CHAP. XIV.] EXAMPLE OF ANALYSIS. 219 



CHAPTER XIV. 



EXAMPLE OF THE ANALYSIS OF A SYSTEM OF EQUATIONS BY THE 

 METHOD OF REDUCTION TO A SINGLE EQUIVALENT EQUATION 

 V= 0, WHEREIN V SATISFIES THE CONDITION V (1 - V) = 0. 



1 T ET us take the remarkable system of premises employed 

 -*^ in the previous Chapter, to prove that " Matter is not a 

 necessary being ;" and suppressing the 6th premiss, viz., Motion 

 exists, examine some of the consequences which flow from the 

 remaining premises. This is in reality to accept as true Dr. 

 Clarke's hypothetical principles ; but to suppose ourselves igno- 

 norant of the fact of the existence of motion. Instances may 

 occur in which such a selection of a portion of the premises of 

 an argument may lead to interesting consequences, though it is 

 with other views that the present example has been resumed. The 

 premises actually employed will be 



1 . If matter is a necessary being, either the property of gravi- 

 tation is necessarily present, or it is necessarily absent. 



2. If gravitation is necessarily absent, and the world is not 

 subject to any presiding intelligence, motion does not exist. 



3. If gravitation is necessarily present, a vacuum is necessary. 



4. If a vacuum is necessary, matter is not a necessary being. 



5. If matter is a necessary being, the world is not subject 

 to a presiding intelligence. 



If, as before, we represent the elementary propositions by the 

 following notation, viz. : 



x = Matter is a necessary being. 



y = Gravitation is necessarily present. 



iv = Motion exists. 



t = Gravitation is necessarily absent. 



z = The world is merely material, and not subject to a 



presiding intelligence. 

 v = A vacuum is necessary. 



