190 CLARKE AND SPINOZA. [CHAP. XIII. 



It must be understood, that by the expression, Let x = 

 " Something is," is meant no more than that x is the repre- 

 sentative symbol of that proposition (XI. 7), the equations 

 x = 1, x = 0, respectively declaring its truth and its falsehood. 

 The equations of the premises are : 



1st. x = 1; 



2nd. x = v{y(\-z) + z(\-y)}i 



3rd. x = v{p(\-q) + q(\-p)}., 



4th. p = vy; 



5th. q = v(\-z); 



and on eliminating the several indefinite symbols v, we have 



1-* = 0; (1) 



r)} = 0; (2) 



y)}-0; (3) 



P0-y)-0; (4) 



qz = . (5) 



6. First, I shall examine whether any conclusions are dedu- 

 cible from the above, concerning the truth or falsity of the 

 single propositions represented by the symbols y, z, p, q, viz., of 

 the propositions, " Something always was ;" " The things which 

 now are have risen from nothing;" " The something which is 

 exists by the necessity of its own nature ;" " The something 

 which is exists by the will of another being." 



For this purpose we must separately eliminate all the symbols 

 but <y, all these but z, &c. The resulting equation will deter- 

 mine whether any such separate relations exist. 



To eliminate x from (1), (2), and (3), it is only necessary to 

 substitute in (2) and (3) the value of # derived from (1). We 

 find as the results, 



yz + (1 - y) (1 - z) = 0. (6) 



W + 0-XK1 -<?) = (7) 



To eliminate p we have from (4) and (7), by addition, 



j>(i-y)+^ + (i-/00-y) = o; ( 8 ) 



whence we find, 



(i-y)(i-y)-o. (9) 



