93 MR. JOSEPH JOHN MURPHY ON AN 



bols of relation, consequently, as analogous to numerical 

 coeflEicients. 



In mathematics, if any one of the following four equa- 

 tions is true, the rest are true : — 



A ' 



The same is true in logic if A and B are understood to be 

 the names of any two individuals or classes, L the relation 

 of A to B, and L~^ the inverse relation of B to A. Let 

 2>, for instance, be the relation of teacher, then the fore- 

 going equations are thus interpreted :— 



The relation of A to B is A is the teacher of B. 



that of teacher. 

 The relation of B to A is B is the pupil of A. 



that of pupil. 



The equivalence of these four forms has the same kind 

 of self- evidence as the principle of identity and contra- 

 diction. 



It is to be observed that we use the copula = with the 

 meaning of the word is, without raising the question 

 whether there may not be many individuals standing in 

 the relation L to B, and many standing in the relation 

 L~^ to A. If it is required that the equation 



shall mean that A is the only teacher of B, then the as- 

 sertion that A is one of the teachers^ or a teacher of B, 

 without implying whether B has other teachers or not, 

 will be expressed by 



A = ALB, 

 and its converse by 



B=Bi-'A. 



