The Four Elements and Their Characteristics according to the Schema in the Early Medieval Anonymous Fragment De Quattuor Elementis
Keywords:
elements, materia, Early Middle Ages, scientific diagram, Plato, Aristotle, Calcidius, Boethius, Isidore of SevillaAbstract
The paper is an attempt to interpret a schema that is part of an early medieval fragment known as the Excerptum de quattuor elementis. In this schema, the individual elements (fire, air, water, earth) are presented as the elements which form the material world using several characterisations typical of the period: as the sum of their natural physical properties in accordance with the Platonic and Aristotelian traditions, as geometric shapes (to put it simply, using the so-called Platonic solids) and as numerical values connected by a 2:1 ratio. The aim of this paper is to propose a possible interpretation of the numerical values and connections found in this schema using contemporary texts and diagrams (especially Calcidius and Isidore of Seville, as well as other sources available at the time), which would include a consistent yet complex characterisation of the elements, their properties and their mutual interconnectedness, as found in the fragmentary text of the Excerptum de quattuor elementis and in the schema itself.
References
Abbo of Fleury and Ramsay, Commentary on the Calculus of Victorius of Aquitaine, ed. A. M. Peden, Oxford, Oxford University Press, 2003.
Adalbold of Utrecht, Commentarius ad Boethii carmen ‘O qui perpetua’ (Cons. 3, 9), in Serta mediaevalia. Textus varii saeculorum X–XIII, ed. R. B. C. Huygens, CCCM 171, Turnhout, Brepols, 2000, pp. 123–140 [= In Cons].
Ambrose of Milan, Exameron, in S. Ambrosii Opera, vol. I, ed. K. Schenkl, CSEL 32/1, Praha – Wien – Leipzig, Tempsky – Freytag, 1896, pp. 1–261.
Aristotle, De generatione et corruptione, in Aristotelis Opera, vol. I, ed. I. Bekker, Berlin, Reimer, 1831 (reprint coed. O. Gigon, Berlin, De Gruyter, 1960) pp. 314–338.
Artmann, Benno – Schäfer, Lothar, ‘On Plato's “Fairest Triangles” (Timaeus 54a)’, Historia Mathematica, vol. 20, 1993, pp. 255–64.
Augustine of Hippo, De libero arbitrio, ed. W. M. Green, in Aurelii Augustini Opera, vol. II, 2, CCSL 29, Turnhout, Brepols, 1970, pp. 211–321.
Bai, Junxiao, ‘Numbers: Harmonic Ratios and Beauty in Augustinian Musical Cosmology’, Cosmos and History. The Journal of Natural and Social Philosophy, vol. 13, no. 3, 2017, pp. 192–217.
Baltes, Matthias, Die Weltentstehung des platonischen Timaios nach den antiken Interpreten, vol. 1, Leiden, Brill, 1976.
Barker, Andrew, ‘Timaeus on Music and the Liver’, in Wright, M. R. (ed.), Reason and Necessity. Essays on Plato's Timaeus, London, Duckworth, 2000, pp. 85–99.
Bede the Venerable, De natura rerum, in Bedae Venerabilis Opera, vol. I: Opera didascalica, ed. C. W. Jones, CCSL 123A, Turnhout, Brepols, 1975, pp. 173–234 [= DNR].
Bergren, Ann, ‘Plato's Timaeus and the Aesthetics of ‘Animate Form’’, in Mohr, R. D. – Sattler, B. (eds.), One Book, the Whole Universe. Plato's Timaeus Today, Las Vegas – Zurich – Athens, Parmenides Publishing, 2010, pp. 343–72.
Boethius, De arithmetica, eds. H. Oosthout – J. Schilling, CCSL 94A, Turnhout, Brepols, 1999 [= Arith.].
Brinkmann, Hennig, Mittelalterliche Hermeneutik, Tübingen, Niemeyer, 1980.
Broadie, Sarah, Nature and Divinity in Plato's Timaeus, Cambridge, Cambridge University Press, 2012.
Caiazzo, Irene, ‘Filosofia della natura e fisica elementare nell'alto medioevo’, in La conoscenza scientifica nell'Alto Medioevo, Spoleto, Fondazione CISAM, 2020, pp. 1059–85.
Caiazzo, Irene, ‘La forme et les qualités des éléments: lectures médiévales du Timée’, in Celia, F. – Ulacco, A. (eds.), Il Timeo. Esegesi greche, arabe, latine. Pisa, Pisa University Press, 2012, pp. 307–45.
