Crossing Curves: A Limit to the Use of Diagrams in Proofs

Philosophia Mathematica 19 (3):281-307 (2011)
Abstract
This paper investigates the following question: when can one reliably infer the existence of an intersection point from a diagram presenting crossing curves or lines? Two cases are considered, one from Euclid's geometry and the other from basic real analysis. I argue for the acceptability of such an inference in the geometric case but against in the analytic case. Though this question is somewhat specific, the investigation is intended to contribute to the more general question of the extent and limits of reliable diagrammatic reasoning in mathematics
Keywords No keywords specified (fix it)
Categories (categorize this paper)
Options
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history Request removal from index
 
Download options
PhilPapers Archive


Upload a copy of this paper     Check publisher's policy on self-archival     Papers currently archived: 9,360
External links
  • Through your library Configure
    References found in this work BETA

    No references found.

    Citations of this work BETA

    No citations found.

    Similar books and articles
    Jessica Carter (2010). Diagrams and Proofs in Analysis. International Studies in the Philosophy of Science 24 (1):1 – 14.
    Nathaniel Miller (2012). On the Inconsistency of Mumma's Eu. Notre Dame Journal of Formal Logic 53 (1):27-52.
    Sun-Joo Shin (1994). Peirce and the Logical Status of Diagrams. History and Philosophy of Logic 15 (1):45-68.
    Catherine Legg (2013). What is a Logical Diagram? In Sun-Joo Shin & Amirouche Moktefi (eds.), Visual Reasoning with Diagrams. Springer. 1-18.
    Analytics

    Monthly downloads

    Added to index

    2011-08-07

    Total downloads

    46 ( #30,294 of 1,088,810 )

    Recent downloads (6 months)

    1 ( #69,735 of 1,088,810 )

    How can I increase my downloads?

    My notes
    Sign in to use this feature


    Discussion
    Start a new thread
    Order:
    There  are no threads in this forum
    Nothing in this forum yet.