CHAP. VII.] OF ELIMINATION. 109 



deem it necessary to add to " wealth" the epithet " transferable," 

 if another part of our reasoning had led us to express the con- 

 clusion, that there is no wealth which is not transferable, yet it 

 pertains to the perfection of this method that it in all cases fully 

 defines the objects represented by each term of the conclusion, 

 by stating the relation they bear to each quality or element of dis- 

 tinction that we have chosen to employ. This is necessary in order 

 to keep the different parts of the solution really distinct and in- 

 dependent, and actually prevents redundancy. Suppose that the 

 pair of terms we have been considering had not contained the 

 word " transferable," and had unitedly been " All wealth," we 

 could then logically resolve the single term " All wealth" into 

 the two terms "All wealth transferable," and "All wealth 

 intransferable." But the latter term is shown to disappear by 

 the "independent relations." Hence it forms no part of the de- 

 scription required, and is therefore redundant. The remaining 

 term agrees with the conclusion actually obtained. 



Solutions in which there cannot, by logical divisions, be pro- 

 duced any superfluous or redundant terms, may be termed pure 

 solutions. Such are all the solutions obtained by the method of 

 development and elimination above explained. It is proper to 

 notice, that if the common algebraic method of elimination were 

 adopted in the cases in which that method is possible in the pre- 

 sent system, we should not be able to depend upon the purity of 

 the solutions obtained. Its want of generality would not be its 

 only defect. 



15. In the second place, it will be remarked, that the con- 

 clusion contains two terms, the aggregate significance of which 

 would be more conveniently expressed by a single term. Instead 

 of " All wealth productive of pleasure, and transferable," and 

 "All wealth not productive of pleasure, and transferable," we 

 might simply say, " All wealth transferable." This remark is 

 quite just. But it must be noticed that whenever any such sim- 

 plifications are possible, they are immediately suggested by the 

 form of the equation we have to interpret ; and if that equation 

 be reduced to its simplest form, then the interpretation to which 

 it conducts will be in its simplest form also. Thus in the original 

 solution the terms wtp and wt(\ - jo), which have unity for their 



