218 MR. JOSEPH JOHN MURPHY ON ADDITION 



7. A and B are the negatives of eacli other; 

 Nothing is both A and B ; 



A and B are the negatives of each other. 



8. A and B are the negatives of each other ; 

 Every thing is either A or B ; 



A and B are the negatives of each other. 



It will be observed that if we add L or L~' to i^ the 

 sum is I, and if we add iV or ilf to — i, the sum is — i. 

 As L and L~^ are positive and N and M negative^ this 

 may be compared with the equation in the logic of ab- 

 solute terms in the systems of Jevons^ MacCoU^ and Pierce^ 



A+AB=A; 



that is to say^ if we add a part to the whole we do not 

 increase the whole. This is expressed by the equation 

 already given, 



L + L^L. 



It will be observed also that of the above eight equations, 

 the sum of three is zero, of two unity, of two negative 

 unity, and of one 



indicating that the A and the B of the equation are each 

 of them a member of a universe wherewith the other is 

 coextensive; in other words, both A and B are co- 

 extensive with the universe. To give an instance of the 

 reasoning : — 



Inertia and gravity are coextensive. 



There is nothing which has neither inertia nor gravity. 



Every thing has both inertia and gravity. 



