CHAP. II.] SIGNS AND THEIR LAWS. 33 



" and," " or," interposed between the terms descriptive of two or 

 more classes of objects, imply that those classes are quite distinct, 

 so that no member of one is found in another. In this and in 

 all other respects the words " and" " or" are analogous with the 

 sign + in algebra, and then* laws are identical. Thus the ex- 

 pression " men and women" is, conventional meanings set aside, 

 equivalent with the expression " women and men." Let x repre- 

 sent "men," y, "women;" and let + stand for "and" and "or," 

 then we have 



* + y = V + z, (3) 



an equation which would equally hold true if x and y represented 

 number s, and + were the sign of arithmetical addition. 



Let the symbol z stand for the adjective " European," then 

 since it is, in effect, the same thing to say " European men and 

 women," as to say " European men and European women," we 

 have 



z(x + y) = zx + zy. (4) 



And this equation also would be equally true were or, y, and z 

 symbols of number, and were the juxtaposition of two literal 

 symbols to represent their algebraic product, just as in the logical 

 signification previously given, it represents the class of objects to 

 which both the epithets conjoined belong. 



The above are the laws which govern the use of the sign 

 +, here used to denote the positive operation of aggregating 

 parts into a whole. But the very idea of an operation effecting 

 some positive change seems to suggest to us the idea of an oppo- 

 site or negative operation, having the effect of undoing what the 

 former one has done. Thus we cannot conceive it possible to 

 collect parts into a whole, and not conceive it also possible to 

 separate a part from a whole. This operation we express in 

 common language by the sign except, as, " All men except 

 Asiatics," " All states except those which are monarchical." 

 Here it is implied that the things excepted form a part of the 

 things from which they are excepted. As we have expressed 

 the operation of aggregation by the sign +, so we may express 

 the negative operation above described by - minus. Thus if x 

 be taken to represent men, and 37, Asiatics, i. e. Asiatic men, 



D 



