54 THE PRINCIPLES OF SCIENCE. 



part of the globe, are described negatively as inorganic. 

 But we might, with at least equal logical correctness, 

 have described the preponderating class of substances as 

 mineral, and then vegetable and animal substances would 

 have been non-mineral. 



It is plain that any positive term, and its corresponding 

 negative divide between them the whole universe of 

 thought : whatever does not fall into one must fall into 

 the other, by the third fundamental Law of Thought, 

 the Law of Duality. It follows at once that there are 

 two modes of representing a difference. Suppose that 

 the things or classes represented by A and B are found 

 to differ, we may indicate the result of the judgment by 

 the notation (see p. 20) 



A-B. 



But we may now represent the same judgment by the 

 assertion that A agrees with those things which differ from 

 B, or that A agrees with the not-B s. Using our notation 

 for negative terms (see p. 17), we obtain 



A = A6 



as the expression of the ordinary negative proposition. 

 Thus if we take A to mean quicksilver, and B solid, then 

 we have the following proposition : 



Quicksilver = Quicksilver not-solid. 

 There may also be several other classes of negative 

 propositions, of which no notice was taken in the old logic. 

 We may have cases where all A s are not-B s, and at the 

 same time all not-B s are A s ; there may, in short, be a 

 simple identity between A and not-B^ which may be 

 expressed in the form 



A=6. 

 An example of this form would be 



Conductors of electricity = non-electrics. 

 We shall also frequently have to deal as results of 



