96 OF INTERPRETATION. [CHAP. VI. 



a?(l-e)(l-w) = 0; (9) 



whence by interpretation 



DIRECT CONCLUSION. Rational beings are all responsible beings 

 who are either free to act, not having voluntarily sacrificed their free- 

 dom, or not free to act, having voluntarily sacrificed their freedom, 

 together with an indefinite remainder (some, none, or all) of beings 

 not responsible, not free, and not having voluntarily sacrificed their 

 freedom. 



FIRST INDEPENDENT RELATION. No responsible beings are at 

 the same time free to act, and in the condition of having voluntarily 

 sacrificed their freedom. 



SECOND. No responsible beings are not free to act, and at the 

 same time in the condition of not having sacrificed their freedom. 



The independent relations above determined may, however, 

 be put in another and more convenient form. Thus (8) gives 



xw = - = z + - (1 - 2), on development ; 



or, xw = v (1 - z) ; (10) 



and in like manner (9) gives 



or, x (1 - w) = vz ; (11) 



and (10) and (11) interpreted give the following Propositions : 



1st. Responsible beings who have voluntarily sacrificed their free- 

 dom are not free. 



2nd. Responsible beings who have not voluntarily sacrificed their 

 freedom are free. 



These, however, are merely different forms of the relations 

 before determined. 



16. In examining these results, the reader must bear in mind, 

 that the sole province of a method of inference or analysis, is to 

 determine those relations which are necessitated by the connexion 

 of the terms in the original proposition. Accordingly, in esti- 

 mating the completeness with which this object is effected, we 

 have nothing whatever to do with those other relations which 



