204 Mr. J. J. Murphy on 



called a weakness in the system, it is a sufficient reply that 

 logical science has never been expected to guarantee the de 

 facto truth of premises ; and it is equally unreasonable to 

 ask it to guarantee the reality of terms. 



When the absolute terms are taken to signify proposi- 

 tions, it would a!so be convenient to express " A is 

 uncertain " by 



A = ° 

 o 



When we thus leave it undetermined whether any term, 

 or name, represents an existing thing, it follows that the 

 existence of its negative is left equally undetermined, and 

 all our terms and their negatives are taken as equally real. 

 As Jevons says, " Every term has its negative in thought." 

 This conduces much to the symmetry of the system. 



We have now to fix on our use of relative terms. I use 

 E (the initial of enclosure) as the symbol of inclusion ; so 

 that the equation 



A = E^ or inversely B = E~^K. 



asserts that A is included in B, or is an enclosure of B ; 

 and B includes A, or is an includent of A. The symbol 

 that I use for exclusion is N (the initial of not\ so that the 

 two equivalent equations 



A = iV^B and B = iVA 



signify that nothing is both A and B. In this case I call 

 A and B excludents of each other. 



As with absolute terms, the corresponding small letter 

 signifies the negative of the term. The negative of a 

 relative term is called its contradictory. Thus the contra- 

 dictories of 



K^E^ and A = iVB 

 are 



A = ^B and A = 7tB, 



signifying respectively " Some A is not B " and some " A is 

 B." 