Caiazzo, Irene, ‘Urso of Salerno on Prime Matter between Plato and Aristotle’, in Jacquart, D. – Weill-Parot, N. (eds.), Substances minérales et corps animés. De la philosophie de la matière aux pratiques médicales (1100–1500), Montreuil, Omniscience, 2012, pp. 19–52.
Caiazzo, Irene, ‘The Four Elements in the Work of William of Conches’, in Guillaume de Conches: Philosophie et science ai XIIe siècle, Firenze, Sismel – Edizioni del Galluzzo, 2011, pp. 3–66.
Calcidius, Commentarius in Platonis Timaeum, in Timaeus a Calcidio translatus commentarioque instructus. Ed. J. H. Waszink. London – Leiden 21975, pp. 57–346 [= In Tim.].
Catalani, Luigi, ‘«Omnia Numerorum Videntur Ratione Formata». A ‘Computable World’ Theory in Early Medieval Philosophy¨’, in Gadducci, F. – Tavosanis, M. (eds.), History and Philosophy of Computing, Berlin – Cham, Springer, 2016, pp. 131–40.
Code, Alan, ‘Aristotle on Plato on Weight’, in Mohr, R. D. – Sattler, B. (eds.), One Book, the Whole Universe. Plato's Timaeus Today, Las Vegas – Zurich – Athens, Parmenides Publishing, 2010, pp. 201–11.
Commentarii et glossae e codice Mettense [to Bede’s DNR], ed. F. Lipp, in Bedae Venerabilis Opera, vol. I: Opera didascalica, CCSL 123A, Turnhout, Brepols, 1975, pp. 192–234.
Eastwood, Bruce S., ‘The diagram of the four elements in the oldest manuscripts of Isidore's «De natura rerum»’, Studi medievali, vol. 42, no. 2, 2001, pp. 547–70.
Excerptum de quattuor elementis, ed. R. A. B. Mynors, in Cassiodorus Senator, Institutiones, Oxford, Clarendon Press, 1937, pp. 167–168 [= EDQE].
Fontaine, Jacques, Isidore de Séville et la culture classique dans l'Espagne wisigothique, Paris, Études Augustiniennes, 1959.
Gill, Mary L., ‘Matter and Flux in Plato's Timaeus’, Phronesis. A Journal for Ancient Philosophy, vol. 32, 1987, pp. 34–53.
Häring, Nicholas M., ‘Four Commentaries on the De Consolatione Philosophiae in MS Heiligenkreuz 130’, Mediaeval Studies, vol. 31, 1969, pp. 287–316.
Hoenig, Christina, ‘Calcidius on Cosmic Harmony’, in Pelosi, F. – Petrucci, F. M. (eds.), Music and Philosophy in the Roman Empire, Cambridge, Cambridge University Press, 2020, pp. 262–85.
Hoenig, Christina, Plato's Timaeus and the Latin Tradition, Cambridge, Cambridge University Press, 2018.
Hoenig, Christina, ‘Timaeus Latinus: Calcidius and the Creation of the Universe’, Rhizomata. A Journal for Ancient Philosophy and Science, vol. 2, 2014, pp. 80–110.
Hoenig, Christina, ‘Εἰκὼς λόγος: Plato in Translation(s)’, Methodos. Savoirs et texts, vol. 13, 2013, URL: http://journals.openedition.org/methodos/2994.
Huygens, Robert B. C., ‘Mittelalterliche Kommentare zum O qui perpetua…’, Sacris Erudiri. A Journal of Late Antique and Medieval Christianity, vol. 6, 1954, pp. 373–427.
Isidore de Séville, Traité de la Nature. Introduction, texte critique, traduction et notes, ed. J. Fontaine, Bordeaux, Féret et Fils, 1960 (reprint Paris, Études Augustiniennes, 2002) [= DNR].
Isidore of Seville, Etymologiarum sive Originum libri XX, ed. W. M. Lindsay, Oxford, Oxford University Press, 1911 [= Etym.].
Kantorowicz, Ernst H., ‘Plato in the Middle Ages’, The Philosophical Review, vol. 51, no. 3, 1942, pp. 312–23.
Macrobius, Commentarius in Somnium Scipionis, ed. J. Willis, Stuttgart – Leipzig, Teubner, 1994.
