96 MR. JOSEPH JOHN MURPHY ON AN 



From the premises 

 we caiij as has been shown^ infer that 



whence 



A=(jL-M)°B=(L-')°B. 



If L means inclusion, then the meaning of the syllogism 

 is as follows : — 



A is an includent of M; 



B is an includent of M ; 



therefore A is a co-includent with B of M ; 



or A is a co-includent with B. 



This is no more than the old logic ' would express by the 

 following : — 



M is A; 



MisB; 

 therefore some A is B. 



But if the premises are the converse of these, as follows — 



A=LM, B=LM, 



the conclusion will be 



A=L°B; 



that is to say, A is a co-enclosure with B — a conclusion 

 not recognized in the old logic ; yet it is valid, and may be 

 important. Let E, for instance, mean Irishmen, W the 

 Duke of Wellington, and P Lord Palmerston ; then from 

 the premises 



W=LE, P=iE, 



we have the conclusion 



V = {LEyW=L°W; 



