A SOUNDNESS ANALYSIS OF ZENO’S OF ELEA DICHOTOMY

Abstract

We are studying three basic interpretations of the Dichotomy aporia, in which Zeno tries to prove the impossibility of movement. In all these interpretations, the key assumption is the dubious statement about the impossibility of performing an infinite sequence of actions in a finite time. However, we show that in the two interpretations of the Dichotomy it is possible to get rid of the dubious key assumption, replacing it with the seemingly much more reliable assumption that covering the distance is representable as a sequence of displacements. Our approach is based on the thesis proved by P. Benacerraf that completing an infinite sequence of movements in an interpretation of the Dichotomy is not sufficient to arrive to the end of the distance.