A new Symbolic Treatment of the Old Logic. 205 



These are respectively identical with the four relatives 

 of the old logic, namely- 



Universal afifirmative. 

 Partial negative. 



Universal negative. 

 Partial affirmative. 



which are, in the language and notation used here, 



E Enclosure, 

 e Non-enclosure. 



N Excludent. 

 n Non-excludent or Participant. 



[All A is 



B 



A<B 



A is an 



enclosure of B 



A = ^B 



'Some A 



is not B 



-A<^ 

 



A is a non-enclosure of B 



A = ^B 



These four relations between any two absolute terms A and 



B are set forth below in the old language and in the 



language used in this paper, with two corresponding 



notations, the one without, and the other with, relative 



terms : — 



'No A is B ; or 



Nothing is both A & B, A < 1^ 



A is an excludent of B 



A = AB 



Some A is B ; or 



Some things are both A & B 



-A<B 



o 



A is a participant of B A = wB 



De Morgan has shown that the symmetry and complete- 

 ness of the system demand the recognition of four other 

 relations, contrapositive to these. The contrapositive of a 

 relation is the relation that subsists between the negatives of 

 its absolute terms ; and the truth of the contrapositive 

 necessarily follows from the truth of the proposition from 

 which it is derived. I propose to indicate the contrapositive 

 by the original relative term with V (the initial of versed') as 

 an index.* Indicating the negatives of A and B by a and b 



+ De Morgan proposes this index, but as a mere synonym of Ihe index - i, 



