CHAP. XIII.] CLARKE AND SPINOZA. 203 



We shall first seek the value of y, the symbol involved in Dr. 

 Clarke's conclusion. First, eliminating x from (1) and (2), we 

 have 



(i-y) If + 0-.p)0 ->)}- o- (5) 



Next, to eliminate r from (4) and (5), we have 



whence 



(l-y)(l-p)-0. (6) 



Lastly, eliminating p from (3) and (6), we have 



which expresses the required conclusion, The first came is an 

 intelligent being. 



Let us now examine what other conclusions are deducible 

 from the premises. 



If we substitute the value just found for y in the equations 

 (1), (2), (3), (4), they are reduced to the following pair of equa- 

 tions, viz., 



(l-*){pr + (l-p)(l-r)}=0, r(l-p) = 0. (7) 

 Eliminating from these equations x, we have 

 r(l -p) = 0, whence r = vp 9 



which expresses the conclusion, If motion has existed by endless 

 successive communication, it has been eternally caused by an eter- 

 nal intelligent being. 



Again eliminating, from the given pair, r, we have 



(l-*)(l-p) = 0, 



or, 1 - x = vp, 



which expresses the conclusion, If motion has existed from eter- 

 nity, it has been eternally caused by some eternal intelligent being. 



Lastly, from the same original pair eliminating p, we get 



(l-a)r=-.0, 

 which, solved in the form 



