Zeno - Zenos Paradox of the Race Course 1. The Paradox Zeno...

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Zeno’s Paradox of the Race Course 1. The Paradox Zeno argues that it is impossible for a runner to traverse a race course. His reason is that “motion is impossible, because an object in motion must reach the half-way point before it gets to the end” (Aristotle, Physics 239b11-13). Why is this a problem? Because the same argument can be made about half of the race course: it can be divided in half in the same way that the entire race course can be divided in half. And so can the half of the half of the half, and so on, ad infinitum . So a crucial assumption that Zeno makes is that of infinite divisibility : the distance from the starting point ( S ) to the goal ( G ) can be divided into an infinite number of parts. 2. Progressive vs. Regressive versions How did Zeno mean to divide the race course? That is, which half of the race course Zeno mean to be dividing in half? Was he saying (a) that before you reach G , you must reach the point halfway from the halfway point to G ? This is the progressive version of the argument: the subdivisions are made on the right-hand side, the goal side, of the race- course. Or was he saying (b) that before you reach the halfway point, you must reach the point halfway from S to the halfway point? This is the regressive version of the argument: the subdivisions are made on the left-hand side, the starting point side, of the race-course. If he meant (a), the progressive version, then he was arguing that the runner could not
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Zeno - Zenos Paradox of the Race Course 1. The Paradox Zeno...

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