Picture-Proofs and Platonism

Croatian Journal of Philosophy 7 (1):81-92 (2007)

Authors
Irina Starikova
Bristol University
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 Analytic Philosophy  Contemporary Philosophy
Categories (categorize this paper)
ISBN(s) 1333-1108
DOI croatjphil20077133
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

Our Archive


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 39,607
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

No references found.

Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles

Proofs and Pictures.James Robert Brown - 1997 - British Journal for the Philosophy of Science 48 (2):161-180.
Proofs, Pictures, and Euclid.John Mumma - 2010 - Synthese 175 (2):255 - 287.
The Surveyability of Long Proofs.Edwin Coleman - 2009 - Foundations of Science 14 (1-2):27-43.
Intuition in Mathematics.Elijah Chudnoff - 2014 - In Barbara Held & Lisa Osbeck (eds.), Rational Intuition. Cambridge University Press.
The Role of Diagrams in Mathematical Arguments.David Sherry - 2009 - Foundations of Science 14 (1-2):59-74.
Diagrams and Proofs in Analysis.Jessica Carter - 2010 - International Studies in the Philosophy of Science 24 (1):1 – 14.
Intuitions in Science: Thought Experiments as Argument Pumps.Darrell Patrick Rowbottom - 2014 - In Anthony R. Booth & Darrell P. Rowbottom (eds.), Intuitions. Oxford University Press. pp. 119-134.

Analytics

Added to PP index
2011-01-09

Total views
44 ( #168,929 of 2,325,388 )

Recent downloads (6 months)
9 ( #141,631 of 2,325,388 )

How can I increase my downloads?

Downloads

My notes

Sign in to use this feature