If Achilles attempts to throw a javelin at a target, before it reaches the target it has to go half the distance (that makes sense), but before it can go half the distance it has to go half of that distance (once again it makes sense), but before it goes half that distance it has to go half that distance. What this means is that the javelin has to go one half the distance, one fourth the distance, one eighth the distance, one sixteenth the distance, ad infinitum. Now the idea has become absurd because it concludes that the javelin will never leave Achilles' hand. And thus, Zeno is showing that motion is an illusion.
After Zeno presented his ideas, and after realizing the absurdity
of them, an ancient Greek philosopher by the name of Diogenes, made
no attempt to refute Zeno's new theories; instead, he got up and
walked across the room, as if proving that motion exists. But this,
of course, did not solve any of Zeno's paradoxes.
Before solving the two paradoxes in
question it will be shown that convergence on an infinite series,
using Calculus and algebra, will not solve these arguments.
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