328 CREATIVE EVOLUTION 



all movement is articulated inwardly. It is either an 

 indivisible bound (which may occupy, nevertheless, a 

 very long duration) or a series of indivisible bounds. 

 Take the articulations of this movement into account, 

 or give up speculating on its nature. 



When Achilles pursues the tortoise, each of his steps 

 must be treated as indivisible, and so must each step of 

 the tortoise. After a certain number of steps, Achilles 

 will have overtaken the tortoise. There is nothing 

 more simple. If you insist on dividing the two motions 

 further, distinguish both on the one side and on the 

 other, in the course of Achilles and in that of the 

 tortoise, the sub-multiples of the steps of each of them ; 

 but respect the natural articulations of the two courses. 

 As long as you respect them, no difficulty will arise, 

 because you will follow the indications of experience. 

 But Zeno s device is to reconstruct the movement of 

 Achilles according to a law arbitrarily chosen. Achilles 

 with a first step is supposed to arrive at the point where 

 the tortoise was, with a second step at the point which 

 it has moved to while he was making the first, and so 

 on. In this case, Achilles would always have a new 

 step to take. But obviously, to overtake the tortoise, 

 he goes about it in quite another way. The move 

 ment considered by Zeno would only be the equivalent 

 of the movement of Achilles if we could treat the 

 movement as we treat the interval passed through, 

 decomposable and recomposable at will. Once you sub 

 scribe to this first absurdity, all the others follow. 1 



1 That is, \ve do not consider the sophism of Zeno refuted by the fact 

 that the geometrical progression a(\-\ l~^&amp;gt; + ~i)+ etc.) in which a 



designates the initial distance between Achilles and the tortoise, and n 

 the relation of their respective velocities has a finite sum if n is greater 

 than i. On this point we may refer to the arguments of F. Evellin, which 