Martianus Capella, De nuptiis Philologiae et Mercurii, ed. J. Willis, Leipzig, Teubner, 1983.
Mayr-Harting, Henry, Church and Cosmos in Early Ottonian Germany. The View from Cologne, Oxford, Oxford University Press, 2007.
McCluskey, Stephen C., ‘Boethius's Astronomy and Cosmology’, in Kaylor, N. H. Jr. – Phillips, P. E. (eds.), A Companion to Boethius in the Middle Ages, Leiden – Boston, Brill, 2012, pp. 47–73.
McKeon, Richard, ‘Medicine and Philosophy in the Eleventh and Twelfth Centuries: The Problem of Elements’, The Thomist: A Speculative Quarterly Review, vol. 24, no. 2–4, 1961, pp. 211–56.
Miller, Dana R., The Third Kind in Plato's Timaeus, Göttingen, Vandenhoeck & Ruprecht, 2003.
Mueller, Ian, ‘What's the Matter? Some Neo-Platonist Answers’, in Mohr, R. D. –Sattler, B. (eds.), One Book, the Whole Universe. Plato's Timaeus Today, Las Vegas – Zurich – Athens, Parmenides Publishing, 2010, pp. 151–63.
Murdoch, John E., Album of Science. Antiquity and the Middle Ages, New York, Scribner's Sons, 1984.
Obrist, Barbara, La cosmologie médiévale. Textes et images. I. Les fondements antiques, Firenze, Sismel – Edizioni del Galluzzo, 2004.
Obrist, Barbara, ‘Wind Diagrams and Medieval Cosmology’, Speculum, vol. 72, no. 1, 1997, pp. 33–84.
Obrist, Barbara, ‘Le diagramme isidorien des saisons, son contenu physique et les représentations figuratives’, Mélanges de l'Ecole française de Rome. Moyen Age, vol. 108, 1996, pp. 95–164.
Plato, Timaeus, in Platonis opera, vol. IV, ed. J. Burnet, Oxford, Oxford University Press, 1903, pp. 17–105 [= Tim.].
Pressouyre, Léon, ‘Le cosmos platonicien de la cathédrale d'Anagni’, Mélanges d'archéologie et d'histoire, vol. 78, no. 2, 1966, pp. 551–93.
Reydams-Schils, Gretchen J., ‘Meta-Discourse: Plato's Timaeus accodring to Calcidius’, Phronesis. A Journal for Ancient Philosophy, vol. 52, 2007, pp. 301–27.
Sattler, Barbara, ‘A Likely Account of Necessity: Plato's Receptable as a Physical and Metaphysical Foundation for Space’, Journal of the History of Philosophy, vol. 50, 2012, pp. 159–95.
Silk, Edmund T., ‘Pseudo-Johannes Scottus, Adalbold of Utrecht and the Early Commentaries on Boethius’, Mediaeval and Renaissance Studies, vol. 3, 1954, pp. 1–40.
Somfai, Anna, ‘Calcidius' Commentary on Plato's Timaeus and its Place in the Commentary Tradition: the Concept of Analogia in Text and Diagrams’, in Adamson, P. – Baltussen, H. – Stone, W. M. F. (eds.), Philosophy, Science and Exegesis in Greek, Arabic and Latin Commentaries, vol. I, London, University of London, 2004, pp. 203–20.
Somfai, Anna, ‘The Eleventh-Century Shift in the Reception of Plato's Timaeus and Calcidius's Commentary’, Journal of the Warburg and Courtauld Institutes, vol. 65, no 1, 2002, pp. 1–21.
Verboon, Annemieke R., Lines of Thought. Diagrammatic representation and the scientific texts of the arts faculty, 1200–1500 [doctoral thesis], Leiden, Leiden University, 2010.
Vossen, Peter, ‘Über die Elementen-Syzygien’, in Bischoff, B. – Brechter, S. (eds.), Liber floridus: Mittellateinischen Studien, St. Ottilien, Eos Verlag, 1950, pp. 33–46.
Winden van, Jacobus C. M., Calcidius on Matter: His Doctrine and Sources, Leiden, Brill, 1965.
Zeyl, Donald, ‘Visualizing Platonic Space’, in Mohr, R. D. –Sattler, B. (eds.), One Book, the Whole Universe. Plato's Timaeus Today, Las Vegas – Zurich – Athens, Parmenides Publishing, 2010, pp. 117–30.
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