CHAPTER V. 



OPPOSITION OF CATEGORICAL JUDGMENTS AND 

 PROPOSITIONS. 



1 10. MEANING OF LOGICAL &quot; OPPOSITION &quot;: THE SQUARE 

 OF OPPOSITION. We have now sufficiently examined the quality 

 and quantity of propositions, and the various interpretations arising 

 from the intension and extension of the terms contained in them, 

 to inquire next into all the possible implications of truth and 

 falsity derivable from any given categorical judgment. These 

 implications are made explicit, partly by way of &quot; opposition,&quot; 

 and partly by way of &quot; eduction &quot;. With the latter we shall deal 

 in the next chapter, with &quot; opposition &quot; in the present one. 



By the Logical Opposition of propositions we mean the relation, 

 in respect of quantity and quality, between any two propositions 

 which have the same subject and predicate ; m , the relation between 

 two propositions identical in matter and different in form (91). 

 Thus, two propositions are said to be logically &quot; opposed &quot; to each 

 other when they have the same subject and predicate, but differ 

 in quantity, or quality, or both. Evidently, two such propositions 

 need not be incompatible with each other ; for instance, A and I 

 (SaP and SiP) are not incompatible, although they are, accord 

 ing to our definition, &quot; opposed &quot; to each other. This purely 

 technical use of the word &quot; opposition&quot; is a little disconcerting 

 because it is so unusual ; but we need some such word to express 

 the general set of relations referred to, and, if this purely logical 

 use of the word &quot; opposition &quot; be noted and remembered, no con 

 fusion can arise. 



We saw in a previous section (91) that, taking the ordinary 

 predicative view of the judgment, the latter either affirms or denies 

 something about either the whole or an indefinite portion ^/&quot;some 

 thing else : thus giving us the four prepositional forms, SaP, 

 SeP, SzP, SoP. The mutual relations between the pairs will, 

 therefore, be : 



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