Picture-Proofs and Platonism

Croatian Journal of Philosophy 7 (1):81-92 (2007)
Abstract
This paper concerns the role of intuitions in mathematics, where intuitions are meant in the Kantian sense, i.e. the “seeing” of mathematical ideas by means of pictures, diagrams, thought experiments, etc.. The main problem discussed here is whether Platonistic argumentation, according to which some pictures can be considered as proofs (or parts of proofs) of some mathematical facts, is convincing and consistent. As a starting point, I discuss James Robert Brown’s recent book Philosophy of Mathematics, in particular, his primarily examples and analogies. I then consider some alternatives and counterarguments, namely John Norton’s opposite view, that intuitions are just pictorially represented logical arguments and are superfluous; and the Kantian transcendental theory of construction in imagination, as it is developed in the works of Marcus Giaquinto and Michael Friedman. Although I support the claim that some intuitions are essential in mathematical justification, I argue that a Platonistic approach to intuitions is partial and one should go further than a Platonist in explaining how some intuitions can deliver new mathematical knowledge
Keywords No keywords specified (fix it)
Categories No categories specified
(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
  •   Try with proxy.
  • 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
    James Robert Brown (1997). Proofs and Pictures. British Journal for the Philosophy of Science 48 (2):161-180.
    Edwin Coleman (2009). The Surveyability of Long Proofs. Foundations of Science 14 (1-2):27-43.
    Elijah Chudnoff (forthcoming). Intuition in Mathematics. In Barbara Held & Lisa Osbeck (eds.), Rational Intuition. Cambridge University Press.
    Jessica Carter (2010). Diagrams and Proofs in Analysis. International Studies in the Philosophy of Science 24 (1):1 – 14.
    Analytics

    Monthly downloads

    Added to index

    2011-01-09

    Total downloads

    11 ( #113,039 of 1,089,053 )

    Recent downloads (6 months)

    1 ( #69,801 of 1,089,053 )

    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.