The role of diagrams in mathematical arguments

Foundations of Science 14 (1-2):59-74 (2009)

David Sherry
Northern Arizona University
Recent accounts of the role of diagrams in mathematical reasoning take a Platonic line, according to which the proof depends on the similarity between the perceived shape of the diagram and the shape of the abstract object. This approach is unable to explain proofs which share the same diagram in spite of drawing conclusions about different figures. Saccheri’s use of the bi-rectangular isosceles quadrilateral in Euclides Vindicatus provides three such proofs. By forsaking abstract objects it is possible to give a natural explanation of Saccheri’s proofs as well as standard geometric proofs and even number-theoretic proofs.
Keywords Diagram  Proof  Anti-platonism  Mathematical reasoning
Categories (categorize this paper)
DOI 10.1007/s10699-008-9147-6
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: 40,131
Through your library

References found in this work BETA

Plato: Meno and Phaedo. Plato - 1980 - Cambridge University Press.
Proofs and Pictures.James Robert Brown - 1997 - British Journal for the Philosophy of Science 48 (2):161-180.

View all 15 references / Add more references

Citations of this work BETA

Perceiving Necessity.Catherine Legg & James Franklin - 2017 - Pacific Philosophical Quarterly 98 (3).
Diagrams and Proofs in Analysis.Jessica Carter - 2010 - International Studies in the Philosophy of Science 24 (1):1 – 14.

Add more citations

Similar books and articles

Picture-Proofs and Platonism.Irina Starikova - 2007 - Croatian Journal of Philosophy 7 (1):81-92.
Diagrams as Sketches.Brice Halimi - 2012 - Synthese 186 (1):387-409.
Figures, Formulae, and Functors.Zach Weber - 2013 - In Sun-Joo Shin & Amirouche Moktefi (eds.), Visual Reasoning with Diagrams. Springer. pp. 153--170.
Proofs, Pictures, and Euclid.John Mumma - 2010 - Synthese 175 (2):255 - 287.
What Perception is Doing, and What It is Not Doing, in Mathematical Reasoning.Dennis Lomas - 2002 - British Journal for the Philosophy of Science 53 (2):205-223.
On Automating Diagrammatic Proofs of Arithmetic Arguments.Mateja Jamnik, Alan Bundy & Ian Green - 1999 - Journal of Logic, Language and Information 8 (3):297-321.
Diagrams and Proofs in Analysis.Jessica Carter - 2010 - International Studies in the Philosophy of Science 24 (1):1 – 14.


Added to PP index

Total views
102 ( #72,334 of 2,237,181 )

Recent downloads (6 months)
9 ( #151,692 of 2,237,181 )

How can I increase my downloads?


My notes

Sign in to use this feature