ACR paragraph. Alisa Demina

Ancient philosopher Zeno formulated his famous paradoxes to criticize the idea of continuous motion in infinitely divisible space and time. One of them is called “Achilles and the tortoise”. Achilles, who is the fastest runner of antiquity, is racing to catch the tortoise that is slowly crawling away from him. Both are moving along a linear path at constant speeds. In order to catch the tortoise, Achilles will have to reach the place where the tortoise presently is. However, by the time Achilles gets there, the tortoise will have crawled to a new location and so on forever. So he will never catch the tortoise. Zeno claims that if we believe that Achilles succeeds and that motion is possible, then we are victims of illusion. Plenty of philosophers tried to solve this paradox. One of the attempts, called “Standard Solution”, uses calculus based on classical Newtonian mechanics. In general, we should abstract the goals of Achilles to a linear continuum of point places along the tortoise’s path. It is necessary to consider an infinite geometric series (10, 1, 1/10 , 1/100...)  and know that a sum of the infinite series could be a finite digit. So there can be the point of “meeting” of Achilles and tortoise in certain conditions. But a purely mathematical solution is not sufficient: the paradox not only deals with abstract mathematics, but how it correlates with physical reality. In this way we just disregard Zeno’s question about space, is it discrete or continuous? So even today Zeno’s paradoxes are open and unsolved.

Argument	Counterargument	Rebuttal
because of  infinite number of points Achilles must reach where the tortoise has already been, he can never reach the tortoise	we should abstract the goals of Achilles to a linear continuum of point places along the tortoise’s path to consider an infinite geometric series there can be the point of “meeting” of Achilles and tortoise in certain conditions	paradox not only deals with abstract mathematics, but how it correlates with physical reality.

Internet Encyclopedia of Philosophy. Zeno's Paradoxes [http://www.iep.utm.edu/zeno-par/]