CHAP. XIII.] CLARKE AND SPINOZA. 197 



tz = q(\ - iv). 

 y = qv. 

 v = q(\ - x). 

 x = qz. 

 w= 1. 



From which, if we eliminate the symbols ^, we have the follow- 

 ing system, viz. : 



*fo*+0-y)0-0}-- 0) 



tzw = 0. (2) 



y(l-tO = o. (3) 



vx = 0. (4) 



*(l-z) = 0. (5) 



1 - MV= 0. (6) 



Now if from these equations we eliminate w, v, z, y^ and t, we 



obtain the equation 



x = 0, 



which expresses the proposition, Matter is not a necessary being. 

 This is Dr. Clarke's conclusion. If we endeavour to eliminate 

 any other set of five symbols (except the set v, z 9 y, t, and x 9 

 which would give w = 1), we obtain a result of the form = 0. 

 It hence appears that there are no other conclusions expressive of 

 the absolute truth or falsehood of any of the elementary propositions 

 designated by single symbols. 



Of conclusions expressed by equations involving two symbols, 

 there exists but the following, viz. : If the world is merely mate- 

 rial, and not subject to a presiding Intelligence, gravitation is not 

 necessarily absent. This conclusion is expressed by the equation 



tz = 0, whence z = q ( 1 - t). 



If in the above analysis we suppress the concluding premiss, ex- 

 pressing the fact of the existence of motion, and leave the hypo- 

 thetical principles which are embodied in the remaining premises 

 untouched, some remarkable conclusions follow. To these I 

 shall direct attention in the following chapter. 



10. Of the remainder of Dr. Clarke's argument I shall briefly 

 state the substance and connexion, dwelling only on certain por- 



