Proofs, pictures, and Euclid

DOI10.1007/s11229-009-9509-9zbMath1198.03021OpenAlexW2081487758MaRDI QIDQ707897

John Mumma

Publication date: 8 October 2010

Published in: Synthese (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11229-009-9509-9

zbMATH Keywords

diagramsEuclid's geometry

Mathematics Subject Classification ID

Methodology of mathematics (00A35) Foundations of classical theories (including reverse mathematics) (03B30) Euclidean geometries (general) and generalizations (51M05) History of Greek and Roman mathematics (01A20) History of geometry (51-03)

Related Items (19)

Proof-checking Euclid ⋮ Operationalism: an interpretation of the philosophy of ancient Greek geometry ⋮ The twofold role of diagrams in Euclid's plane geometry ⋮ Constructive geometrical reasoning and diagrams ⋮ What is a Logical Diagram? ⋮ Can We “Show” the Correctness of Reasoning? On the Role of Diagrammatic Spatialization in Logical Justification ⋮ The eco-cognitive model of abduction. Ἀπαγωγή now: naturalizing the logic of abduction ⋮ On the representational role of Euclidean diagrams: representing \textit{qua} samples ⋮ On the inconsistency of Mumma's Eu ⋮ Material representations in mathematical research practice ⋮ On fluidity of the textual transmission in Abraham bar Ḥiyya's \textit{Ḥibbur ha-Meshiḥah ve-ha-Tishboret} ⋮ Schopenhauer on Diagrammatic Proof ⋮ Logic of imagination. Echoes of Cartesian epistemology in contemporary philosophy of mathematics and beyond ⋮ Prolegomena to a cognitive investigation of Euclidean diagrammatic reasoning ⋮ Carroll's infinite regress and the act of diagramming ⋮ Cognitive artifacts for geometric reasoning ⋮ From Euclidean geometry to knots and nets ⋮ The Eu approach to formalizing Euclid: a response to ``On the inconsistency of Mumma's Eu ⋮ Rigor and the Context-Dependence of Diagrams: The Case of Euler Diagrams

Cites Work

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• The axiomatic method. With special reference to geometry and physics. Proceedings of an International Symposium held at the University of California, Berkeley, December 26, 1957 -- January 4, 1958
• Why Do We Prove Theorems?
• Proofs and Pictures
• The Derivation-Indicator View of Mathematical Practice
• A Critique of a Formalist-Mechanist Version of the Justification of Arguments in Mathematicians' Proof Practices
• Visualization in Logic and Mathematics
• A FORMAL SYSTEM FOR EUCLID’SELEMENTS

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