2 04 CLARKE AND SPINOZA. [CHAP. XIII. 



gives the conclusion, If motion has existed from eternity, it has not 

 existed by an endless successive communication. 



Solved under the form 



r = vx, 



the above equation leads to the equivalent conclusion, If motion 

 exists by an endless successive communication, it began in time. 



13. Now it will appear to the reader that the first and last of 

 the above four conclusions are inconsistent with each other. The 

 two consequences drawn from the hypothesis that motion exists 

 by an endless successive communication, viz., 1st, that it has 

 been eternally caused by an eternal intelligent being ; 2ndly, that 

 it began in time, are plainly at variance. Nevertheless, they are 

 both rigorous deductions from the original premises. The oppo- 

 sition between them is not of a logical, but of what is technically 

 termed a material, character. This opposition might, however, 

 have been formally stated in the premises. We might have 

 added to them a formal proposition, asserting that " whatever is 

 eternally caused by an eternal intelligent being, does not begin in 

 time." Had this been done, no such opposition as now appears 

 in our conclusions could have presented itself. Formal logic 

 can only take account of relations which are formally expressed 

 (VI. 16) ; and it may thus, in particular instances, become ne- 

 cessary to express, in a formal manner, some connexion among 

 the premises which, without actual statement, is involved in the 

 very meaning of the language employed. 



To illustrate what has been said, let us add to the equations 

 (2) and (4) the equation 



px = 0, 



which expresses the condition above adverted to. We have 



(l-x) ipr + (l-p)(l-r)} + r (1 - p) + px = 0. (8) 

 Eliminating p from this, we find simply 



r = 0, 



which expresses the proposition, Motion does not exist by an end- 

 less successive communication. If now we substitute for r its value 

 in (8), we have 



(1 - x) (1 - p) + px = 0, or, 1 - x = /?; 



