David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Synthese 186 (1):55-102 (2012)
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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References found in this work BETA
Charles Parsons (2008). Mathematical Thought and its Objects. Cambridge University Press.
Michael Friedman (2012). Kant on Geometry and Spatial Intuition. Synthese 186 (1):231-255.
Jeremy Avigad, Edward Dean & John Mumma (2009). A Formal System for Euclid's Elements. Review of Symbolic Logic 2 (4):700--768.
Lisa Shabel (2003). Mathematics in Kant's Critical Philosophy: Reflections on Mathematical Practice. Routledge.
Charles Chihara (2004). A Structural Account of Mathematics. Clarendon Press.
Citations of this work BETA
Dominique Tournès (2012). Diagrams in the Theory of Differential Equations (Eighteenth to Nineteenth Centuries). Synthese 186 (1):257-288.
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