositions. Thus, AAA denotes a syllogism 

 made up of three universal affirmative propositions, and 

 IEO signifies one composed of a particular affirmative 

 major premiss, a universal negative minor premiss, and 

 a particular negative conclusion " as Jones is a man, 

 no man is without a backbone, therefore Jones is not 

 without a backbone." 



There are sixty-four possible ways of arranging three 

 letters, and therefore there are sixty-four conceivable 

 moods for syllogisms, but all these save twelve would, if 

 used, sin against one or other of the ten rules just laid 

 down. 



Syllogisms are further said to differ as to figure that 

 is, according to the position of the middle term, and there 

 are four such figures. These may be represented by 

 letters which serve perfectly to represent valid syllogistic 

 forms, whatever real terms may be substituted for such 

 forms. If the premisses with such real terms be actually 

 true, the conclusion necessarily will be actually true 

 likewise. 



The four figures may also be represented by the 

 following diagrams, which portray the relative extent 

 and relations of whatever may be represented by the 

 terms. 



* See ante, p. 291. 



