Beyond Aristotle: Indivisibles and Infinite Divisibility in the Later Middle Ages

Total Page：16

File Type：pdf, Size：1020Kb

BEYOND ARISTOTLE: INDIVISIBLES AND INFINITE DIVISIBILITY IN THE LATER MIDDLE AGES John E. Murdoch The basic text for late medieval Latin atomism and its critics was Aristotle’s Physics, especially Book VI. Here the atoms or indivisibles he considered and combatted were extensionless, a conception that can be found in scholastic debate about atoms all the way to Galileo and his atomi non quanti.1 The medieval atomists were clustered in the fourteenth-century,2 as were their Aristotelian critics. Figure 1 provides the basic dramatis personae of the fourteenth-century atomists and their critics. The list of atomists is nearly complete, save for the followers of Wyclif. The list of their critics is naturally less complete, being made up of chiefl y those who name their atomist opponents. Yet even without such identifi cation, we can often tell other critics, such as John Buridan and his school, because they oppose specifi c identifi able atomist arguments. The question of the motives for the late medieval atomism is pretty murky. The motives for Greek atomism are, at least to some extent, an answer to Parmenides’s monism and center in attempts to explain natural phenomena (if not always totally successfully). Equally clear are the motives for the Arabic atomism of the Mutakallimun: namely, to put all causal relations into the hands of God through the mechanism of the doctrine of continuous creation. However, in the case of late medieval atomism there is not such a wholesale application to nature or to a God who creates the universe anew at every instant. 1 Galileo Galilei, Discorsi e dimostrazione matematiche intorno a due nuove scienze, vol. 8, p. 72. There is, of course, the quite separate consideration of minima naturalia that arises out of Aristotle’s criticism of Anaxagoras in Physics, I, ch. 4. For the medieval history, as well as the historiography, of this kind of atomism or corpuscularianism, see Murdoch, “The Medieval and Renaissance Tradition of Minima Naturalia”. 2 For the earlier medieval atomism by the likes of Isidore of Seville, William of Conches, etc., see Pabst, Atomentheorien des lateinischen Mittelalters. For the standard treat- ments of the medieval atomism of the fourteenth century, see Duhem, Le système du monde, vol. 7, pp. 3–157; Maier, “Kontinuum, Minima und aktuell Unendliches,” In Die Vorläufer galileis im 14. Jahrhundert 2nd ed., pp. 155–215; and, more briefl y, Murdoch, “Infi nity and Continuity.” 16 john e. murdoch Dramatis personae INDIVISIBILISTS ARISTOTELIANS E Henry of Harclay William of Alnwick OFM N G Walter Chatton OFM Adam Wodeham OFM L I Crathorn OP Thomas Bradwardine S H John Wyclif William of Ockham OFM Roger Rosetus OFM Walter Burley C Gerard of Odo OFM John the Canon O N Nicholas Bonetus OFM T I John Gedo N E Marcus Trevisano N T Nicholas Autrecourt A L Single line arrows represent (named) criticism Double line arrows represent verbatim borrowing Fig. 1. Fourteenth-Century Indivisibilism and its Critics.

Copy Link

Recommended publications

Galileo's Assayer
University of Nevada, Reno Galileo's Assayer: Sense and Reason in the Epistemic Balance A thesis submitted in partial fulfillment of the requirements for the degree of Master of Arts in History. by James A Smith Dr. Bruce Moran/Thesis Advisor May 2018 c by James A Smith 2018 All Rights Reserved THE GRADUATE SCHOOL We recommend that the thesis prepared under our supervision by JAMES A. SMITH entitled Galileo's Assayer: Sense and Reason in the Epistemic Balance be accepted in partial fulfillment of the requirements for the degree of MASTER OF ARTS Bruce Moran, Ph.D., Advisor Edward Schoolman, Ph.D., Committee Member Carlos Mariscal, Ph.D., Committee Member Stanislav Jabuka, Ph.D., Graduate School Representative David W. Zeh, Ph.D., Dean, Graduate School May, 2018 i Abstract Galileo's The Assayer, published in 1623, represents a turning point in Galileo's philo- sophical work. A highly polemical \scientific manifesto," The Assayer was written after his astronomical discoveries of the moons of Jupiter and sunspots on a rotating sun, but before his mature Copernican work on the chief world systems (Ptolemaic versus Copernican). The Assayer included major claims regarding the place of math- ematics in natural philosophy and how the objects of the world and their properties can be known. It's in The Assayer that Galileo wades into the discussion about the ultimate constituents of matter and light, namely, unobservable particles and atoms. Galileo stressed the equal roles that the senses and reason served in the discovery of knowledge, in contradistinction to Aristotelian authoritarian dogma that he found to hinder the processes of discovery and knowledge acquisition.
