The role of diagrams in mathematical argument

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

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.

Original languageEnglish (US)
Pages (from-to)59-74
Number of pages16
JournalFoundations of Science
Volume14
Issue number1-2
DOIs
StatePublished - 2009

Fingerprint

Diagrams
Abstract Objects

Keywords

  • Anti-platonism
  • Diagram
  • Mathematical reasoning
  • Proof

ASJC Scopus subject areas

  • General

Cite this

The role of diagrams in mathematical argument. / Sherry, David M.

In: Foundations of Science, Vol. 14, No. 1-2, 2009, p. 59-74.

Research output: Contribution to journalArticle

@article{e2d9285f69e0492cbb5b4ff34145c8d9,
title = "The role of diagrams in mathematical argument",
abstract = "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 = "Anti-platonism, Diagram, Mathematical reasoning, Proof",
author = "Sherry, {David M}",
year = "2009",
doi = "10.1007/s10699-008-9147-6",
language = "English (US)",
volume = "14",
pages = "59--74",
journal = "Foundations of Science",
issn = "1233-1821",
publisher = "Springer Netherlands",
number = "1-2",

}

TY - JOUR

T1 - The role of diagrams in mathematical argument

AU - Sherry, David M

PY - 2009

Y1 - 2009

N2 - 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.

AB - 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.

KW - Anti-platonism

KW - Diagram

KW - Mathematical reasoning

KW - Proof

UR - http://www.scopus.com/inward/record.url?scp=60449114152&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=60449114152&partnerID=8YFLogxK

U2 - 10.1007/s10699-008-9147-6

DO - 10.1007/s10699-008-9147-6

M3 - Article

VL - 14

SP - 59

EP - 74

JO - Foundations of Science

JF - Foundations of Science

SN - 1233-1821

IS - 1-2

ER -