AND MULTIPLICATION OF LOGICAL RELATIVES. 219 



These eiglit equations work out less symmetrically than 

 we might have expected; but their asymmetry may, 

 perhaps, point to some principle which I do not now see. 



Every syllogism has its reciprocal. This is found by 

 substituting for the factors their reciprocals, and writing 

 them in reversed order. Thus, if L and M be any two 

 relatives, the syllogism 



LxM 



has for its reciprocal 



M-'xL-' ; 

 that is to say 



{LxM)-'=M-'xL-\ 



This is also true in arithmetic ; but in arithmetic we do 

 not need to reverse the position of the factors, as this has 

 no effect. 



Every relative term has its corresponding denial ; and 

 these we propose to write as follows : — 



L, or enclosure, is denied by I, or indifferent ; 

 L~^, or includent, „ 7~', or indeterminant ; 



N, or excludent, „ n, or participant ; 



M, or alternative, „ m, or inessential*. 



The following is a fuller statement of the same : — 



1. A=Z/B; or A is B. 

 Denied by 



2. A=7B ; or some A is not B. 



* Tlieso verbal expressions are, I think, more self -explaining than De 

 Morgan's equivalent ones. 



