Synthese

, Volume 186, Issue 1, pp 55–102

The twofold role of diagrams in Euclid’s plane geometry

Article

Abstract

Proposition I.1 is, by far, the most popular example used to justify the thesis that many of Euclid’s geometric arguments are diagram-based. Many scholars have recently articulated this thesis in different ways and argued for it. My purpose is to reformulate it in a quite general way, by describing what I take to be the twofold role that diagrams play in Euclid’s plane geometry (EPG). Euclid’s arguments are object-dependent. They are about geometric objects. Hence, they cannot be diagram-based unless diagrams are supposed to have an appropriate relation with these objects. I take this relation to be a quite peculiar sort of representation. Its peculiarity depends on the two following claims that I shall argue for: (i) The identity conditions of EPG objects are provided by the identity conditions of the diagrams that represent them; (ii) EPG objects inherit some properties and relations from these diagrams.

Keywords

Euclid Plane geometry Diagrams 

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© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.CNRS, IHPST (UMR 8590 of CNRS, University of Paris 1, and ENS Paris)ParisFrance

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