CHAP. II.] SIGNS AND THEIR LAWS. 27 



operations of reasoning are conducted will be considered in the 

 following Proposition : 



PROPOSITION I. 



All the operations of Language, as an instrument of reasoning, 

 may be conducted by a system of signs composed of the following ele- 

 ments, viz. : 



1st. Literal symbols, as x, y, fyc., representing things as subjects 

 of our conceptions. 



2nd. Signs of operation, as +, -, x , standing for those operations 

 of the mind by which the conceptions of things are combined or re- 

 solved so as to form new conceptions involving the same elements. 



3rd. The sign of identity, = . 



And these symbols of Logic are in their use subject to definite 

 laws, partly agreeing with and partly differing from the laws of the 

 corresponding symbols in the science of Algebra. 



Let it be assumed as a criterion of the true elements of ra- 

 tional discourse, that they should be susceptible of combination 

 in the simplest forms and by the simplest laws, and thus com- 

 bining should generate all other known and conceivable forms of 

 language ; and adopting this principle, let the following classifi- 

 cation be considered. 



CLASS I. 



5. Appellative or descriptive signs, expressing either the name 

 of a thing., or some quality or circumstance belonging to it. 



To this class we may obviously refer the substantive proper 

 or common, and the adjective. These may indeed be regarded as 

 differing only in this respect, that the former expresses the sub- 

 stantive existence of the individual thing or things to which it 

 refers ; the latter implies that existence. If we attach to the 

 adjective the universally understood subject " being" or " thing," 

 it becomes virtually a substantive, and may for all the essential 

 purposes of reasoning be replaced by the substantive. Whether 

 or not, in every particular of the mental regard, it is the same 

 thing to say, "Water is a fluid thing," as to say, "Water is 

 fluid ;" it is at least equivalent in the expression of the processes 

 of reasoning. 



