86 THE PRINCIPLES OF SCIENCE. 



The order of statement, in short, has no effect upon the 

 meaning of an aggregate of alternatives, so that the Law 

 of Commutativeness holds true of the disjunctive symbol. 



As we have admitted the possibility of joining as alter- 

 natives terms which are not really different, the ques- 

 tion arises, How shall we treat two or more alternatives 

 when they are clearly shown to be the same 1 If we 

 have it asserted that P is Q or R, and it is afterwards 

 proved that Q is but another name for R, the result is 

 that P is either R or R. How shall we interpret such a 

 statement ? What would be the meaning, for instance, of j 

 'wreath or anadem' if, on referring to a dictionary, we 

 found anadem described as a wreath \ I take it to be 

 self-evident that the meaning would then become simply 

 * wreath/ Accordingly we may affirm the general law 



A | A = A. 



Any number of identical alternatives may always be ! 

 reduced to, and are logically equivalent to, any one of 

 those alternatives. This is a law which distinguishes 

 mathematical terms from logical terms, because it ob-l 

 viously does not apply to the former. I propose to call-] 

 it the Law of Unity, because it must really be involved 

 in any definition of a mathematical unit. This law is 

 closely analogous to the Law of Simplicity, AA = A ; and 

 the nature of the connection is worth v of attention. 



* 



I am not aware that logicians have in any adequate way 

 noticed the close relation between combined and dis- 

 junctive terms, namely that every disjunctive term is the . 

 negative of a corresponding combined term, and vice versd. 

 Consider the term 



Malleable dense metal. 



How shall we describe the class of things which are not 



O 



malleable-dense-metals ? Whatever is included under that 

 term must have all the qualities of malleability, denseness, 

 and metallic nature. Wherever any one or more of the 



