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2012 On the Inconsistency of Mumma's Eu
Nathaniel Miller
Notre Dame J. Formal Logic 53(1): 27-52 (2012). DOI: 10.1215/00294527-1626509

Abstract

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.

Citation

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Nathaniel Miller. "On the Inconsistency of Mumma's Eu." Notre Dame J. Formal Logic 53 (1) 27 - 52, 2012. https://doi.org/10.1215/00294527-1626509

Information

Published: 2012
First available in Project Euclid: 9 May 2012

zbMATH: 1248.03022
MathSciNet: MR2925267
Digital Object Identifier: 10.1215/00294527-1626509

Subjects:
Primary: 03A05
Secondary: 03B30, 51M99

Rights: Copyright © 2012 University of Notre Dame

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Vol.53 • No. 1 • 2012
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