98 OF INTERPRETATION. [CHAP. VI. 



The independent relations here given are the same as we 

 before arrived at, as they evidently ought to be, since whatever 

 relations prevail independently of the existence of a given class 

 of objects ?/, prevail independently also of the existence of the con- 

 trary class 1 - y. 



The direct solution afforded by the first equation is : Irra- 

 tional persons consist of all irresponsible beings who are either free to 

 act, or have voluntarily sacrificed their liberty, and are not free to 

 act ; together with an indefinite remainder of irresponsible beings 

 who have not sacrificed their liberty, and are not free to act. 



18. The propositions analyzed in this chapter have been of 

 that species called definitions. I have discussed none of which 

 the second or predicate term is particular, and of which the ge- 

 neral type is Y = vX, Y and X being functions of the logical 

 symbols #, y, z 9 &c., and v an indefinite class symbol. The ana- 

 lysis of such propositions is greatly facilitated (though the step 

 is not an essential one) by the elimination of the symbol v, and 

 this process depends upon the method of the next chapter. I 

 postpone also the consideration of another important problem 

 necessary to complete the theory of single propositions, but of 

 which the analysis really depends upon the method of the reduc- 

 tion of systems of propositions to be developed in a future page 

 of this work. 



