"The Twofold Role of Diagrams in Euclid’s Plane Geometry" by Marco Panza
 

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.

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.

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