The forgotten individual: diagrammatic reasoning in mathematics

Synthese 186 (1):149-168 (2012)
  Copy   BIBTEX

Abstract

Parallelism has been drawn between modes of representation and problem-sloving processes: Diagrams are more useful for brainstorming while symbolic representation is more welcomed in a formal proof. The paper gets to the root of this clear-cut dualistic picture and argues that the strength of diagrammatic reasoning in the brainstorming process does not have to be abandoned at the stage of proof, but instead should be appreciated and could be preserved in mathematical proofs

Other Versions

No versions found

Links

PhilArchive

    This entry is not archived by us. If you are the author and have permission from the publisher, we recommend that you archive it. Many publishers automatically grant permission to authors to archive pre-prints. By uploading a copy of your work, you will enable us to better index it, making it easier to find.

    Upload a copy of this work     Papers currently archived: 101,934

External links

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

Through your library

Similar books and articles

A Diagrammatic Inference System with Euler Circles.Koji Mineshima, Mitsuhiro Okada & Ryo Takemura - 2012 - Journal of Logic, Language and Information 21 (3):365-391.
Diagrams as sketches.Brice Halimi - 2012 - Synthese 186 (1):387-409.
Speedith: A Reasoner for Spider Diagrams.Matej Urbas, Mateja Jamnik & Gem Stapleton - 2015 - Journal of Logic, Language and Information 24 (4):487-540.
Proof: Its Nature and Significance.Michael Detlefsen - 2008 - In Bonnie Gold & Roger A. Simons (eds.), Proof and Other Dilemmas: Mathematics and Philosophy. Mathematical Association of America. pp. 3-32.
On automating diagrammatic proofs of arithmetic arguments.Mateja Jamnik, Alan Bundy & Ian Green - 1999 - Journal of Logic, Language and Information 8 (3):297-321.
Proof: Its nature and significance.Michael Detlefsen - 2008 - In Bonnie Gold & Roger A. Simons (eds.), Proof and Other Dilemmas: Mathematics and Philosophy. Mathematical Association of America. pp. 1.

Analytics

Added to PP
2012-03-20

Downloads
132 (#168,321)

6 months
11 (#377,362)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Sun-Joo Shin
Yale University

References found in this work

Critique of Pure Reason.Immanuel Kant - 1929 - Cambridge: Cambridge University Press. Edited by J. M. D. Meiklejohn. Translated by Paul Guyer & Allen W. Wood.
Critique of Pure Reason.I. Kant - 1787/1998 - Philosophy 59 (230):555-557.
The Foundations of Geometry.David Hilbert - 1899 - Open Court Company (This Edition Published 1921).
Logical reasoning with diagrams.Gerard Allwein & Jon Barwise (eds.) - 1996 - New York: Oxford University Press.

View all 9 references / Add more references