LOGIC 291 



Propositions may be categorical or hypothetical, and the 

 latter may be either conditional (as, if X then Y), or 

 disjunctive (as, either X or Y). 



"Categorical" propositions may be universal or 

 particular, and each of them may be either affirmative or 

 negative. Thus every categorical proposition is either : 



A universal affirmative which may be repre- 

 sented by A. 



(e.g., all whales are mammals.) 

 A universal negative E. 



(e.g., no whales are fishes.) 

 A particular affirmative I. 



(e.g., some whales are toothed.) 

 A particular negative O. 



(e.g. some whales are not toothed.) 



Propositions which differ as to being universal or 

 particular, are said to differ in quantity. Those which 

 differ as to being affirmative or negative, are said to differ 

 in quality. 



Four kinds of opposition may thus exist between 

 judgments, and they may be: (i) Contradictories; (2) Con- 

 traries; (3) Subcontraries ; or (4) Subalterns. 



A Contraries E 



OS 



0, y 



\ ^ | 



Subcontraries O 



