CHAP. XIII.] CLARKE AND SPINOZA. 195 



x = Beings which have arisen out of nothing. 



y = Beings which have been produced by an external 



cause. 



z = Beings which are self-existent. 

 w = The unchangeable and independent Being. 



Then we have 



x(l - y) (1 - z) + y (1 - x) (1 - z) + z(\ - x} (1 - y) = 1, (1) 



x = 0, (2) 



w = v(l-y), (3) 



from the last of which eliminating v 9 



wy = 0. (4) 



Whenever, as above, the value of a symbol is given as or 1, it 

 is best eliminated by simple substitution. Thus the elimination 

 of x gives 



y(i-*) + *(i-y)=i; (5) 



or, yz + (l-y)(l-z) = 0. (6) 



Now adding (4) and (6), and eliminating y, we get 

 w(\ -z) = 0, 



/. 10 = VZ\ 



the interpretation of which is, The unchangeable and indepen- 

 dent being is necessarily self-existing. 



Of (5), in its actual form, the interpretation is, Every being 

 has either be en produced by an external cause, or it is self-existent. 



9. In Dr. Samuel Clarke's observations on the above propo- 

 sition occurs a remarkable argument, designed to prove that the 

 material world is not the self-existent being above spoken of. 

 The passage to which I refer is the following : 



" If matter be supposed to exist necessarily, then in that ne- 

 cessary existence there is either included the power of gravitation, 

 or not. If not, then in a world merely material, and in which no 

 intelligent being presides, there never could have been any mo- 

 tion ; because motion, as has been already shown, and is now 

 granted in the question, is not necessary of itself. But if the 



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