Skip to content
Licensed Unlicensed Requires Authentication Published by De Gruyter May 18, 2022

Clotho’ Spindle: Xenocrates’ Doctrine of Indivisibles

  • Olga Alieva EMAIL logo

Abstract

This paper offers a reconstruction of Xenocrates’ theory of indivisibles which would not commit him to the idea of ‘jerky motion’ criticized by Aristotle in Physica VI, yet would perfectly square with Plato’s Timaeus, the basis of Xenocrates’ canon. Relying on Alexander’s, Porphyry’s, and Themistius’s accounts of his theory, as well on a detailed analysis of De lineis insecabilibus, I suggest that Xenocrates’ minima, contrary to what Aristotle implies, are not to be understood as more or less stable particulars, like tiny chunks of matter, moving about or leaping in physical space from point A to point B. Yet Xenocrates’ minima do remain ‘physical’ and ‘corporeal’ in a more Platonic sense of these words, not presupposing any kind of leaping, jumping, or jerking. This explains why Xenocrates associated the sensible realm with one of the three Fates, namely Clotho.

  1. Funder Name: National Research University Higher School of Economics

  2. Funder Id: http://dx.doi.org/10.13039/501100007251

  3. Grant Number: HSE Academic Fund Programme, 20-01-029

Algra, K. 1994. Concepts of Space in Greek Thought. Leiden.10.1163/9789004320871Search in Google Scholar

Baltes, M. 1976. Die Weltentstehung des platonischen Timaios nach den antiken Interpreten. Teil 1. Leiden.10.1163/9789004320512_002Search in Google Scholar

–. 1988. “Zur Theologie des Xenokrates”. In Knowledge of God in the Graeco-Roman World. Ed. R. B. van den Broek/T. Baarda/J. Mansfeld. Leiden, 43–68.Search in Google Scholar

Barker, A. 2009. “Heraclides and Musical History”. In Heraclides of Pontus: Discussion. Ed. W. W. Fortenbaugh/E. Pender. New Brunswick, 273–98.Search in Google Scholar

–. 2015. Porphyry’s Commentary on Ptolemy’s Harmonics: A Greek Text and Annotated Translation. Cambridge.Search in Google Scholar

–. (ed.) 1989. Greek Musical Writings. Vol. II: Harmonic and Acoustic Theory. Cambridge.Search in Google Scholar

Barnes, J. (ed.) 1984. The Complete Works of Aristotle. The Revised Oxford Translation. Vol. 2. Princeton.10.1515/9781400835850Search in Google Scholar

Bett, R. (trans.) 2005. Sextus Empiricus: Against the Logicians. New York.10.1017/CBO9780511815232Search in Google Scholar

–. (trans.) 2012. Sextus Empiricus: Against the Physicists. New York.Search in Google Scholar

Brisson, L. 1998. Le Même et l’Autre dans la structure ontologique du Timée de Platon. St. Augustin.Search in Google Scholar

–. 2000. Lectures de Platon. Paris.Search in Google Scholar

–. 2000a. “Le rôle des mathématiques dans le Timée selon les interprétations contemporaines”. In Le Timée de Platon: contributions à l’histoire de sa réception. Ed. A. Neschke-Hentschke. Louvain, 295–315.Search in Google Scholar

Carter, J. W. 2019. Aristotle on Earlier Greek Psychology: The Science of Soul. Cambridge.10.1017/9781108646321Search in Google Scholar

Cherniss, H. 1944. Aristotle’s Criticism of Plato and the Academy. Baltimore.Search in Google Scholar

–. l954. “A Much Misread Passage of the Timaeus (Timaeus 49C7–50B5)”. The American Journal of Philology 75.2, 113–30.10.2307/292030Search in Google Scholar

–. 1959. “Review: Le Περὶ Φιλοσοφίας d’Aristote et la théorie platonicienne des idées et des nombres by H. D. Saffrey”. Gnomon 31.1, 36–51.Search in Google Scholar

