Toth e il pensiero trans-euclideo in Aristotele (Toth and trans-euclidean thought in Aristotle) - Nicola Umberto Animobono (Science & Philosophy, 2025)
Abstract For about 2000 years the postulate of parallels, enunciated by Euclid, was a source of doubts (postulate or theorem?) clarified with the birth of non-Euclidean geometry. In the light of this new knowledge of geometry, Toth, a Greek scholar and historian of mathematics, glimpses typical properties of geometry today defined as non-Euclidean in some writings of Aristotle. To clearly highlight free will, the Stagirite uses geometric examples partly taken from the geometry known at the time, partly uses its negation, that is, he shows, involuntarily, the presuppositions of the geometry that we know today as non-Euclidean, without delving into the possible logical coexistence of antithetical statements. This short note is an invitation to read Aristotle in a re-interpretative way. Keywords: Toth, Aristotle, free will, non-euclidean geometry.