How Achilles and Hector Missed Each Other: A Difficulty in the Theory of Motion That Distinguish the Passage of an Open Space Interval from the Passage of its Closure
DOI:
https://doi.org/10.47850/RL.2022.3.4.5-27Keywords:
the Oncoming Motions Paradox, “at-at theory of motion”, B. Russell, P. Benacerraf, continuum, open intervals, Zeno’s Paradoxes, the Arrow Paradox, the Dichotomy ParadoxAbstract
In this paper, I construct a new aporia against movement. First, I analyze the widely accepted “at‑at theory of motion” that was proposed by B. Russell. I show that an attempt to define on the basis of this theory a wide class of species of motion (including uniform motion) fails due to the fact that a moving object, after the expiration of open time intervals, can be at any point in space, and therefore can make “leaps”. Next, I propose an improved version of the “at-at theory of motion”, according to which the spatial interval passed by a moving object is a function of the time interval during which the object moved. But it turns out that such an understanding of movement leads to the Oncoming Motions Paradox: moving from two opposite ends of the interval towards each other, Achilles and Hector can successfully go through this entire interval, having visited every point of it, but not having met each other at any point of this interval. In the last part of the paper, I show that attempts to define motion through infinitesimal analysis either offer no less paradoxical solutions than Zeno’s paradoxes themselves, or these attempts are not immune to the occurrence of the Oncoming Motions Paradox.
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