Medieval Cosmology : Theories of Infinity, Place, Time, Void, and the Plurality of Worlds

These selections from Le système du monde, the classic ten-volume history of the physical sciences written by the great French physicist [Pierre Duhem](http://www.encyclopedia.com/topic/Pierre_Maurice_Marie_Duhem.aspx#1) (1861-1916), focus on cosmology, Duhem's greatest interest. By reconsidering the work of such Arab and Christian scholars as Averroes, Avicenna, Gregory of Rimini, Albert of Saxony, Nicole Oresme, Duns Scotus, and William of Occam, Duhem demonstrated the sophistication of medieval science and cosmology. * * * For the incredible story regarding the opposition to the publication of this work, which lasted a half-century, see [Stanley L. Jaki](http://www.sljaki.com/)'s [*Reluctant Heroine*](https://isidore.co/calibre/#panel=book_details&book_id=9479) (1992). * * * Condensing the 10-volume work of the author [Le système du monde, Vols. 1–10, Hermann, Paris, 1913–1959] was certainly not an easy task. In fact the present book is not a digest of Duhem's work but a selection of several chapters devoted to the five following themes: infinity, place, time, void and plurality of worlds. The selected chapters, with the exception of one, are taken from Duhem's volumes VII–X, to wit, posthumous parts of Le système du monde which deal with abstract foundations of medieval cosmology. Consequently the outline of Duhem's work in the English translation is modified as compared to the French publication. This change as well as the selection of chapters are justified by the translator as follows: (1) a topical arrangement instead of a chronological one or one by author was chosen by Duhem himself in the last part published before he died (Volumes VI–IX); (2) all the selected chapters deal with medieval commentaries on Books III and IV of Aristotle's Physics in which the author proceeds topically; (3) this selection provides the reader with the best set of chapters by which to judge Duhem's bold historical thesis: that the condemnations of the Averroësism brought forth by Étienne Tempier (Bishop of Paris) in 1277 were the "birth certificate'' of modern science. So we have here a coherent book which will give to a wider readership a representative idea of Duhem's monumental work—which still remains unreplaced for the specialists. The English translation is very close to the French text within a few minute shades. As to Duhem's French translations of Medieval Latin texts the translator adopted the attitude of rendering Duhem's translations as faithfully as possible and of giving all pertinent references to the original texts. Duhem's footnotes are also translated with some bracketed additional precisions or references. One also finds a bibliography of the medieval works cited by Duhem, with up-to-date references, a selected Duhem bibliography and a selected bibliography of works on medieval physics published after Duhem's books. This English translation is introduced by an interesting foreword by Jaki on Duhem's life and work. Reviewed by [Anne Tihon](http://ams.rice.edu/mathscinet/search/author.html?mrauthid=228835) Contents 6 Foreword, by Stanley L. Jaki 12 Preface 20 Part I: The Two Infinites 34 1. Infinitely Small and Infinitely Large (VII, 3-88) 36 Actual Infinity in Number and the Immortality of the Soul 36 Geometric Arguments against Infinite Divisibility 51 Are Invisibles Pure Abstractions? 53 The Nature Minimum of a Substance 68 Infinite Divisibility: Categorematic and Syncategorematic Infinities 78 The Concept of Limit: Maximum and Minimum 89 2. Infinitely Large (VII, 89-157) 106 The Scholastic Formulation of the Problem of the Infinitely Large 106 The Possibility of the Syncategorematic Infinite 111 The Possibility of the Categorematic Infinite: First Attempts 122 The Possibility of the Categorematic Infinite: The Doctrine of Gregory of Rimini 142 Gregory of Rimini's Adversaries: John Buridan and Albert of Saxony 152 Gregory of Rimini's Followers: Nicole Oresme and Marsilius of Inghen 159 3. Infinity in Fifteenth-Century Cosmology: Paul of Venice (X, 392-96) 166 Part II: Place 170 4. Theory of Place before the Condemnations of 1277 (VII, 158-202) 172 Arabic Theory of Place 172 The Questions of Master Roger Bacon 176 Albertus Magnus 181 Saint Thomas Aquinas 186 Giles of Rome 192 Graziadei of Ascoli 196 Roger Bacon 202 The Place of the World in the Firmament: Campanus of Novara and Pierre d'Ailly 206 5. Theory of Place from the Condemnations of 1277 to the End of the Fourteenth Century (VII, 202-302) 212 A Proposition