Are Euclid's Diagrams Representations? On an Argument by Ken Manders

In Maria Zack & Dirk Schlimm (eds.), Research in History and Philosophy of Mathematics. The CSHPM 2019-2020 Volume. Birkhäuser. pp. 115-127 (2022)
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Abstract

In his well-known paper on Euclid’s geometry, Ken Manders sketches an argument against conceiving the diagrams of the Elements in ‘semantic’ terms, that is, against treating them as representations—resting his case on Euclid’s striking use of ‘impossible’ diagrams in some proofs by contradiction. This paper spells out, clarifies and assesses Manders’s argument, showing that it only succeeds against a particular semantic view of diagrams and can be evaded by adopting others, but arguing that Manders nevertheless makes a compelling case that semantic analyses ought to be relegated to a secondary role for the study of mathematical practices.

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David Waszek
École Normale Supérieure

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