A new Symbolic Treatment of the Old Logic. 209 



E Enclosure 



(All A is B) 

 N Excludent 



(No A is B) 

 E^ Includent 



(All not-A is not-B) 

 N"" Alternative 



(All not-B is A) 



n Participant 



(Some A is B) 

 e Non-enclosure 



(Some A is not B) 

 li' Non-alternative 



(Some not-A is not-B) 

 e^ Non-includent 



(Some not-B is A) 



There are some other relative terms vi^hich I shall have 



to use. 



When I is used as a relative, it signifies identity : — the 



equation 



A=iB 



asserts that A is one with B. The equation 



A = (-i)B 



asserts that B is defined as whatever is not A, so that (—1) 

 has the meaning of exclusive alternative. 



The use of i as a relative term makes it necessary to use 

 U (the initial of Universe) in the sense that 



A = C/'B, and conversely B = U~^k 



signify that A is co-extensive with the universe which 

 contains B. And 



A = (9 B, and conversely B ^ (9~^A 



assert that A does not exist in the same universe with B. 



Before we go on to the subject of syllogisms, we have to 

 consider the combination into a resultant relation of two 

 simultaneous relations between the same terms. 



We have four total relative terms ; and four objects 

 admit of being combined into six pairs. The six pairs in 

 this case, with the resultant relations into which they 

 combine, are as follows : — they are stated both in language, 

 and in " canonical equations " wherein the relations only 

 are expressed. 



