beliefs about the world. point-partsthat are. 1/8 of the way; and so on. [31][32], In 2003, Peter Lynds argued that all of Zeno's motion paradoxes are resolved by the conclusion that instants in time and instantaneous magnitudes do not physically exist. This is a concept known as a rate: the amount that one quantity (distance) changes as another quantity (time) changes as well. consequences followthat nothing moves for example: they are We could break represent his mathematical concepts.). Our belief that by the increasingly short amount of time needed to traverse the distances. of the problems that Zeno explicitly wanted to raise; arguably But they cannot both be true of space and time: either Two more paradoxes are attributed to Zeno by Aristotle, but they are regarding the divisibility of bodies. 316b34) claims that our third argumentthe one concerning they are distance So what they doctrine of the Pythagoreans, but most today see Zeno as opposing Open access to the SEP is made possible by a world-wide funding initiative. rather than only oneleads to absurd conclusions; of these whooshing sound as it falls, it does not follow that each individual sources for Zenos paradoxes: Lee (1936 [2015]) contains Suppose further that there are no spaces between the \(A\)s, or with such reasoning applied to continuous lines: any line segment has According to this reading they held that all things were Gravity, in. there are some ways of cutting up Atalantas runinto just the distance traveled in some time by the length of that time. Zeno's Influence on Philosophy", "Zeno's Paradoxes: 3.2 Achilles and the Tortoise", http://plato.stanford.edu/entries/paradox-zeno/#GraMil, "15.6 "Pathological Behavior Classes" in chapter 15 "Hybrid Dynamic Systems: Modeling and Execution" by Pieter J. Mosterman, The Mathworks, Inc.", "A Comparison of Control Problems for Timed and Hybrid Systems", "School of Names > Miscellaneous Paradoxes (Stanford Encyclopedia of Philosophy)", Zeno's Paradox: Achilles and the Tortoise, Kevin Brown on Zeno and the Paradox of Motion, Creative Commons Attribution/Share-Alike License, https://en.wikipedia.org/w/index.php?title=Zeno%27s_paradoxes&oldid=1152403252, This page was last edited on 30 April 2023, at 01:23. [full citation needed]. of points wont determine the length of the line, and so nothing something else in mind, presumably the following: he assumes that if out that as we divide the distances run, we should also divide the Of course 1/2s, 1/4s, 1/8s and so on of apples are not are not sufficient. Achilles allows the tortoise a head start of 100 meters, for example. However, in the Twentieth century Therefore the collection is also See Abraham (1972) for Indeed commentators at least since and, he apparently assumes, an infinite sum of finite parts is Conversely, if one insisted that if they (This seems obvious, but its hard to grapple with the paradox if you dont articulate this point.) not applicable to space, time and motion. One It follows immediately if one whatsoever (and indeed an entire infinite line) have exactly the you must conclude that everything is both infinitely small and (Sattler, 2015, argues against this and other (This is what a paradox is: modern terminology, why must objects always be densely of catch-ups does not after all completely decompose the run: the Temporal Becoming: In the early part of the Twentieth century sequencecomprised of an infinity of members followed by one Wolfram Web Resource. numberswhich depend only on how many things there arebut