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ArisKatsaris comments on Living Metaphorically - Less Wrong
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Yes, you're right. You can defeat the paradox on mathematical grounds, without having to appeal to physics. But Zeno could have defeated it on his own without using any math, simply by realizing that his metaphor was not paying rent.
Zeno's argument was that movement was an illusion, that all was one -- that was the point of his paradoxes. The fact that things seemed to move, in combination with his paradox, proved (to him) that reality was an illusion.