58 DIVISION OF PROPOSITIONS. [CHAP. IV. 



which are metallic and non-elastic, and those which are elastic 

 and non-metallic." Here the word those means hard substances. 

 so that the expression really means. Hard substances except hard 

 substances, metallic, non-elastic, and hard substances non-metallic, 

 elastic ; the word except extending to both the classes which 

 follow it. The complete expression is 



x- xz-y 

 or, x-xz (\-y]-xy(\-z). 



9. The preceding Proposition, with the different illustrations 

 which have been given of it, is a necessary preliminary to the 

 following one, which will complete the design of the present 

 chapter. 



PROPOSITION III. 



To deduce from an examination of their possible varieties a gene- 

 ral method for the expression of Primary or Concrete Propositions. 



A primary proposition, in the most general sense, consists of 

 two terms, between which a relation is asserted to exist. These 

 terms are not necessarily single-worded names, but may represent 

 any collection of objects, such as we have been engaged in consi- 

 dering in the previous sections. The mode of expressing those 

 terms is, therefore, comprehended in the general precepts above 

 given, and it only remains to discover how the relations between 

 the terms are to be expressed. This will evidently depend upon 

 the nature of the relation, and more particularly upon the ques- 

 tion whether, in that relation, the terms are understood to be 

 universal or particular, i. e. whether we speak of the whole of 

 that collection of objects to which a term refers, or indefinitely of 

 the whole or of a part of it, the usual signification of the prefix, 

 " some." 



Suppose that we wish to express a relation of identity be- 

 tween the two classes, " Fixed Stars" and " Suns," i. e. to 

 express that " All fixed stars are suns," and " All suns are fixed 

 stars." Here, if x stand for fixed stars, and y for suns, we shall 



have 



x = y 



for the equation required. 



