The role of diagrams in mathematical argument

Research output: Contribution to journalArticle

13 Scopus citations

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 - Jan 1 2009

Keywords

  • Anti-platonism
  • Diagram
  • Mathematical reasoning
  • Proof

ASJC Scopus subject areas

  • General
  • History and Philosophy of Science

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