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Document Details : Title: Achilles and the Tortoise 2500 Years after Zeno Author(s): THEUNISSEN, Theo , OUD, Johan H.L. Journal: Logique et Analyse Volume: 255 Date: 2021 Pages: 245-265 DOI: 10.2143/LEA.255.0.3290189 Abstract : After a short introduction to the well-known paradox of Achilles and the tortoise, originating from the 5th century B.C. and attributed by both Plato and Aristotle to Zeno of Elea, we present an overview of important solutions and discussion themes of the paradox, using only basic mathematics. In addition to the limit solution, based on Cauchy’s limit concept, a simpler but less well-known geometric solution is provided. This yields not only the exact distance but also the exact amount of time that Achilles needs to pass the tortoise. Subsequently, we discuss the philosophical background of the paradox. In particular, what Zeno wanted to prove with the paradox and how Aristotle in his criticism foreshadowed both the limit and the geometric solution. Next, the paradox is placed in the perspective of modern quantum theory. This leads to the replacement of classic continuous spacetime by ‘granular’ spacetime and to a new discrete solution of the paradox in terms of granular spacetime. Finally, the problem of supertasks in addition to other topics related to the paradox are dealt with. |
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