CHAP. IV.] DIVISION OF PROPOSITIONS. 63 



and similarly in any other case. Thus we have the following 

 Kule: 



RULE. To express any proposition of the form " No x's are 

 ys," convert it into the form " All xs are not ys" and then proceed 

 as in the previous case. 



13. Consider, lastly, the case in which the subject of the 

 proposition is particular, e. g. " Some men are not wise." Here, 

 as has been remarked, the negative not may properly be referred, 

 certainly, at least, for the ends of Logic, to the predicate wise ; 

 for we do not mean to say that it is not true that " Some men 

 are wise," but we intend to predicate of " some men" a want of 

 wisdom. The requisite form of the given proposition is, there- 

 fore, " Some men are not- wise." Putting, then, y for "men," 

 x for " wise," i. e. "wise beings," and introducing v as the sym- 

 bol of a class indefinite in all respects but this, that it contains 

 some individuals of the class to whose expression it is prefixed, 

 we have 



vy = v(l - x). 



14. We may comprise all that we have determined in the 

 following general Rule : 



GENERAL RULE FOR THE SYMBOLICAL EXPRESSION OF PRIMARY 

 PROPOSITIONS. 



1st. If the proposition is affirmative, form the expression of the 

 subject and that of the predicate. Should either of them be particular, 

 attach to it the indefinite symbol v, and then equate the resulting ex- 

 pressions. 



2ndly. If the proposition is negative, express first its true mean- 

 ing by attaching the negative particle to the predicate, then proceed as 

 above. 



One or two additional examples may suffice for illustration. 



Ex. " No men are placed in exalted stations, and free from 

 envious regards." 



Let y represent "men," x, " placed in exalted stations," z 9 

 " free from envious regards." 



Now the expression of the class described as "placed in 



