Toth e il pensiero trans-euclideo in Aristotele (Toth and trans-euclidean thought in Aristotle)
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 pro...
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| Format: | Article |
| Language: | English |
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Accademia Piceno Aprutina dei Velati
2025-06-01
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| Series: | Science & Philosophy |
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| Online Access: | http://eiris.it/ojs/index.php/scienceandphilosophy/article/view/1673 |
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| Summary: | 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.
Sunto
Per cica 2000 anni il postulato delle parallele, enunciato da Euclide, è stato fucina di dubbi (postulato o teorema?) chiariti con la nascita dela Geometria Non-Euclidea.
Alla luce d queste nuove conoscenze di geometria, Toth, grecista e storico della matematica, in alcuni scritti di Aristotele intravede proprietà tipiche di geometria non euclidea. Lo Stagirita, per descrivere con rigore il libero arbitrio, usa esempi geometrici, in parte prelevati dalla geometria all’epoca nota, in parte ponendo la sua negazione, ovvero mostra, involontariamente, i presupposti della geometria, oggi definita non euclidea, senza approfondire la possibile coesistenza logica di affermazioni antitetiche.
Questa breve nota è un invito alla lettura d’Aristotele in chiave re-interpretativa.
Parole chiave: Toth, Aristotele, libero arbitrio, geometria non-euclidea. |
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| ISSN: | 2282-7757 2282-7765 |