CHAP. II.] SIGNS AND THEIR LAWS. 35 



may be resolved into this element, and one of the signs included 

 under Class i. For as those signs are used to express quality or 

 circumstance of every kind, they may be employed to express 

 the active or passive relation of the subject of the verb, considered 

 with reference either to past, to present, or to future time. 

 Thus the Proposition, " Caesar conquered the Gauls," may be 

 resolved into " Caesar is he who conquered the Gauls." The 

 ground of this analysis I conceive to be the following : Unless 

 we understand what is meant by having conquered the Gauls, 

 i. e. by the expression " One who conquered the Gauls," we 

 cannot understand the sentence in question. It is, therefore, 

 truly an element of that sentence ; another element is " Caesar," 

 and there is yet another required, the copula is, to show the 

 connexion of these two. I do not, however, affirm that there is 

 no other mode than the above of contemplating the relation ex- 

 pressed by the proposition, " Caesar conquered the Gauls ;" but 

 only that the analysis here given is a correct one for the particu- 

 lar point of view which has been taken, and that it suffices for 

 the purposes of logical deduction. It may be remarked that the 

 passive and future participles of the Greek language imply the 

 existence of the principle which has been asserted, viz. : that the 

 sign is or are may be regarded as an element of every personal 

 verb. 



13. The above sign, is or are, may be expressed by the sym- 

 bol =. The laws, or as would usually be said, the axioms which 

 the symbol introduces, are next to be considered. 



Let us take the Proposition, " The stars are the suns and the 

 planets," and let us represent stars by #, suns by y, and planets 

 by z ; we have then 



* = y + * (7) 



Now if it be true that the stars are the suns and the planets, it 

 will follow that the stars, except the planets, are suns. This 

 would give the equation 



* - z = y, (8) 



which must therefore be a deduction from (7). Thus a term z 

 has been removed from one side of an equation to the other by 



D 2 



