CHAP. II.] SIGNS AND THEIR LAWS. 29 



" horned white sheep," i. e. that collection of things to which 

 the name " sheep," and the descriptions " white" and " horned" 

 are together applicable. 



Let us now consider the laws to which the symbols x,y, &c., 

 used in the above sense, are subject. 



7. First, it is evident, that according to the above combina- 

 tions, the order in which two symbols are written is indifferent. 

 The expressions xy and yx equally represent that class of things 

 to the several members of which the names or descriptions x and 

 y are together applicable. Hence we have, 



xy=yx. (1) 



In the case of x representing white things, and y sheep, either 

 of the members of this equation will represent the class of " white 

 sheep." There may be a difference as to the order in which the 

 conception is formed, but there is none as to the individual things 

 which are comprehended under it. In like manner, if x represent 

 " estuaries," and y " rivers," the expressions xy and yx will in- 

 differently represent " rivers that are estuaries," or u estuaries 

 that are rivers," the combination in this case being in ordinary 

 language that of two substantives, instead of that of a substantive 

 and an adjective as in the previous instance. Let there be a 

 third symbol, as z, representing that class of things to which the 

 term " navigable" is applicable, and any one of the following 

 expressions, 



zxy, zyx, xyz, &c., 



will represent the class of " navigable rivers that are estuaries." 



If one of the descriptive terms should have some implied re- 

 ference to another, it is only necessary to include that reference 

 expressly in its stated meaning, in order to render the above 

 remarks still applicable. Thus, if x represent "wise" and y 

 " counsellor," we shall have to define whether x implies wisdom 

 in the absolute sense, or only the wisdom of counsel. With such 

 definition the law xy = yx continues to be valid. 



We are permitted, therefore, to employ the symbols x, y, z, fyc. 9 in 

 the place of the substantives, adjectives, and descriptive phrases subject 

 to the rule of interpretation, that any expression in which several of 

 these symbols are written together shall represent all the objects or indi- 



