Notre Dame Journal of Formal Logic

On the Inconsistency of Mumma's Eu

Nathaniel Miller

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In several articles, Mumma has presented a formal diagrammatic system Eu meant to give an account of one way in which Euclid's use of diagrams in the Elements could be formalized. However, largely because of the way in which it tries to limit case analysis, this system ends up being inconsistent, as shown here. Eu also suffers from several other problems: it is unable to prove several wide classes of correct geometric claims and contains a construction rule that is probably computationally intractable and that may not even be decidable.

Article information

Notre Dame J. Formal Logic Volume 53, Number 1 (2012), 27-52.

First available in Project Euclid: 9 May 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

diagrams case analysis geometry


Miller, Nathaniel. On the Inconsistency of Mumma's Eu. Notre Dame J. Formal Logic 53 (2012), no. 1, 27--52. doi:10.1215/00294527-1626509.

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