2o8 Mr. J. J. Murphy on 



The eight relations are also arranged as contrapositives. 

 to each other ; these differ in phase : — 



E Enclosure. E^ Includent. 



N Excludent. N^ Alternative. 



e Non-enclosure. e^ Non-includent. 



n Participant. tt^ Non-alternative. 



They are also arranged as contradictories to each 

 other : — these differ both in quantity ^ total or partial, and 

 in sign^ positive or negative. A proposition is positive, or 

 affirmative, when its terms are of the same sign, and 

 negative when they are of opposite signs. Thus the 

 relation of alternative is a negative one, because its form is 

 "not-A is B": — but that of non-alternative is positive,, 

 because its form is " some not-A is not-B." The relation 

 which we call includent is, in the present system, doubly 

 negative, and therefore positive, being here treated as the 

 contrapositive of enclosure : — 



primarily means "All not-A is not-B." We also call 

 syllogisms positive when the relations expressed in their 

 premises are of the same sign ; — negative, when they are 

 of opposite signs. The conclusion of a positive syllogism 

 is a positive proposition, and vice versa. 



In the following, the positives are in the left column and 

 the contradictory negatives at the right : — 



E Enclosure. e Non-enclosure. 



E^ Includent. ^ Non-includent. 



n Participant. N Excludent. 



rC Non-alternative iV^ Alternative. 



They are also arranged with each partial opposite to its. 

 total. 