Coope, U. 2005. Time for Aristotle: Physics IV. 10–14. Oxford.10.1093/0199247900.001.0001Search in Google Scholar

Crivelli, P. 2020. “Division and Classification: Philebus 14c–20a”. In Plato’s Philebus: A Philosophical Discussion. Ed. P. Dimas/R. E. Jones/G. R. Lear. Oxford, 34–54.10.1093/oso/9780198803386.003.0003Search in Google Scholar

Diels H. (ed.) 1882–95. Simplicius. In Aristotelis physicorum libros commentaria, 2 vols. Berlin.10.1515/9783110805017Search in Google Scholar

Dillon, J. 1985. “Xenocrates’ Metaphysics: Fr. 15 (Heinze) Re-Examined”. Ancient Philosophy 5, 47–52.10.5840/ancientphil19855126Search in Google Scholar

–. 2003. The Heirs of Plato: A Study of the Old Academy, 347–274 B.C. Oxford; New York.Search in Google Scholar

–. 2003a. “The Timaeus in the Old Academy”. In Plato’s Timaeus as Cultural Icon. Ed. G. J. Reydams-Schils. Notre Dame, 80–94.Search in Google Scholar

–. 2004. “Atomism in the Old Academy”. Proceedings of the Boston Area Colloquium in Ancient Philosophy 19, 1–17.Search in Google Scholar

–. 2007. “Review: Die Philosophie des Xenokrates im Kontext der alten Akademie by D. Thiel”. The Journal of Hellenic Studies 127, 240–41.Search in Google Scholar

–. 2019. “Xenocrates on Plato, Pythagoras and the Poets”. Méthexis 31, 67–81.10.1163/24680974-03101004Search in Google Scholar

Dillon, J./D. O’Meara, tr. 2006. Syrianus. On Aristotle Metaphysics 13–14. London.Search in Google Scholar

Dörrie, H. 1967. “Xenokrates”. In Paulys Realencyclopaedie der classischen Altertumswissenschaft, vol. IX A.2. Stuttgart, 1512–28.Search in Google Scholar

Drozdek, A. 2007. Greek Philosophers as Theologians: The Divine Arche. Aldershot.Search in Google Scholar

–. 2003. Xenocrates, Fr. 15. Minerva. Revista de Filología Clásica 16, 45–51.Search in Google Scholar

Düring, I. 1968. Aristoteles. In: Paulys Realenzyklopädie der classischen Altertumswissenschaften, supp. XI. Stuttgart,159–336.Search in Google Scholar

–. 1934. Ptolemaios und Porphyrios über die Musik. Hildesheim (repr. 1987).Search in Google Scholar

Federspiel, M. (trans.) 2017. Pseudo-Aristote. Des couleurs. Des sons. Du souffle. Paris.Search in Google Scholar

Forcignanò, F. 2017. Forme, linguaggio, sostanze: il dibattito sulle idee nell’Accademia antica. Milano.Search in Google Scholar

Furley, D. J. 1967. Two Studies in the Greek Atomists. Study I: Indivisible Magnitudes. Princeton.10.1515/9781400879458Search in Google Scholar

Gaiser, K. 1962. Platons ungeschriebene Lehre: Studien zur systematischen und geschichtlichen Begründung der wissenschaften in der platonischen Schule. Stuttgart.Search in Google Scholar

Gerson, L. Ph. 2013. From Plato to Platonism. Ithaca.10.7591/cornell/9780801452413.001.0001Search in Google Scholar

Gottschalk, H. B. 1968. “The De Audibilibus and Peripatetic Acoustics”. Hermes 96(3), 435–60.Search in Google Scholar

Gutas, D. (ed.) 2010. Theophrastus On First Principles (known as his Metaphysics): Greek Text and Medieval Arabic Translation. Leiden.Search in Google Scholar

Guthrie, W. K. Ch. 1978. A History of Greek Philosophy, vol. V. London.10.1017/CBO9780511518430Search in Google Scholar

