CHAP. VI.] OF INTERPRETATION. 95 



have voluntarily sacrificed their freedom," and apply to it the 

 preceding analysis. 



Let x stand for responsible beings. 

 y rational beings. 

 z those who are free to act, 

 w ,, those who have voluntarily sacrificed their 



freedom of action. 



In the expression of this definition I shall assume, that the 

 two alternatives which it presents, viz. : " Rational beings free 

 to act," and " Rational beings whose freedom of action has been 

 voluntarily sacrificed," are mutually exclusive, so that no indivi- 

 duals are found at once in both these divisions. This will per- 

 mit us to interpret the proposition literally into the language of 



symbols, as follows : 



x = yz 4 yw. (6) 



Let us first determine hence the relation of "rational beings" to 

 responsible beings, beings free to act, and beings whose freedom 

 of action has been voluntarily abjured. Perhaps this object will 

 be better stated by saying, that we desire to express the relation 

 among the elements of the premiss in such a form as will enable 

 us to determine how far rationality may be inferred from respon- 

 sibility, freedom of action, a voluntary sacrifice of freedom, and 

 their contraries. 



From (6) we have 



x 



z+ w 



and developing the second member, but rejecting terms whose 

 coefficients are 0, 



y^ xzw + xz(\ -w) + x(l -z)w + -x(\-z)(\-w) 



whence, equating to the terms whose coefficients are - and -, 

 we have 



y = xz (1 - w) + xw (1 - z) + v (1 - x) (1 - z) (1 - w) ; (7) 



xzw = ; (8) 



