CHAP. VII.] OF ELIMINATION. 113 



ply, transferable, and not productive of pleasure. And reversely, 

 Whatever is limited in supply, transferable, and productive of plea- 

 sure, is wealth. Reverse interpretations, similar to the above, are 

 always furnished when the final development introduces terms 

 having unity as a coefficient. 



18. NOTE. The fundamental equation /(1)/(0) = 0, ex- 

 pressing the result of the elimination of the symbol x from any 

 equation f(x) = 0, admits of a remarkable interpretation. 



It is to be remembered, that by the equation /(#) = is im- 

 plied some proposition in which the individuals represented by 

 the class x, suppose " men," are referred to, together, it may be, 

 with other individuals ; and it is our object to ascertain whether 

 there is implied in the proposition any relation among the other 

 individuals, independently of those found in the class men. Now 

 the equation /(I) = expresses what the original proposition 

 would become if men made up the universe, and the equation 

 /(O) = expresses what that original proposition would become 

 if men ceased to exist, wherefore the equation /(I) /(O) = ex- 

 presses what in virtue of the original proposition would be 

 equally true on either assumption, i. e. equally true whether 

 "men" were "all things" or "nothing." Wherefore the theo- 

 rem expresses that what is equally true, whether a given class of 

 objects embraces the whole universe or disappears from existence, 

 is independent of that class altogether, and vice versa. Herein 

 we see another example of the interpretation of formal results, 

 immediately deduced from the mathematical laws of thought, into 

 general axioms of philosophy. 



