The Twofold Role of Diagrams in Euclid’s Plane Geometry
Document Type
Article
Publication Date
4-13-2012
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.
Recommended Citation
Panza, M. The twofold role of diagrams in Euclid’s plane geometry. Synthese 186, 55–102 (2012). https://doi.org/10.1007/s11229-012-0074-2
Comments
This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Synthese, volume 186, in 2012 following peer review. The final publication may differ and is available at Springer via https://doi.org/10.1007/s11229-012-0074-2.