[Show full text]
On the Infinite in Leibniz's Philosophy
On the Infinite in Leibniz's Philosophy Elad Lison Interdisciplinary Studies Unit Science, Technology and Society Ph.D. Thesis Submitted to the Senate of Bar-Ilan University Ramat-Gan, Israel August 2010 This work was carried out under the supervision of Dr. Ohad Nachtomy (Department of Philosophy), Bar-Ilan University. Contents א.……………………………….…………………………………………Hebrew Abstract Prologue…………………………………………………………...………………………1 Part A: Historic Survey Methodological Introduction…………………………………………………………..15 1. Aristotle: Potential Infinite………………………………………………………….16 2. Thomas Aquinas: God and the Infinite………………………………………..…….27 3. William of Ockham: Syncategorematic and Actual Infinite……………………..….32 4. Rabbi Abraham Cohen Herrera: Between Absolute Unity and Unbounded Multitude………………………………………………………………………..….42 5. Galileo Galilei: Continuum Constructed from Infinite Zero's………………………49 6. René Descartes: Infinite as Indefinite…………………………………………….…58 7. Pierre Gassendi: Rejection of the Infinite…………………………………………...69 8. Baruch Spinoza: Infinite Unity…………………………………………………...…73 9. General Background: Leibniz and the History of the Infinite……………………....81 Summary…………………………………………………………………………….…94 Part B: Mathematics Introduction…………………………………………………………………………….99 1. 'De Arte Combinatoria' as a Formal Basis for Thought: Retrospective on Leibniz's 1666 Dissertation………………………………………………………………....102 2. Leibniz and the Infinitesimal Calculus……………………………………….……111 2.1. Mathematical Background: Mathematical Works in 16th-17th Centuries…..111 2.2. Leibniz's Mathematical Development…………………………………….…127
[Show full text]
A New Vision of the Senses in the Work of Galileo Galilei
Perception, 2008, volume 37, pages 1312 ^ 1340 doi:10.1068/p6011 Galileo's eye: A new vision of the senses in the work of Galileo Galilei Marco Piccolino Dipartimento di Biologia, Universita© di Ferrara, I 44100 Ferrara, Italy; e-mail: [email protected] Nicholas J Wade University of Dundee, Dundee DD1 4HN, Scotland, UK Received 4 December 2007 Abstract. Reflections on the senses, and particularly on vision, permeate the writings of Galileo Galilei, one of the main protagonists of the scientific revolution. This aspect of his work has received scant attention by historians, in spite of its importance for his achievements in astron- omy, and also for the significance in the innovative scientific methodology he fostered. Galileo's vision pursued a different path from the main stream of the then contemporary studies in the field; these were concerned with the dioptrics and anatomy of the eye, as elaborated mainly by Johannes Kepler and Christoph Scheiner. Galileo was more concerned with the phenomenology rather than with the mechanisms of the visual process. His general interest in the senses was psychological and philosophical; it reflected the fallacies and limits of the senses and the ways in which scientific knowledge of the world could be gathered from potentially deceptive appearances. Galileo's innovative conception of the relation between the senses and external reality contrasted with the classical tradition dominated by Aristotle; it paved the way for the modern understanding of sensory processing, culminating two centuries later in Johannes Mu« ller's elaboration of the doctrine of specific nerve energies and in Helmholtz's general theory of perception.
