202 Mr. J. J. Murphy on 



purpose in exposition. Every proposition and process known 

 to the old logic may be shown with equal clearness without^ 

 or with, the use of symbols of relation, but not with equal 

 neatness and conciseness. 



The " logic of relatives " is not a distinct branch of the 

 science, but only a distinct treatment of it. This is so at 

 least within the limits of the old logic, though the higher 

 branches of the science can scarcely be studied at all 

 without using such symbols. 



I use Roman letters for the absolute terms, and italics 

 for the relative ones ; and, following De Morgan, I use 

 capitals for positive terms, and the corresponding small 

 letters for the corresponding negatives. Thus if A, for 

 instance, is taken to signify matter, a signifies whatever is 

 immaterial. 



Following Boole, I use i as the symbol for everything — • 

 not necessarily the entire universe, but the totality of 

 things that form the subject of discourse ; and o as the 

 symbol for nothing, or that which has no existence, though 

 it may be described, e.g., a dragon or a centaur. Thus the 

 equations 



A = I and A - o 



signify respectively " A is coextensive with the universe," 

 and " A does not exist." But if we use, as we may do, our 

 absolute terms to signify not things but propositions, these 

 equations will respectively assert "A is true" and "A is false." 

 As implied above, the copula = signifies indentity or 

 constant coexistence. The copulas < and > signify in- 

 clusion within a class ; thus, the inequation 



A<B 



states that A is included in B. But if, as before, we take A 

 and B as the symbols not of things but of propositions, it 

 states that the case of A being true is included in the case 