Heinze, R. 1892. Xenokrates: Darstellung der Lehre und Sammlung der Fragmente. Leipzig.Search in Google Scholar

Hett, W. S. (trans.) 1936. Aristotle. Minor Works. Cambridge, MA.Search in Google Scholar

Huby, P./Taylor, C. C. W. (trans.) 2011. Simplicius. On Aristotle Physics 1.3–4, London.Search in Google Scholar

Isnardi Parente, M. 1981. “Le peri ideôn d’Aristote: Platon ou Xénocrate?” Phronesis 26.2, 135–52.10.1163/156852881X00213Search in Google Scholar

–. 1982. “Un fragment de Xénocrate et le problème de la connaissance sensible”. Revue philosophique de la France et de l’étranger 172(2), 293–305.Search in Google Scholar

–. 1996. “Les témoignages sur Speusippe et Xénocrate dans le premier livre du De Anima”. In Corps et âme: sur le De anima d’Aristote. Ed. G. R. Dherbey/C. Viano. Paris, 107–23.Search in Google Scholar

–. 2008. “Senocrate in Sesto Empirico”. Rivista di Storia della Filosofia 63.3, 477–83.Search in Google Scholar

–. (ed.) 2012. Senocrate e Ermodoro: Testimonianze e frammenti. Edizione rivista e aggiornata a cura di Tiziano Dorandi. Pisa.Search in Google Scholar

–. 2018. “Xénocrate de Chalcédoine”. In Dictionnaire des philosophes antiques, vol. 7. Ed. R. Goulet. Paris, 194–208.Search in Google Scholar

Kenney, J. P. 2010. Mystical Monotheism: A Study in Ancient Platonic Theology. Eugene.Search in Google Scholar

Krämer, H. J. 1964. Der Ursprung der Geistmetaphysik: Untersuchungen zur Geschichte des Platonismus zwischen Platon und Plotin. Amsterdam.Search in Google Scholar

–. 1971. Platonismus und hellenistische Philosophie. Berlin (repr. 2012).Search in Google Scholar

Lederman, H. 2014. “Ho pote on esti and Coupled Entities: A Form of Explanation in Aristotle’s Natural Philosophy”. Oxford Studies in Ancient Philosophy 46, 109–64.10.1093/acprof:oso/9780198712923.003.0004Search in Google Scholar

Lee, E. N. 1966. “On the Metaphysics of the Image in Plato’s Timaeus”. The Monist 50(3), 341–68.10.5840/monist196650326Search in Google Scholar

Muniz, F./Rudebusch, G. 2004. “Plato, Philebus 15b: A Problem Solved”. The Classical Quarterly 54(2), 394–405.10.1093/clquaj/bmh047Search in Google Scholar

Nicol, A.T. 1936. “Indivisible Lines”. The Classical Quarterly 30. 2, 120–26.10.1017/S0009838800012957Search in Google Scholar

Pines, Sh. 1961. “A New Fragment of Xenocrates and Its Implications”. Transactions of the American Philosophical Society 51(2), 3–34.10.2307/1005801Search in Google Scholar

Raffa, M. 2016. Claudio Tolemeo, Armonica. Con il Commentario di Porfirio. Milan.Search in Google Scholar

Reeve, C. D. C. (trans.) 2016. Aristotle: Metaphysics. Indianapolis.Search in Google Scholar

–. (trans.) 2018. Aristotle: Physics. Indianapolis.Search in Google Scholar

Roark, T. 2011. Aristotle on Time: A Study of the Physics. Cambridge.10.1017/CBO9780511753664Search in Google Scholar

Ross, W. D. 1923–24. Aristotle’s Metaphysics. A Revised Text with Introduction and Commentary, 2 vols. Oxford.Search in Google Scholar

–. 1936. Aristotle’s Physics: A Revised Text with Introduction and Commentary. Oxford.Search in Google Scholar

