INFINITY IN THE PRESOCRA TICS: A BIBLIOGRAPHICAL AND PHILOSOPHICAL STUDY Infinity in the Presocratics: A BmLIOGRAPHICAL AND PHILOSOPHICAL STUDY by LEO SWEENEY, S. J. The Catholic University of America Foreword by JOSEPH OWENS, C. S8. R. Pontifical Institute of Mediaeval Studies II MARTINUS NIJHOFF / THE HAGUE /1972 @ 1972 by Martinus Nijhoff, The Hague, Netherlands All rights reserved, including the right to translate or to reproduce this book or parts thereof in any form ISBN-13:978-90-247-1170-3 e-1SBN-13:978-94-010-2729-8 DOl: 10.1007/978-94-010-2729-8 To Lee and Adrian Powell, James, John, Jeffrey, Jean, Jay, Jane, Jerry and Mary Ann TABLE OF CONTENTS Abbreviations IX Permissions XIV Foreword by Joseph Owens xvn Introduction xx Mondolfo XXIII Sinnige xxvn Methodology and acknowledgements XXXI CHAPTER ONE: SECONDARY LITERATURE ON ANAXIMANDER 1 Ancient Sources 2 Recent Studies on Anaximander 5 Vlastos, Jaeger, Burch, Kraus 5 Cherniss, Cornford, Matson, McDiarmid 8 HOlscher, Kirk 14 Wisniewski, Kahn 20 Guazzoni Foa, Solmsen, Classen 26 Paul Seligman 29 Guthrie, Gottschalk 33 F. M. Cleve 39 Stokes, Bicknell 41 Other Studies? 49 CHAPTER Two: ANAXIMANDER AND OTHER IONIANS 55 Anaximander 55 Anaximenes, Xenophanes, Heraclitus 65 Conclusion 73 CHAPTER THREE: PYTHAGORAS 74 J. E. Raven 75 vm TABLE OF CONTENTS J. A. Philip 84 Conclusions 91 CHAPTER FOUR: THE ELEATICS 93 Parmenides 93 Burnet, Raven and Guthrie 94 Joseph Owens 97 Loenen 99 Taran 102 Conclusions 105 Zeno 110 Jesse De Boer 112 H. N. Lee 117 Conclusions 119 Melissus 124 Fragment 9 125 Fragment 7 127 Fragment 3 129 Conclusions 130 CHAPTER FIVE: POST-PARMENIDEAN PHILOSOPHERS 136 Empedocles 137 Anaxagoras 144 Infinity and Matter 146 Infinity and Mind 151 Conclusions 155 The Atomists 155 Atomists and Parmenides 156 Indivisibility 161 Infinity 169 CHAPTER SIX: IN RETROSPECT 174 Appendix: Additional Studies on Anaximander 180 Bibliography 185 Index of Topics 206 Index of Passages 214 Index of Names 218 ABBREVIATIONS The following list gives abbreviations of studies frequently referred to within the text or footnotes, as well as in "Bibliography" infra. Ab­ breviations for titles of journals are ordinarily those given in L'annee philologique (Paris: Societe d'Edition "Les Belles Lettres"). ABG Archiv fur Begriffsgeschichte (Bonn: Bouvier). AC L'Antiquite Classique (Louvain). AFC Anales de Filologia Clasica (Buenos Aires: Fac. de Filos. y Letras). AGPh Archiv fur Geschichte der Philosophie (Berlin: W. de Gruyter). AIPhO Annuaire de l'lnstitut de Philologie et d'Histoire Orientales de l'Universite Libre de Bruxelles (Bruxelles: Secret. de l'Institut). AlP American JournaL of PhiloLogy (Baltimore: Johns Hopkins U. Press). APQ American Philosophical Quarterly (Pittsburgh, Pa.: University of Pittsburgh). ASSPh Annuaire de La Societe Suisse de Philosophie (Basel: Verl. fUr Recht und Gesellschaft). BAGB Bulletin de l'Association G. Bude (Paris: Les Belles Lettres). Bailey Cyril Bailey, The Greek Atomists and Epicurus (Oxford: Claren­ don Press, 1928). Bicknell Bicknell, P. J. "To apeiron, apeiros aer and to periechon," Acta Classica, 9 (1966), 27-48. BIPS British Journal for the Philosophy of Science (Cambridge University Press). Burnet, EGP John Burnet, Early Greek Philosophy (London: A. and C. Black, Ltd., [4th ed.] 1930). Cherniss, ACPP Harold Cherniss, Aristotle's Criticism of Presocratic Philosophy (New York: Octagon Books, Inc., 1964). x ABBREVIATIONS CJ Classical Journal (Athens, Ohio: Ohio University). CP Classical Philology (Chicago: University of Chicago Press). CQ Classical Quarterly (Oxford University Press). Cornford,PP F. M. Cornford, Plato and Parmenides. Parmenides' "Way of Truth" and Plato's "Parmenides" Translated with an Introduc­ tion and a Running Commentary (New York: Liberal Arts Press, 1957). Cornford, Prin. Sap. F. M. Cornford, Principium Sapientiae: The Origins of Greek Philosophical Thought (Cambridge: University Press, 1952). CR Classical Review (Oxford University Press). CW The Classical World (Newark, N.J.: Rutgers State University). DK Diels, H. and Kranz, W. Die Fragmente der Vorsokratiker, 3 vols. (ZUrich: Weidmann, [6th ed.] 1951; reprinted 1966). EP Encyclopedia of Philosophy, ed. Paul Edwards (New York: The Macmillan Company and the Free Press, 1967). Frankel, Wege und Formen Hermann Frankel, Wege und F ormen friih­ griechischen Denkens, herausgegeben von Franz Tietze (2nd ed.; MUnchen: C. H. Beck, 1960). Frankel, Dichtung Hermann Frankel, Dichtung und Philosophie des friihen Griechentums (2nd ed.; Munchen: C. H. Beck, 1962). Furley. David J. Furley, Two Studies in Greek Atomists: Indivisible Magnitudes: Aristotle and Epicurus on Voluntary Action (Princeton University Press, 1967). Furley "Aristotle and the Atomists" David J. Furley, "Aristotle and the Atomists on Infinity," Naturphilosophie bei Aristoteles und Theophrast (Verhandlungen des 4. Symposium Aristotelicum). (Heidelberg: Lothar Stiehm, 1969). Pp. 85-96. G w. K. C. Guthrie, A History of Greek Philosophy. Volume One: The Earlier Presocratics and the Pythagoreans. Volume Two: The Presocratic Tradition from Parmenides to Democritus. (Cambridge: University Press, 1962 and 1965). GM Giornale de Metajisica (Genova: Universita). Heath Sir Thomas Heath, A History of Greek Mathematics. Volume One: From Thales to Euclid. Volume Two: From Aristarchus to Diophantus (Oxford: Clarendon Press, 1921). HSCP Harvard Studies in Classical Philology (Cambridge, Mass.: Harvard University Press). IPQ I nternational Philosophical Quarterly (New York: Fordham University Press). ABBREVIA TIONS XI Jaeger, TEGP Werner Jaeger, The Theology of the Early Greek Philosophers (Oxford: Clarendon Press, 1947). 'HI Journal of the History of Ideas (New York: College of the City of New York). JHP Journal of the History of Philosophy (Berkeley: University of California Press). IRS Journal of Hellenic Studies (London). IP Journal of Philosophy (Columbia University). Kahn Charles H. Kahn, Anaximander and the Origins of Greek Cosmology (New York: Columbia University Press, 1960). Kerferd G. B. Kerferd, "'Recent Work on Presocratic Philosophers," American Philosophical Quarterly, 2 (1965), 130-40. Kerschensteiner Jula Kerschensteiner, Kosmos: Quellenkritische Unter­ suchungen zu den Vorsokratikern (Munchen: C. H. Beck, 1962). KR G. S. Kirk and J. E. Raven, The Presocratic Philosophers. A