Gli argomenti di Zenone contro la possibilità del movimento e la loro rivalutazione ad opera di matematici e fisici

Abstract

The order in which Aristotle presents in Physics the four famous Zeno’s paradoxes on the impossibility of movement is implicitly based on the intersection between two different conceptual pairs: 1) direct demonstration or reductio ad absurdum; 2) infinite divisibility or discrete space and discrete time. “The Dichotomy” is a direct demonstration that presupposes (at least) the infinite divisibility of space. “Achilles (and the Tortoise)” starts from the same assumption, but it is a reductio ad absurdum. “The Arrow” goes back to being a direct demonstration but presupposes discrete space and discrete time unlike “The Dichotomy”. “The Stadium” starts from the same assumption as “The Arrow” but it is a reductio ad absurdum as “Achilles (and the Tortoise)”. This quadripartite scheme of Zeno’s paradoxes helps to understand that considering Zeno a precursor of quantum mechanics does not find any solid foundation in the Aristotelian text and highlights that the solution given by Aristotle’s to Zeno’s paradoxes, although less rigorous than the solution given to them by B. Russell and other mathematicians, is not entirely different from their solution, for Aristotle, too, realized that the result of a sum having an infinite number of addends can be a finite number (today we would say a real number).