ii.] TERMS. 31 



There are many grammatical usages concerning the 

 junction of words and phrases to which we need pay no 

 attention in logic. We can never say in ordinary language 

 " of wood table," meaning " table of wood ; " but we may 

 consider "of wood" as logically an exact equivalent of 

 " wooden " ; so that if 



X = of wood, 



Y = table, 



there is no reason why, in our symbols, XY should not be 

 just as correct an expression for " table of wood " as YX. 

 In this case indeed we might substitute for " of wood " the 

 corresponding adjective " wooden," but we should often fail 

 to find any adjective answering exactly to a phrase. There 

 is no single word by which we could express the notion 

 " of specific gravity 10*5 :" but logically we may consider 

 these words as forming an adjective ; and denoting this by 

 S and metal by P, we may say that SP means " metal of 

 specific gravity IO'5." It is one of many advantages in 

 these blank letter- symbols that they enable us completely 

 to neglect all grammatical v peculiarities and to fix our 

 attention solely on the purely logical relations involved. 

 Investigation will probably show that the rules of grammar 

 are mainly founded upon traditional usage and have little 

 logical signification. This indeed is sufficiently proved by 

 the wide grammatical differences which exist between 

 languages, though the logical foundation must be the 

 same. 



Symbolic Expression of the Law of Contradiction. 



The synthesis of terms is subject to the all-important 

 Law of Thought, described in a previous section (p. 5) and 

 called the Law of Contradiction. It is self-evident that no 

 quality can be both present and absent at the same time 

 and place. This fundamental condition of all thought and 

 of all existence is expressed symbolically by a rule that a 

 term and its negative shall never be allowed to come into 

 combination. Such combined terms as Aa, B&, Cc, &c., are 

 self-contradictory and devoid of all intelligible meaning. 

 If they could represent anything, it would be what cannot 

 exist, and cannot even be imagined in the mind. They 

 can therefore only enter into our consideration to suffer 



