

LOGIC OF I:I:LaT1\BB. T 



It is evident that in this way all conjugatives may be expressed a* \ Lion of oon- 



jugatives of two correlates. * 



The interpretation of such combinations as L" m . etc.. is not vci otM When the 



conjugative and its first correlative can be taken together apart from the second 

 correlative, as in (La)m and (La) m and (£■) in and (/"')", there is no perplexit be- 

 cause in such cases (La) or (L a ) is a simple relative. We have thei fore, onh to ill 

 the betrayer to an enemy an inimical betrayer, when we have 



(La)m = inimical betrayer of a man = betrayer of a man to an cneni) ol him, 

 (La) m = inimical betrayer of every man =ss betrayer of every man to an enemy of him. 



And we have only to call the betrayer to every enemy an unbound) I betrayer, in 

 order to get 



(L a )m = unbounded betrayer of a man = betrayer of a man t<> every enemy of bin 

 (£«) m = unbounded betrayer of every man = betrayer of even man to every enemy 



of him. 

 The two terms La m and L am are not quite so easily interpret 1 Imagine a separated 

 into infinitesimal relatives, A f ,A„,A M , etc., each of which is relative to but one ittdi 

 vidual which is m. Then, because all powers of A t ,A ti ..\ ti , etc., higher than the 

 first, vanish, and because the number of such terms must he [m], we have, 



«m — ( A/ Jfr A„ -fr k M ~fc etc.)* = (Am >,(4,m),(4 m), etc. 



or if M', M", M'", etc., are the individual m's, 



am = (A,WUAjrUAjn,*te. 



It is evident from this that La™ is a betrayer to an A / of M '. to an A it of M . to an A, 

 of M w . etc.. in short of all men to some enemy of them all. In order to interpret 



k* we have only to take the negative of it. This, by (124), is (1 - L |«», or a non- 

 betrayer of all men to some enemy of them. Hence, *", or that whirl, is * f tbj 

 is a betrayer of some man to each enemy of all men. To interpret b(am), m m 

 put it in the form (1 — L)V - «)». This is ■ non-betrayer of a man to all non-nemies 

 of all men." Now, a non-betrayer of some X to every V, is the same , a betrayer of 

 all X's to nothing but what is not Y; and the negative of ■ non-enemy of all m< 

 « enemy of a man." Thus, *(am) is, "betrayer of all men to nothing but an enem 

 of a man." To interpret ^m we may put it in the form (1 - LP "«>m, whr - 

 « non-betrayer of a man to every non-enemy of him." This is a logical sum of terms 

 each of which is ■ non-betrayer of an individual man M to every non-enemy of M 

 Each of these terms is the same as "betrayer of M to nothing but an enemy of K 



