136 MR. JOSEPH JOHN MURPHY ON THE 



The following equations are necessarily true : — 



RiY = i-'rj, 

 and ♦ 



R- 1 iX = i-'r-'x 



That is to say : — 



A teacher of every Y is a not-teacher of none but not- 

 Y's; 



and 



A pupil of every X is a not-pupil of none but not-X's. 



"All knowledge is relative;" that is to say, only rela- 

 tions can be the objects of knowledge ; — and we may treat 

 the common logic as a particular case of the system ex- 

 pounded here, the relative term in this case being inter- 

 preted to mean identity or coexistence. Let us use C 

 (the initial letter of coexistent) as the relative term ; then 

 c will signify non-identical or non-coexistent. " All X is 



Y " thus becomes " Every X is identical with a Y" or 

 " The attribute X is always coexistent with the attribute 



Y •" and the proposition will be written, in our notation, 



iX<CY. 



The contrary of this, as shown above, is 



iX<ci Y. 



That is to say, " Every X is non-identical with every Y ;" 

 or, in common language, " No X is identical with any Y" 

 Such a proposition is invertible ; — if no X is identical with 

 any Y, then no Y is identical with any X ; — not because 

 it is negative, but because it is doubly total. 



