EXTENSION OF THE ORDINARY LOGIC. 95 



expressed in our system by " A is included in B/' Using 

 L as the symbol of inclusion, we write it 



A=LB. 



Its converse is " B is included in A /' and this we express 



by 



B = L-'A. 

 In the old logic, 



All A is B 



becomes, by conversion. 



Some B is A. 

 But this is an inadequate and indeed an inaccurate ac- 

 count of the subject, because, when reconverted. 



Some B is A 

 becomes only 



Some A is B ; 



so that by reconversion we do not get back the original 

 proposition, which by any satisfactory theory of conversion 

 we ought to do. 

 We postulate that 



L'-=L. 



This is not true of all relations, but it is true of many, 

 and among others of inclusion. When asserted of that 

 relation, it means that if A is included in M, and M in B, 

 then A is included in B ; or, more briefly, the enclosure 

 of an enclosure is an enclosure. This is the expression in 

 our system of the canon of the old " syllogism in Barbara.^' 

 And conversely, 



[L-y=L-^; 



that is to say, the includent of an includent is an in- 

 cludent. These words, enclosure and includent, will be 

 found useful. 



