Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-18T20:59:43.682Z Has data issue: false hasContentIssue false
  • English
  • Français

SIMPLICIUS ON THE FILLING OF SPACE, IN CAELO 655.9–656.5: A DELIBERATE MISTAKE?

Published online by Cambridge University Press:  11 August 2021

D. R. Lloyd
D. R. Lloyd*
Affiliation:
School of Chemistry, Trinity College, Dublin, Ireland
*
*Email: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

In In cael. 655.9–656.5 Simplicius reports an argument in which an apparent justification is offered for the false claim by Aristotle that ‘pyramids’ (regular tetrahedra) can completely fill space. This argument was analysed by Ian Mueller in an Appendix to his translation of In caelo, and the outline of an alternative has been presented in Myrto Hatzimichali's study of Potamo of Alexandria. In this article I contest Mueller's interpretation, and expand on the one reported by Hatzimichali. I also contest Mueller's claim that a version of his interpretation can be found in the partial commentary by Peter of Auvergne. It is suggested here that the ‘justification’ reported by Simplicius is a deliberate slip in logic, which is accompanied by a carefully constructed cover-up involving some quite tricky geometry. Simplicius makes frequent reference to Alexander of Aphrodisias, but it is argued here that he has been very selective with these citations.

Type
Research Article
Information
The Cambridge Classical Journal , Volume 67 , December 2021 , pp. 93 - 118
Copyright
Copyright © The Author(s), 2021. Published by Cambridge University Press on behalf of The Cambridge Philological Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

I thank Dr Myrto Hatzimichali and Professor David Sedley for drawing the problem in Simplicius which is the subject of this article to my attention some years ago, and Dr Hatzimichali for many very useful discussions since. I am grateful to Professor Marjorie Senechal for providing her unpublished translation of Struik's (1925) article, to the referee of this article for some very useful comments, to Dr Elisa Coda for allowing me to see a provisional copy of the relevant section of her Themistius translation, to Mr Laszlo Bardos for permission to reproduce his illustrations shown in Figures 4, 5 and 6, and for providing high-resolution copies of them, and to the current holders of the copyright, Bristol Classical Press (an imprint of Bloomsbury Publishing Plc), for permission to reproduce the citations from Mueller (2009).

References

Works cited

Aquinas, T. (1852–73) Opera omnia, xix.179, Parma. (The Leonina edition (Rome 1882) does not include the contribution from Peter of Auvergne.)Google Scholar
Chen, E. R., Engel, M. and Glotzer, S. C. (2010) ‘Dense crystalline dimer packings of regular tetrahedra’, Discrete & Computational Geometry 44.2, 253–80.CrossRefGoogle Scholar
Coda, E. (2014) ‘Reconstructing the text of Themistius’ paraphrase of the De Caelo: the Hebrew and Latin versions on the three meanings of the term “Heaven”’, Studia Graeco-Arabica 4, 1–15.Google Scholar
Coda, E. (forthcoming) Themistius: Paraphrasis of the De Caelo, Commentaria in Aristotelem Graeca et Byzantina, Berlin.Google Scholar
Courtenay, W. J. (2015) ‘Peter of Auvergne, master in arts and theology at Paris’, in Flueler, C., Lanza, L. and Toste, M. (eds.), Peter of Auvergne: university master of the 13th century, Berlin, 13–28.Google Scholar
Falcon, A. (2015) Review of Rescigno 2008, Aestimatio: Critical Reviews in the History of Science 12, 6–12.Google Scholar
Fedorov, E. S. (1885) An introduction to the theory of figures, Notices of the Imperial Petersburg Mineralogial Society ser. 2, 21, 1–279. (English translation in Symmetry of crystals, American Crystallographic Association Monograph 7 (1971) 50–131).Google Scholar
Hatzimichali, M. (2011) Potamo of Alexandria and the emergence of eclecticism in late Hellenistic philosophy, Cambridge.CrossRefGoogle Scholar
Heath, T. L. (1926) The thirteen books of Euclid's Elements, Cambridge.Google Scholar
Heiberg, I. L. (1894) Simplicii in Aristotelis De caelo, Commentaria in Aristotelem Graeca 7, Berlin.CrossRefGoogle Scholar
Kelvin, L. (1887) ‘On the division of space with minimum partitional area’, The Philosophical Magazine ser. 5, 24, 503–14.Google Scholar
Kittel, C. (2004) Introduction to solid state physics, 8th edn, New York.Google Scholar
Landauer, S. (1902) Themistii in libros Aristotelis De caelo paraphrasis hebraice et latine, Berlin.CrossRefGoogle Scholar
Lloyd, D. R. (2006) ‘Symmetry and asymmetry in the construction of “elements” in the Timaeus’, CQ, 56, 459–74.CrossRefGoogle Scholar
Mueller, I. (2009) Simplicius: On Aristotle On the heavens 3.7–4.6, Ancient Commentators on Aristotle, London.Google Scholar
Mueller, I. (2018) ‘Space-filling pyramids fom Aristotle to Jan Brozek’, RPhilos 143.2, 159–80.Google Scholar
Rescigno, A. (2008) Alessando di Afrodisia. Commento al De caelo di Aristotele. Frammenti del secondo, terzo, e quarto libro, Amsterdam.Google Scholar
Struik, D. J. (1925) ‘Het Probleem “de implementione loci”’, Nieuw Archief voor Wiskunde ser. 2, 15, 121–37.Google Scholar
Walker, C. and Starmer, K. (eds.) (1999) Miscarriages of justice: a review of justice in error, London.Google Scholar