[Show full text]
The Epistemology Under Locke's Corpuscularianism
THE EPISTEMOLOGY UNDER LOCKE’S CORPUSCULARIANISM Michael Jacovides 1. MACHINES AS MODELS OF INTELLIGIBILITY The intelligibility of our artifacts suggests to many seventeenth century thinkers that nature works along analogous lines, that the same principles that explain the operations of artifacts explain the operations of natural bodies.1 We may call this belief ‘corpuscularianism’ when conjoined with the premise that the details of the analogy depend upon the sub-microscopic textures of ordinary bodies and upon the rapidly moving, imperceptibly tiny corpuscles that surround these bodies.2 Locke’s sympathy for corpuscularianism comes out clearly where he describes the implications of our inability to perceive the sub-microscopic world. If we could, he conjectures, various perplexities would be unknotted. We would solve mysteries of pharmacology, since did we know the Mechanical affections of the Particles of Rhubarb, Hemlock, Opium, and a Man, as a Watchmaker does those of a Watch, whereby it performs its Opera- tions, and of a File which by rubbing on them will alter the Figure of any of the Wheels, we should be able to tell before Hand, that Rhubarb will purge, Hemlock kill, and Opium make a man sleep; as well as a Watch-maker can, that a little piece of Pa- per, laid on the Balance, will keep the Watch from going, till it be removed; or that some small part of it, being rubb’d by a file, the Machin would quite lose its Motion, and the Watch go no more3 (4.3.25). Locke borrows the expression ‘mechanical affections’ from Robert Boyle, who uses it to denote mo- tion, size, figure, and arrangement of parts “because to them men willingly refer the various opera- tions of mechanical engines”4.
[Show full text]
Styles of Experimental Reasoning in Early Modern Chemistry
Styles of Experimental Reasoning in Early Modern Chemistry By Victor Dan Boantza A thesis submitted in conformity with requirements for the degree of Doctor of Philosophy Institute for the History and Philosophy of Science and Technology University of Toronto © Copyright by Victor Dan Boantza 2009 Styles of Experimental Reasoning in Early Modern Chemistry Victor Dan Boantza Doctor of Philosophy Institute for the History and Philosophy of Science and Technology University of Toronto 2009 Abstract The science of chemistry has undergone two major transformative changes during the early modern period, both closely related to two of the most revolutionary episodes in the history of Western science. The dissertation consists of a historical-analytical comparative exploration of early modern chemical thought and practice based on two series of interconnected case studies related, respectively, to the seventeenth-century Scientific Revolution and the eighteenth-century Chemical Revolution. Although rarely considered together in the context of the history of chemistry, during both Revolutions, similar forces combined to generate crises in chemical knowledge and practice, to use a well-known Kuhnian notion. Differences in nature and historical evolution notwithstanding, both instances featured attempts at quantification and physicalist reductions of chemistry: during the 1660s-1680s Boyle advanced a reconciliation of chymical experimental knowledge with the budding mechanical philosophy, predicated upon the physically governed laws of matter and motion; during the last third of the eighteenth-century, Lavoisier (et al.) submitted chemical phenomena to the ‘rule of the balance’, as a part of an all-encompassing experimentalist, theoretical and linguistic reformation anchored in the conservation of weight principle.
[Show full text]
Galileo Galilei by Beatrix Mccrea Galileo Galilei Was an Italian Physicist, Engineer, and Astronomer Bestknown for Disc
3/24/2019 Galileo Galilei - Google Docs Galileo Galilei By Beatrix McCrea Galileo Galilei was an Italian physicist, engineer, and astronomer bestknown for discovering the four largest moons on Jupiter and his theory of gravity. His theory of gravity stated that if a bowling ball and a feather dropped at the same time in space they would land at the same time. He also invented the thermometer and an astronomical telescope. Galileo Galilei was born to Vincenzo Galilei and Giulia Ammanniti in Piza, Italy on February 15, 1564. He was the first of six children. There were two things that happened which led Galileo to find that he loved math and science. On The Famous People the text states “the first incident happened in 1581 when he first noticed that a chandelier despite swinging in small and large arcs took almost the same time to return to the first position.” The other incident was when he accidentally attended a geometry lecture. Both these incidents made Galileo find his love for science. Galileo discovered the four largest moons on Jupiter. On Biography.com it says Galileo Galilei was best known for discovering Jupiter and it’s four biggest moons. The names were Io, Europa, Ganymede, and Callisto. They were discovered by Galileo in January of 1610. Galileo used a better version of the telescope that made him made to see the four moons. Galileo Galilei had a very popular theory of gravity, that if there was no air resistance (like in space) you would drop a bowling ball and a feather and they would land at the exact same time.
