CHAP. XIII.] CLARKE AND SPINOZA. 199 



We have on expressing the above, and eliminating the indefinite 



symbols, 



xy(l-z) = 0. (1) 



x(l - w) = 0. (2) 



w(l-t) = 0. (3) 



tz = 0. (4) 



Eliminating in succession t, w, and z, we get 



... 



the interpretation of which is, Whatever is self-existent is in- 

 finite. 



In Prop. vn. it is argued that the self-existent being must of 

 necessity be One. The' order of the proof is, that the self-exis- 

 tent being is "necessarily existent," that "necessity absolute in 

 itself is simple and uniform, and without any possible difference 

 or variety," that all "variety or difference of existence" implies 

 dependence ; and hence that " whatever exists necessarily is the 

 one simple essence of the self-existent being." 



The conclusion is also made to flow from the following pre- 

 mises : 



1 . If there are two or more necessary and independent beings, 

 either of them may be supposed to exist alone. 



2. If either may be supposed to exist alone, it is not a contra- 

 diction to suppose the other not to exist. 



3. If it is not a contradiction to suppose this, there are not 

 two necessary and independent beings. 



Let us represent the elementary propositions as follows : 

 x = there exist two necessary independent beings. 

 y = either may be supposed to exist alone. 

 z - it is not a contradiction to suppose the other not to exist. 



We have then, on proceeding as before, 



*0-y)-o. (i) 



y(i-*)-o. (2) 



zx = 0. (3) 



