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Mathematical Philosopy: Zeno’s Paradoxes In the fifth century B.C.E., Zeno of Elea offered arguments that led to conclusions contradicting what we all know from our physical experience–that runners run, that arrows fly, and that there are many different things in the world. The arguments were paradoxes for the ancient Greek philosophers.

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Zeno of Elea shows Youths the Doors to Truth and False (Veritas et Falsitas) by Pellegrino Tibaldi. Zeno of Elea (c. 490 – c. 430 BC) was a pre-Socratic Greek philosopher of Magna Graecia and a member of the Eleatic School founded by Parmenides. Aristotle called him the inventor of the dialectic. He is best known for his paradoxes.

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Zeno of Elea was a pre-socratic philosopher. Zeno generated the argument that motion is impossible, claiming that to get from point A to point B, we need to reach the halfway mark and then traverse to the median of the remaining distance. Mathematically, the remaining distance can be divided into 1/2, then 1/4, then 1/8, then 1/16 and so on, ad infinitum. Many debates have been generated regarding this argument and that is why it is called a paradox.

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Zeno’s Paradoxes | Internet Encyclopedia of Philosophy