CHAP. XIII.] CLARKE AND SPINOZA. 207 



all the predicates are particular, and the conjunctions either, or, 

 as absolutely disjunctive, we have the following equations : 



(l -t). 



t = vw. 

 From which, if we separately eliminate the symbol v, we have 



xt = 0, (2) 



p)}t = Q ) (4) 



^ f(l-t0)=.0. (5) 



Let it be required, first, to find what conclusion the premises 

 warrant us in forming respecting absolute evils, as concerns their 

 dependence upon moral evils, and the consequences of moral 

 evils. 



For this purpose we must determine t in terms of z and r. 

 The symbols w, x 9 y, p, q must therefore be eliminated. The 

 process is easy, as any set of the equations is reducible to a single 

 equation by addition. 



Eliminating w from (1) and (5), we have 



The elimination of/? from (3) and (4) gives 



yqr + yqt + yt(l-r)(\-q) = Q. (7) 



The elimination of q from this gives 



yt(l - r) - 0. (8) 



The elimination of x between (2) and (6) gives 



t{yz+(l-y)(l-z))-Q, (9) 



The elimination of y from (8) and (9) gives 



t(l - z) (1 - r) = 0. 

 This is the only relation existing between the elements t, z, and r. 



