The One and the Dyad: the Foundations of Ancient Mathematics. What Exists Instead of Infinite Space in Euclid’s Elements?
The One and the Dyad: the Foundations of Ancient Mathematics. What Exists Instead of Infinite Space in Euclid’s Elements?
Author(s): Zbigniew KrólSubject(s): Ancient World, Philosophy of Science
Published by: Instytut Filozofii i Socjologii Polskiej Akademii Nauk
Keywords: Euclidean geometry; Euclid’s Elements; ancient mathematics; Plato’s unwritten doctrine; philosophical hermeneutics; history of science and mathematics; philosophy of mathematics;
Summary/Abstract: 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 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.
Journal: Archiwum Historii Filozofii i Myśli Społecznej
- Issue Year: 59/2014
- Issue No: 59
- Page Range: 55-82
- Page Count: 28
- Language: English