Condemned by Etienne Tempier: Richard of Middleton 212 John Duns Scotus 216 John of Jandun 221 The Scotist School 230 John of Bassols 239 William of Ockham 240 Walter Burley 253 Nicholas Bonet 262 John Buridan 270 Albert of Saxony 280 Marsilius of Inghen and John Buridan II 285 The immobility of Place and God's Immutability: Thomas Wilton, Francis of Mayronnes, Nicholas Bonet, and Nicole Oresme 290 6. Place in Fifteenth-Century Cosmology 302 Nicholas of Orbellis (X, 50) 302 George of Brussels and Thomas Bricot (X, 79-81) 303 Fifteenth-Century Albertists and Thomists (X, 159-60) 304 Parisian Doctrines in Germany (X, 204-10) 305 Paul of Venice (X, 396-412) 310 Part III: Time 326 7. Time (VII, 363-411) 328 Time according to John Duns Scotus 328 Time according to Peter Aureol 333 Time according to William of Ockham 338 Time according to William Ockham (continued): The Absolute Clock 342 The Analogy between Time and Place: Franciscus de Marchia 354 Is the Absolute Clock Arbitrarily Chosen? Walter Burley, John Buridan, Albert of Saxony, and Marsilius of Inghen 356 The Atomism of Gerard of Odon and Nicholas Bonet 364 Movement and Time according to Nicholas Bonet. Although Continuous in the Mind, Successive Beings Are Discontinuous in Reality 371 Time according to Nicholas Bonet: Physical Time and Mathematical Time 384 The Problem of the Absolute Clock according to Graziadei of Ascoli 392 Conclusion of the Problem of the Absolute Clock 394 8. Time in Fifteenth-Century Cosmology 398 Paul of Venice (X, 415-17) 398 Part IV: Void 400 9. Void and Movement in the Void (VIII, 7-60) 402 The Void and Arabic Philosophy: Ibn Bajja 402 The Impossibility of Void and Scholasticism before 1277: Ibn Bajja's Argument. Saint Thomas Aquinas and the Concept of Mass 410 The Impossibility of Void and Scholasticism before 1277: The Void and the Plurality of Worlds 420 The Condemnations of 1277 and the Possibility of Void 425 Godfrey of Fontaines 425 Henry of Ghent 426 Richard of Middleton 429 Ramon Lull 431 William Varon 432 John Duns Scotus 433 Joannes Canonicus 436 Petrus Aquilanus 437 Robert Holkot 437 Walter Burley 438 John Buridan 441 Albert of Saxony and Marsilus of Inghen 443 Nicole Oresme 444 Graziadei of Ascoli 446 10. Void in Fifteenth-Century Cosmology 448 Nicholas of Orbellis (X, 50-51) 448 John Hennon (X, 60-62) 449 George of Brussels and Thomas Bricot (X, 81-84) 450 Parisian Doctrines in Germany (X, 210-13) 453 Paul of Venice (X, 417-22) 455 Part V: The Plurality of Worlds 462 11. THe Problem of the Plurality of Worlds in Peripatetic Philosophy (I, 230-41) 464 Aristotle and the Plurality of Worlds 464 The Plurality of Worlds according to Simplicius and Averroes 468 12. The Problem of the Plurality of Worlds in Scholastic Philosophy (IX, 363-430) 474 Scholasticism and the Plurality of Worlds before the Condemnations of 1277. The Plurality of Worlds and the Void: Michael Scot, William of Auvergne, and Roger Bacon. The Plurarlity of Worlds and the Change in Weight according to Its Distance from the Center of the World: Albertus Magnus and Saint Thomas Aquinas 474 The Plurality of Worlds and the Condemnations of 1277: Godfrey of Fontaines, Henry of Ghent, Richard of Middleton, and Giles of Rome 482 William Varon, John of Bassols, and Thomas of Strasburg 488 John of Jandun 493 William of Ockham and Robert Holkot 495 John Buridan and Albert of Saxony 499 Oxford University and the Assimilation of Weight to Magnetic Attraction 504 The Return to Platonic Theory of Weight: Nicole Oresme 505 The Spot on the Lunar Disk (The Man on the Moon) 512 13. The Plurality of Worlds in Fifteenth-Century Cosmology 532 John Hennon (X, 70-72) 532 George of Brussels and Thomas Bricot (X, 94-95) 533 Paul of Venice (X, 437-440) 535 John Major (Etudes II, 92-94) 536 Gaetano of Thienis (Etudes II, 415-16) 537 Nicholas of Cusa (X, 319-24) 538 Notes 544 Bibliography of Works Cited by Duhem (with References to Modern Editions and English Translations) 584 Selected Duhem Bibliography: Historical and Philosophical Works 612 Selected Bibliography of Works on Medieval Physical Sciences after Dunhem 616 Index 630

These selections from Le système du monde, the classic ten-volume history of the physical sciences written by the great French physicist Pierre Duhem (1861-1916), focus on cosmology, Duhem's greatest interest. By reconsidering the work of such Arab and Christian scholars as Averroes, Avicenna, Gregory of Rimini, Albert of Saxony, Nicole Oresme, Duns Scotus, and William of Occam, Duhem demonstrated the sophistication of medieval science and cosmology.