Visual imagery and geometric enthymeme: The example of euclid I.

Behavioral and Brain Sciences 25 (2):202-203 (2002)
  Copy   BIBTEX

Abstract

Students of geometry do not prove Euclid's first theorem by examining an accompanying diagram, or by visualizing the construction of a figure. The original proof of Euclid's first theorem is incomplete, and this gap in logic is undetected by visual imagination. While cognition involves truth values, vision does not: the notions of inference and proof are foreign to vision.

Categories

Keywords

Reprint years

DOI

10.1017/s0140525x02420043

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 93,867

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

My notes

Similar books and articles

Herbrand’s theorem and non-euclidean geometry.Michael Beeson, Pierre Boutry & Julien Narboux - 2015 - Bulletin of Symbolic Logic 21 (2):111-122.
Enthymemathical proofs and canonical proofs in Euclid's plane geometry.Abel Lassalle & Marco Panza - 2018 - In Claudio Bartocci (ed.), The Philosophers and Mathematics. Springer Verlag. pp. 127-144.
Greek Mathematics to the Time of Euclid.Ian Mueller - 2018 - In Sean D. Kirkland & Eric Sanday (eds.), A Companion to Ancient Philosophy. Evanston, Illinois: Northwestern University Press. pp. 686–718.
To Prove the Evident: On the Inferential Role of Euclidean Diagrams.Davide Crippa - 2009 - Teorie Vědy / Theory of Science 31 (2):101-112.
Proofs, pictures, and Euclid.John Mumma - 2010 - Synthese 175 (2):255 - 287.
The twofold role of diagrams in Euclid’s plane geometry.Marco Panza - 2012 - Synthese 186 (1):55-102.
Nathaniel Miller. Euclid and his twentieth century rivals: Diagrams in the logic of euclidean geometry. Csli studies in the theory and applications of diagrams.John Mumma - 2008 - Philosophia Mathematica 16 (2):256-264.
Geometry and Spatial Intuition: A Genetic Approach.Rene Jagnow - 2003 - Dissertation, Mcgill University (Canada)
The Eu Approach to Formalizing Euclid: A Response to “On the Inconsistency of Mumma’s Eu”.John Mumma - 2019 - Notre Dame Journal of Formal Logic 60 (3):457-480.
“That small and unsensible shape”: Visual Representations of the Euclidean Point in Sixteenth-Century Print.Michael Jeremy Barany - 2012 - Spontaneous Generations 6 (1):148-159.

Analytics

Added to PP
2009-01-28

Downloads
65 (#243,015)

6 months
4 (#1,004,663)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

No citations found.

Add more citations

References found in this work

No references found.

Add more references