CHAP. VI.] OF INTERPRETATION. 93 



The latter function presupposes, as a condition of its interpreta- 

 tion, that the class represented by y is wholly contained in the 

 class represented by x ; the former function does not imply any 

 such requirement. 



Now if V is independently interpretable, and if w represent 

 the collection of individuals which it contains, the equation 

 w = V will hold true without entailing as a consequence the va- 

 nishing of any of the constituents in the development of V\ 

 since such vanishing of constituents would imply relations among 

 the classes of things denoted by the symbols in V. Hence the 

 development of V will be of the form 



the coefficients a 1? a 2 > &c. all satisfying the condition 



! (1 - fli) = 0, 2 (1 - 2 ) = 0, &c. 

 Hence by the reasoning of Prop. 4, Chap. v. the function V will 



be subject to the law 



V(\ - 7) = 0. 



This result, though evident d priori from the fact that V is sup- 

 posed to represent a class or collection of things, is thus seen to 

 follow also from the properties of the constituents of which it is 

 composed. The condition V(\ - V) = may be termed "the 

 condition of interpretability of logical functions." 



14. The general form of solutions, or logical conclusions de- 

 veloped in the last Proposition, may be designated as a " Relation 

 between terms." I use, as before, the word " terms" to denote 

 the parts of a proposition, whether simple or complex, which are 

 connected by the copula " is" or " are." The classes of things re- 

 presented by the individual symbols may be called the elements 

 of the proposition. 



15. Ex. 1. Resuming the definition of " clean beasts," 

 (VI. 6), required a description of "unclean beasts." 



Here, as before, x standing for " clean beasts," ?/for "beasts 

 dividing the hoof," z for " beasts chewing the cud," we have 



x = yz; (5) 



whence 



I- x = 1 -yz-, 



and developing the second member, 