Critical History with a Selection of Texts (Cambridge: Univer­ sity Press, [4th printing] 1963). Krober Gunter Krober, Wissenschaft und Weltanschauung in der Antike von den Anfiingen bis Aristoteles (Berlin: VEB Deutscher Verlag der Wissenschaften, 1966). Loenen J. H. M. M. Loenen, Parmenides, Melissus, Gorgias. A Reinter­ pretation of Eleatic Philosophy (Assen: Royal Van Gorcum Ltd., 1959). LThPh Laval TMologique et Philosophique (Quebec; Ed. de l'Universite Laval). MH Museum Helveticum. Revue Suisse pour l'Etude de I'Antiquite classique (Bale: Schwabe). Mondolfo Rodolfo Mondolfo, L'infinito nel pensiero dell'antichita clas­ sica (Firenze: "La Nuova Italia" Editrice, 1956). Mourelatos A. P. D. Mourelatos. The Route of Parmenides (New Haven: Yale U. Press, 1970). MS Mediaeval Studies (Toronto: Pontifical Inst. of Mediaeval Studies). NeE The New Catholic Encyclopedia (New York: McGraw-Hill Book Company, 1967). NS The New Scholasticism (Washington, D.C.: The American Catholic Philosophical Association). Owens, Hist. Joseph Owens, C. Ss. R., A History of Ancient Western Philosophy (New York: Appleton-Century-Crofts, Inc., 1959). PAS Proceedings of the Aristotelian Society (Great Britain). XII ABBREVIA TIONS Philip J. A. Philip, Pythagoras and Early Pythagoreanism (Toronto: University Press, 1966). PQ Philosophical Quarterly (St. Andrews, Scotland: University of St. Andrews Press). PR Philosophical Review (Ithaca, New York: Cornell University). Raven, PE J. E. Raven, Pythagoreans and Eleatics: An Account of the Interaction Between the Two Opposed Schools During the Fifth and Early Fourth Centuries B. C. (Cambridge: University Press, 1948). RE Realencyclopadie des klassischen Altertums, ed. Wissowa, Kroll et al. (Stuttgart: J. B. Metzler; Alfred Druckenmiiller, 1892- ). RecSR Recherches de Science Religieuse (Paris). REG Revue des Etudes Grecques (Paris: Les Belles Lettres). RFil (Madrid) Revista de Filosofia (Madrid: lnst. Luis Vives). RFNS Revista di Filosofia Neo-scolastica (Italy). RhM Rheinisches Museum (Frankfurt: Sauerlander). RM Review of Metaphysics (Catholic U. of America). RPhilos Revue philosophique de la France et l'Etranger. RPhL Revue Philosophique de Louvain (Louvain: Institut Superieur de Philosophie). RIL Rendiconti dell'Istituto Lombardo (Milano: 1st. Lombardo). RMM Revue de Metaphysique et de Morale (Paris: Colin). RPh Revue de Philologie (Paris: Klincksieck). RS Revue de Synthese (Paris: Albin Michel). RSF Revista critica di Storia della Filoso/ia (Firenze: La Nuova Italia). RSPh Revue des Sciences Philosophiques et Theologiques (Paris: Vrin). SIFC Studi Italiani di Filologia Classica (Firenze: Le Monnier). Sinnige Theo Gerard Sinnige, Matter and Infinity in the Presocratic Schools and Plato (Assen: Van Gorcum and Company; New York: Humanities Press, 1968). Solmsen, Aristotle's System Friedrich Solmsen, Aristotle's System of the Physical World. A Comparison with his Predecessors (Ithaca, New York: Cornell University Press, 1960). Stokes Stokes. M. C. "Hesiodic and Milesian Cosmogonies," Phronesis, 7 (1962), 1-25 and 8 (1963), 1-34. TAPA Transactions and Proceedings of the American Philological As­ sociation (Cleveland: Press