Diagrammatizing Mathematics: Some Remarks on a Revolutionary Aspect of Ancient Greek Mathematics

Abstract

This paper endeavors to put forward a new interpretation of the ancient mathematical diagram by trying to solve the riddle from the viewpoint of semiotic model theory: on the basis of understanding diagrams as signs that represent their objects as iconic relational ‘models’, it is argued that it is possible to adequately determine, first, what diagrams “are” and, second, which function they fulfill in the process of ancient mathematical reasoning.

In this vein, this paper will: 1) make some remarks on why diagrams have been regarded as problematic; 2) interpret ancient mathematical diagrams as iconic signs as defined in the framework of Charles S. Peirce’s sign theory; 3) discuss how diagrams relate to the textual part of ancient mathematical propositions; and 4) make some suggestions as to how ancient Greek mathematics had distinctive features that made it, in the sense of Thomas Kuhn’s theory of scientific revolutions, incommensurably different from all the previous ancient mathematical approaches (including early Greek mathematics) as well as from modern mathematics.