Question: Explain Zeno’s Racetrack Paradox for the conclusion that motion is impossible.

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Explain Zeno’s Racetrack Paradox for the conclusion that motion is impossible.

Zeno’s Racetrack Paradox is one of the most famous paradoxes in philosophy. It goes like this: suppose a tortoise and Achilles are racing. The tortoise has a head start, so Achilles can never catch up to the tortoise, right? Wrong! Here’s why: First, let’s suppose that Achilles runs at twice the speed of the tortoise. So when Achilles reaches the point where the tortoise started, the tortoise will have only moved half as far as Achilles. But then when Achilles catches up to that point, the tortoise will have moved another quarter of the distance… and so on. In other words, Achilles will always be catching up to the tortoise, but he can never quite catch up. The paradox is that if motion is possible, then Achilles should be able to catch up to the tortoise; but if motion is not possible, then Achilles can never even start running! One way to try to resolve the paradox is to say that when Achilles reaches the point where the tortoise started, the tortoise will have moved half as far as Achilles—but that’s only because we’re assuming that Achilles is moving at twice the speed of the tortoise. In reality, Achilles is moving at his own speed and the tortoise is moving at its own speed, so they will both just keep moving at their own speeds forever and never reach each other. However, this solution doesn’t really work, because it implies that motion is an illusion—that Achilles and the tortoise are just sitting still and never actually moving anywhere. But that doesn’t make much sense, either. So what’s the resolution to Zeno’s Racetrack Paradox? Unfortunately, there isn’t one that everyone agrees on. Some people say that the paradox can be resolved by understanding that space and time are continuous, rather than discrete (like a racetrack). Others say that the paradox doesn’t really show anything about motion; it’s just a confusing way of looking at things. Whatever the resolution to the paradox may be,....