Notre Dame Journal of Formal Logic

The Eu Approach to Formalizing Euclid: A Response to “On the Inconsistency of Mumma’s Eu”

John Mumma

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Abstract

In line with Ken Manders’s seminal account of Euclid’s diagrammatic method in the “The Euclidean Diagram,” two proof systems with a diagrammatic syntax have been advanced as formalizations of the method FG and Eu. In a paper examining Eu, Nathaniel Miller, the creator of FG, has identified a variety of technical problems with the formal details of Eu. This response shows how the problems are remedied.

Article information

Source
Notre Dame J. Formal Logic, Volume 60, Number 3 (2019), 457-480.

Dates
Received: 4 October 2013
Accepted: 18 August 2017
First available in Project Euclid: 2 July 2019

Permanent link to this document
https://projecteuclid.org/euclid.ndjfl/1562033114

Digital Object Identifier
doi:10.1215/00294527-2019-0012

Mathematical Reviews number (MathSciNet)
MR3985621

Subjects
Primary: 03A05: Philosophical and critical {For philosophy of mathematics, see also 00A30}
Secondary: 51M99: None of the above, but in this section 03B30: Foundations of classical theories (including reverse mathematics) [See also 03F35]

Keywords
elementary geometry diagrams formalization

Citation

Mumma, John. The Eu Approach to Formalizing Euclid: A Response to “On the Inconsistency of Mumma’s Eu”. Notre Dame J. Formal Logic 60 (2019), no. 3, 457--480. doi:10.1215/00294527-2019-0012. https://projecteuclid.org/euclid.ndjfl/1562033114


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References

  • [1] Kulvicki, J., “Knowing with images: Medium and message,” Philosophy of Science, vol. 77 (2010), pp. 295–313.
  • [2] Macbeth, D., Realizing Reason: A Narrative of Truth and Knowing, Oxford University Press, Oxford, 2014.
  • [3] Manders, K., “The Euclidean diagram,” pp. 112–18 in Philosophy of Mathematical Practice, edited by P. Mancosu, Oxford University Press, Oxford, 2008.
  • [4] Miller, N., Euclid and His Twentieth Century Rivals: Diagrams in the Logic of Euclidean Geometry, CSLI Publications, Stanford, CA, 2007.
  • [5] Miller, N., “On the Inconsistency of Mumma’s Eu,” Notre Dame Journal of Formal Logic, vol. 53 (2012), pp. 27–52.
  • [6] Mumma, J., “Ensuring generality in Euclid’s diagrammatic arguments,” pp. 222–35 in Diagrammatic Representation and Inference, edited by G. Stapelton, J. Howse, and J. Lee, Springer, Berlin, 2008.
  • [7] Mumma, J., “Proofs, pictures, and Euclid,” Synthese, vol. 175 (2010), pp. 255–87.
  • [8] Mumma, J., “The role of geometric content in elementary geometrical reasoning,” Les Études Philosophiques, vol. 97 (2011/2), pp. 243–258.
  • [9] Mumma, J., “Constructive geometrical reasoning and diagrams,” Synthese, vol. 186 (2012), pp. 103–19.
  • [10] Mumma, J., “Intuition formalized: Ancient and modern methods of proof in elementary Euclidean geometry,” Ph.D. dissertation, Carnegie Mellon University, Pittsburgh, 2006.
  • [11] Shimojima, A., “Operational constraints in diagrammatic reasoning,” pp. 27–48 in Logical Reasoning with Diagrams, edited by G. Allewen and J. Barwise, vol. 6 in Studies in Logic and Computation, Oxford University Press, New York, 1996.