### 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 language | English (US) |
---|---|

Pages (from-to) | 59-74 |

Number of pages | 16 |

Journal | Foundations of Science |

Volume | 14 |

Issue number | 1-2 |

DOIs | |

State | Published - 2009 |

### Fingerprint

### Keywords

- Anti-platonism
- Diagram
- Mathematical reasoning
- Proof

### ASJC Scopus subject areas

- General

### Cite this

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

Research output: Contribution to journal › Article

*Foundations of Science*, vol. 14, no. 1-2, pp. 59-74. https://doi.org/10.1007/s10699-008-9147-6

}

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 -