Aleksandar Draskovic
University of Belgrad
The aim of this talk is to elucidate Galileo’s solution to Aristotle’s paradox of the wheel. Specifically, Galileo, through a specific understanding of the circle (which is supposed to represent a wheel), offered a solution to Aristotle’s paradox according to which two concentric circles, where one is inscribed within the other (thus smaller than it), have equal circumference. The specificity of Galileo’s solution lies in his consideration of the circle as a polygon with actually infinitely many angles. In the first part of the presentation, I will explain Aristotle’s paradox of the wheel, as well as the solution Galileo proposed. The second part will address hypothetical machines performing so-called “super-tasks”: I will clarify the concept of super-tasks and analyze several well-known examples of machines envisioned to perform them. In the third part of the talk, I will try to demonstrate that Galileo’s solution to the paradox is itself paradoxical, or more precisely, I will argue that if the circle is conceived as a polygon with infinitely many angles, a problem akin to Zeno’s “Dichotomy” paradox arises. Similarly, I will attempt to show that Galileo’s wheel is actually an example of a machine intended to perform a super-task. The final part of the presentation will be devoted to considering Galileo’s solution from a broader perspective – from the angle of the debate between finitists and infinitists. My ultimate goal will be to demonstrate how Galileo’s infinitistic solution to the paradox can pinpoint a serious problem for the infinitist position.
Chair: Annica Vieser
Time: September 11th, 15:30 – 16:00
Location: HS E.002
SOPhiA 2026 