394 NOTES ON BOOLE'S LAWS OF THOUGHT. 



Laws of Thought. I shall not stop to inquire into the limita- 

 tions which it may perhaps require. 

 The general truth of the equations 



a? 2 = x and xy yx 



appears to suffer another exception in the case of relative terms, 

 that is, of adjectives of which the interpretation is functional of 

 the object to which they are applied. A small St Bernard dog 

 is not simpliciter a small dog ; the word meaning that which is 

 less than the medium size of the class of objects to which it is 

 applied. Here neither s 2 = s nor sx = xs. If we say that in 

 order to save all these equations we may employ a different 

 symbol for every application of the adjective small, how can we 

 express the meaning which is common to them all, and in virtue 

 of which the word small exists as an element of language ? 



Diffident as I am with respect to all these remarks on a 

 method in which I find so much to admire, I am yet more so 

 with respect to the following. But it seems to me that we 

 cannot say that 



x (I - x) = 



expresses proprio vigore, that is, in virtue of antecedent conven- 

 tions, what is called the principle of contradiction. 



In ordinary language we have words which, independently 

 of this principle, express negation : we say red, not red, and the 

 like; but in the symbols employed in the Laws of Thought there 

 is no other means of expressing not red than by 1 x, x de- 

 noting red. Now the interpretation of this symbol 1 x seems 

 to me to be given by the principle of contradiction, and there- 

 fore I should rather say that the equation 



is interpreted by that principle than that it expresses it. In 

 accordance with this view the equation 



x* = x 

 would appear to be independent of the principle of contradiction. 