[Show full text]
Empirical Support for the Corpuscular Theory in the Seventeenth Century
EMPIRICAL SUPPORT FOR THE CORPUSCULAR THEORY IN THE SEVENTEENTH CENTURY 1. INTRODUCTION The purpose of this paper is to evaluate the empirical content and experimental foundation of the early seventeenth-century corpuscular hypothesis. Supported by ontological, epistemological, and mathematical arguments, observational and experimental evi• dence played an important part in creating those patterns of thought that were instrumental in the transformation and, even• tually, acceptance of the corpuscular theory of matter. Compared to the rise of astronomy and mechanics, the success of seventeenth-century atomism is ambiguous. Unlike other physical theories of the time the atomic doctrine was not based on exper• iments likely to be accepted by today's scientific standards. In Galileo's inclined plane and his law of falling bodies or in Newton's theory of colors and his experimentum crucis with the prism, for example, theory and experiment, observation and conclu• sion were connected in a way still acceptable to us. In atomism, however, this is not the case, although almost all corpuscular theories of the seventeenth century explicitly claimed to be derived from and based upon experience. Yet, it was not until the nineteenth century that experimental results made the atoms at least plausible. The difficult relationship between seventeenth century atomism and its experimental foundation has been obscured to some extent by later historians. When the standard histories of atomism were written at the end of the nineteenth century1, a final experi• mental confirmation of the corpuscular nature of matter was still lacking. Twentieth-century historians, on the other hand, have underestimated the empirical difficulties involved in early modern atomism.2 Knowing that there are atoms in nature, they could hardly imagine how the protagonists of the scientific revolution should not have arrived at this same conclusion.
[Show full text]
New Perspectives on Galileo the University of Western Ontario Series in Philosophy of Science
NEW PERSPECTIVES ON GALILEO THE UNIVERSITY OF WESTERN ONTARIO SERIES IN PHILOSOPHY OF SCIENCE A SERIES OF BOOKS ON PHILOSOPHY OF SCIENCE, METHODOLOGY, AND EPISTEMOLOGY PUBLISHED IN CONNECTION WITH THE UNIVERSITY OF WESTERN ONTARIO PHILOSOPHY OF SCIENCE PROGRAMME Managing Editor J. 1. LEACH Editorial Board J. BUB, R. E. BUTTS, W. HARPER, J. HINTIKKA, D. J. HOCKNEY, C. A. HOOKER, 1. NICHOLAS, G. PEARCE VOLUME 14 NEW PERSPECTIVES ON GALILEO Papers Deriving from and Related to a Workshop on Gali/eo held at Virginia Polytechnic Institute and State University, 1975 Edited by ROBERT E. BUTTS Department of Philosophy, the University of Western Ontario, London, Canada and JOSEPH C. PITT Department of Philosophy and Religion, Virginia Polytechnic Institute and State University, Blacksburg, Virginia, U.S.A. D. REIDEL PUBLISHING COMPANY DORDRECHT : HOLLAND / BOSTON: U.S.A. Library of Congress Cataloging in Publication Data Main entry under title: New perspectives on Galileo. (The University of Western Ontario series in philosophy of science ; v. 14) Bibliography: p. Includes index. 1. S cience-Methodology -Congresses. 2. Science-Philosophy-Congresses. 3. Galilei, Galileo,1564-1642. I. Butts, Robert E. II. Pitt, JosephC. Q174.N48 509 /.2'4 77-17851 ISBN-I3: 978-90-277-0891-5 e-ISBN: 978-94-009-9799-8 DOl: 10.1007/978-94-009-9799-8 Published by D. Reidel Publishing Company, P.O. Box 17, Dordrecht, Holland Sold and distributed in the U.S.A., Canada, and Mexico by D. Reidel Publishing Company,lnc. Lincoln Building, 160 Old Derby Street, Hingham, Mass. 02043, U.S.A. All Rights Reserved Copyright © 1978 by D.
[Show full text]
The Grounds for and Excellence of the Corpuscular Or Mechanical Philosophy
The Grounds for and Excellence of the Corpuscular or Mechanical Philosophy Robert Boyle 1674 Copyright © Jonathan Bennett 2017. All rights reserved [Brackets] enclose editorial explanations. Small ·dots· enclose material that has been added, but can be read as though it were part of the original text. Occasional •bullets, and also indenting of passages that are not quotations, are meant as aids to grasping the structure of a sentence or a thought. Every four-point ellipsis . indicates the omission of a brief passage that seems to present more difﬁculty than it is worth. Longer omissions are reported between brackets in normal-sized type.—This short piece by Boyle opens and closes in the form of a letter; there is no known addressee; and most of the thing reads as though it wasn’t really addressed to any individual.—The section-breaks and -headings are not Boyle’s. First launched: March 2010 Excellence of mechanism Robert Boyle Contents Introduction 1 Four points 2 The versatility of mechanism 3 The world’s soul etc. 6 The top trio 7 Challenges that mechanisms could survive 8 Mechanism isn’t scary 10 Decoding the world 11 Recapitulation 12 Excellence of mechanism Robert Boyle Glossary a priori: When Boyle uses this phrase on page 11 he principle: Throughout the early modern period ‘principle’ isn’t using it in the sense that Kant made famous 80 years (like its cousins in French and Latin) sometimes meant, as it later. That is, he isn’t talking about proving independently does today, a proposition that has some privilege of basicness of all experience that your theory is true.