Sachs, E. 1917. Die fünf platonischen Körper. Berlin.Search in Google Scholar

Sattler, B. 2020. The Concept of Motion in Ancient Greek Thought: Foundations in Logic, Method, and Mathematics. Cambridge.10.1017/9781108775199Search in Google Scholar

Schütrumpf, E. (ed.)/Stork, P./van Ophujsen, J./Prince, S. (trans.) 2017. Heraclides of Pontus: Texts and Translations. London.10.4324/9780203790151Search in Google Scholar

Sedley, D. 1976. “Epicurus and His Professional Rivals”. In Études sur l’épicurisme antique. Ed. J. Bollack/Laks, A. Lille, 119–59.10.4000/books.septentrion.118335Search in Google Scholar

–. 2002. “The Origins of Stoic God”. In Traditions of Theology: Studies in Hellenistic Theology, Its Background and Aftermath. Ed. D. Frede/A. Laks. Leiden, 41–83.Search in Google Scholar

–. 2003. Plato’s Cratylus. Cambridge.Search in Google Scholar

–. 2021. “Xenocrates’ Invention of Platonism”. In Authority and Authoritative Texts in the Platonist Tradition. Ed. M. Erler/J. E. Heßler/F. Petrucci. Oxford, 12–37.Search in Google Scholar

Silverman, A. 2002. The Dialectic of Essence. Princeton.10.1515/9781400825349Search in Google Scholar

Sorabji, R. 1983. Time, Creation, and the Continuum: Theories in Antiquity and the Early Middle Ages. London.Search in Google Scholar

Strang, C./Mills, K. W. 1974. “Plato and the Instant”. Proceedings of the Aristotelian Society, Supplementary Volume 48, 63–96.10.1093/aristoteliansupp/48.1.63Search in Google Scholar

Thiel, D. 2006. Die Philosophie des Xenokrates im Kontext der Alten Akademie. München.10.1515/9783110921182Search in Google Scholar

Timpanaro Cardini, M. (ed.) 1970. Pseudo-Aristotele: De lineis insecabilibus. Milano.Search in Google Scholar

Todd, R. B. (ed.) 2013. Themistius: On Aristotle On the Soul. London.Search in Google Scholar

Van Riel, G. 2021. “Matter Doesn’t Matter: On the Status of Bodies in the Timaeus (30a–32b and 53c–61c)”. In Plato’s Timaeus: Proceedings of the Tenth Symposium Platonicum Pragense. Ed. Ch. Jorgenson/F. Karfík/Š. Špinka. Leiden, 169–86.10.1163/9789004437081_010Search in Google Scholar

Verde, F. 2013. Elachista. La dottrina dei minimi nell’epicureismo. Leuven.10.2307/j.ctt9qdznpSearch in Google Scholar

Wehrli, F. 1969. Die Schule des Aristoteles: Texte und Kommentar. Heft 7 : Herakleides Pontikos. Basel.Search in Google Scholar

Zeller, E./Mondolfo, R. 1974. La filosofia dei greci nel suo sviluppo storico. Parte II, volume III/2, a cura di Margherita Isnardi Parente. Firenze.Search in Google Scholar

Zeller, E. 1875. Die Philosophie der Griechen in ihrer geschichtlichen Entwicklung. Theil 2, Abth. 1. 3. Aufl. Leipzig.Search in Google Scholar

Zeyl, D. J., (trans.) 2000. Plato: Timaeus. Indianapolis.Search in Google Scholar

Zhmud, L. 2012. Pythagoras and the Early Pythagoreans. Oxford.10.1093/acprof:oso/9780199289318.001.0001Search in Google Scholar

Published Online: 2022-05-18
Published in Print: 2023-11-20

© 2022 Walter de Gruyter GmbH, Berlin/Boston

Downloaded on 13.5.2024 from https://www.degruyter.com/document/doi/10.1515/agph-2021-0030/html
Scroll to top button