## Notre Dame Journal of Formal Logic

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

### On the Inconsistency of Mumma's Eu

#### 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.

#### Article information

**Source**

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

**Dates**

First available in Project Euclid: 9 May 2012

**Permanent link to this document**

http://projecteuclid.org/euclid.ndjfl/1336586236

**Digital Object Identifier**

doi:10.1215/00294527-1626509

**Mathematical Reviews number (MathSciNet)**

MR2925267

**Zentralblatt MATH identifier**

06040393

**Subjects**

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

**Keywords**

diagrams case analysis geometry

#### Citation

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. http://projecteuclid.org/euclid.ndjfl/1336586236.