CHAP. IV.] DIVISION OF PROPOSITIONS. 59 



In the proposition, " All fixed stars are suns," the term "all 

 fixed stars" would be called the subject, and " suns" the predi- 

 cate. Suppose that we extend the meaning of the terms subject 

 and predicate in the following manner. By subject let us mean 

 the first term of any affirmative proposition, i. e. the term which 

 precedes the copula is or are ; and by predicate let us agree to 

 mean the second term, i. e. the one which follows the copula ; 

 and let us admit the assumption that either of these may be uni- 

 versal or particular, so that, in either case, the whole class may 

 be implied, or only a part of it. Then we shall have the follow- 

 ing Rule for cases such as the one in the last example : 



10. RULE. When both Subject and Predicate of a Proposition 

 are universal, form the separate expressions for them, and connect them 

 by the sign =. 



This case will usually present itself in the expression of the 

 definitions of science, or of subjects treated after the manner of 

 pure science. Mr. Senior's definition of wealth affords a good 

 example of this kind, viz. : 



" Wealth consists of things transferable, limited in supply, 

 and either productive of pleasure or preventive of pain." 



Before proceeding to express this definition symbolically, it 

 must be remarked that the conjunction and is superfluous. 

 Wealth is really defined by its possession of three properties or 

 qualities, not by its composition out of three classes or collections 

 of objects. Omitting then the conjunction and, let us make 



w = wealth. 



t = things transferable. 



s = limited in supply. 



p = productive of pleasure. 



r = preventive of pain. 



Now it is plain from the nature of the subject, that the ex- 

 pression, "Either productive of pleasure or preventive of pain," 

 in the above definition, is meant to be equivalent to " Either pro- 

 ductive of pleasure ; or, if not productive of pleasure, preventive 

 of pain." Thus the class of things which the above expression, 

 taken alone, would define, would consist of all things productive 



