it.j FORM AND BECOMING 311 



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 sup- 

 posed 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 movement 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, we do not consider the sophism of Zeno refuted by the fact 

 that the geometrical progression a (l4~-^- + ^ 2 "T"»3" r " •••» etc -) — m 

 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 1. On this point we may refer to the arguments of 

 P. Evellin, which we regard as conclusive (see Evellin, Infini et quanlitS, 

 Paris, 1880, pp. 63-97; cf. Revue philosophique, vol. xi., 1881, pp. 564- 



