The One and the Dyad: the Foundations of Ancient Mathematics. What Exists Instead of Infinite Space in Euclid’s Elements?

Zbigniew Król

This paper contains a new interpretation of Euclidean geometry. It is argued that ancient Euclidean geometry was created in a quite different intuitive model (or frame), without infinite space, infinite lines and surfaces. This ancient intuitive model of Euclidean geometry is reconstructed in the connection with Plato’s unwritten doctrine. The model creates a kind of “hermeneutical horizon” determining the explicit content and mathematical methods used. In the first section of the paper, it is argued that there are no actually infinite concepts in Euclid’s Elements. In the second section, it is argued that ancient mathematics is based on Plato’s highest principles: the One and the Dyad and the role of agrapha dogmata is unveiled.

Krol-59

Słowa kluczowe: Euclidean geometry · Euclid’s Elements · ancient mathematics · Plato’s unwritten doctrine · philosophical hermeneutics · history of science and mathematics · philosophy of mathematics · philosophy of science

Zbigniew Król — Profesor nadzwyczajny w Zakładzie Filozofii Nauki, Socjologii i Podstaw Techniki, Wydział Administracji i Nauk Społecznych, (Politechnika Warszawska) oraz w Zespole Filozofii i Hermeneutyki Matematyki oraz w Zespole Badań nad Filozofią Antyczną i Historią Ontologii w Instytucie Filozofii i Socjologii PAN (Warszawa). Obszar jego badań obejmuje m.in. filozofię matematyki i nauki, historię matematyki, filozofii i nauki, logikę, matematykę, ontologię i teorię poznania.

Zbigniew Król – Associated Professor at the department of the Philosophy of Science, Sociology and Foundations of Technology, Faculty of Administration and Social Science, Warsaw University of Technology, and at the two departments at the Institute of Philosophy and Sociology of the Polish Academy of Sciences (Warsaw, Poland): of the Philosophy and Hermeneutics of Mathematics and of the Inquiries on Ancient Philosophy and the History of Ontology. His research concerns the philosophy of mathematics and science, history of mathematics and science, logic, mathematics, ontology and epistemology.

Zbigniew Król – Associated Professor at the department of the Philosophy of Science, Sociology and Foundations of Technology, Faculty of Administration and Social Science, Warsaw University of Technology, and at the two departments at the Institute of Philosophy and Sociology of the Polish Academy of Sciences (Warsaw, Poland): of the Philosophy and Hermeneutics of Mathematics and of the Inquiries on Ancient Philosophy and the History of Ontology. His research concerns the philosophy of mathematics and science, history of mathematics and science, logic, mathematics, ontology and epistemology.

Pismo założone przez Leszka Kołakowskiego, Bronisława Baczkę i Jana Garewicza ukazuje się nieprzerwanie od 1957 r.

Instytut Filozofii i Socjologii PAN Archiwum Warszawskiej Szkoły Historii Idei Bibliografia Filozofii Polskiej The Interlocutor Wydawnictwo IFiS PAN Polskie Towarzystwo Filozoficzne
© Archiwum Historii Filozofii i Myśli Społecznej 1957-2010.