196 CLARKE AND SPINOZA. [CHAP. XIII. 



power of gravitation be included in the pretended necessary ex- 

 istence of matter : then, it following necessarily that there must 

 be a vacuum (as the incomparable Sir Isaac Newton has abun- 

 dantly demonstrated that there must, if gravitation be an uni- 

 versal quality or affection of matter), it follows likewise, that 

 matter is not a necessary being. For if a vacuum actually be, 

 then it is plainly more than possible for matter not to be." 

 (pp. 25, 26). 



It will, upon attentive examination, be found that the actual 

 premises involved in the above demonstration are the following : 



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

 vitation is necessarily present, or it is necessarily absent. 



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

 subject to any presiding Intelligence, motion does not exist. 



3rd. If the property of gravitation is necessarily present, the 

 existence of a vacuum is necessary. 



4th. If the existence of a vacuum is necessary, matter is not a 

 necessary being. 



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

 to a presiding Intelligence. 



6th. Motion exists. 



Of the above premises the first four are expressed in the de- 

 monstration ; the fifth is implied in the connexion of its first and 

 second sentences ; and the sixth expresses a fact, which the au- 

 thor does not appear to have thought it necessary to state, but 

 which is obviously a part of the ground of his reasoning. Let us 

 represent the elementary propositions in the following manner : 



Let x = Matter is a necessary being. 



y = Gravitation is necessarily present. 



t = Gravitation is necessarily absent. 



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



any presiding Intelligence. 

 w = Motion exists. 

 v = A vacuum is necessary. 



Then the system of premises will be represented by the following 

 equations, in which q is employed as the symbol of time indefi- 

 nite: 



