202 CLARKE AND SPINOZA. [CHAP. XIII. 



2. If motion has existed from eternity, either it has been 

 eternally caused by some eternal intelligent being, or it is self- 

 existent, or it must have existed by endless successive communi- 

 cation. 



3. If motion has been eternally caused by an eternal intelli- 

 gent being, the first cause is an intelligent being. 



4. If it is self-existent, matter is at rest and not at rest. 



5. That motion has existed by endless successive communi- 

 cation, and that at the same time it is not self-existent, and has 

 not been eternally caused by some eternal intelligent being, is 

 false. 



To express these propositions, let us assume 



x = Motion began in time (and therefore) 

 1 - x Motion has existed from eternity. 

 y = The first cause is an intelligent being. 

 p = Motion has been eternally caused by some eternal intelli- 



gent being. 



q = Motion is self-existent. 



r = Motion has existed by endless successive communication. 

 s = Matter is at rest. 



The equations of the premises then are 



q = vs (1 - s) = 0. 



'0 -?) 0-p)-o. 



Since, by the fourth equation, q = 0, we obtain, on substituting 

 for q its value in the remaining equations, the system 



x = vy, 1 - x = v {p(l - r) + r (1 -/?)), 

 p = vij, r(l-p) = Q, 



from which eliminating the indefinite symbols v, we have the 



final reduced system, 



*(l-y)-0, (l) 



(l-)(pr+(l-.p)0-r)}-0, (*> 



/,(l-y) = 0. (3) 



r(l-p)-0. (4) 