[Show full text]
History of Philosophy: Early Modern (PHIL 210-3)
History of Philosophy: Early Modern (PHIL 210-3) Professor Baron Reed Spring Quarter, 2019 office: 3-421 Kresge Hall Lutkin Hall email: [email protected] T/TH 12:30-1:50 office hours: T 2:00-3:00, and by appointment Course Description: The transition from the Medieval to the Modern era in philosophy began, roughly, in the late 16th and early 17th centuries and ended, again roughly, in the late 18th century. New methods of acquiring knowledge, along with a radically different conception of the world, permanently transformed the philosophical enterprise and the broader culture. In this course we will examine the views of some of the most important modern philosophers—especially Descartes, Spinoza, Leibniz, Bayle, Locke, Berkeley, and Hume—on the nature of God, causation, substance, mind, knowledge, and the material world. Additional readings will be drawn from Elizabeth, Galileo, Masham, Boyle, Shepherd, and Du Châtelet. Course Objectives: The course has two primary objectives: (A) To reach a deeper understanding of the philosophical developments that followed in the wake of the Reformation and that accompanied, and made possible, the rise of modern science and the broader Enlightenment; and (B) To develop critical thinking, reading, and writing skills, particularly in light of the new attention to philosophical method in the Early Modern period. Emphasis will be placed on both philosophical and historical methods of reading primary sources, as we attempt to understand both the views of these philosophers in their own terms and as they relate to the work of other philosophers and to broader cultural developments. Required Texts: Ariew, Roger and Watkins, Eric (eds.).
[Show full text]
1 Locke on Newton's Principia Mathematica: Mathematics but Not
Locke on Newton’s Principia mathematica: Mathematics but not Natural Philosophy? Michael J. White In his Essay concerning Human Understanding, John Locke explicitly refers to Newton’s Philosophiae naturalis principia mathematica in laudatory but restrained terms: “Mr. Newton, in his never enough to be admired Book, has demonstrated several Propositions, which are so many new Truths, before unknown to the World, and are farther Advances in Mathematical Knowledge” (An Essay Concerning Human Understanding, ed. P. H. Nidditch [Clarendon Press, 1975], 4.7.3). Locke’s restraint stands in contrast to such effusive tributes as Edmund Halley’s Ode (“Come celebrate with me in song the name/ Of Newton, to the Muses dear; for he/ Unlocked the hidden treasuries of Truth:/ So richly through his mind had Phoebus cast/ The radiance of his own divinity./ Nearer the gods no mortal may approach”) or the famous epitaph of Alexander Pope (“Nature and Nature’s laws lay hid in night; / God said, Let Newton be! and all was light”). Of course, Locke was neither a poet nor inclined to make use of a poet’s license. There can be little doubt, I think, that he respected Newton’s prodigious intellect and admired his accomplishments. In the Essay’s “Epistle to the Reader” of 1700, “the incomparable Mr. Newton” is numbered along with Boyle, Sydenham, and Huygens as one of the commonwealth of learning’s master-builders in advancing the sciences. Also more expansive is the 1688 review of Newton’s Principia in Le Clerc’s Bibliothèque universelle et historique, which many scholars now believe was written by Locke, and a passage from Locke’s 1693 Some Thoughts Concerning Education.
[Show full text]
If You Were Not Here Last Week... Please Come to The
http://www.physics.smu.edu/pseudo IF YOU WERE NOT HERE LAST WEEK... PLEASE COME TO THE FRONT OF THE CLASS AND SEE PROF. COTTON. http://www.physics.smu.edu/pseudo “Any sufficiently advanced technology is indistinguishable from magic.” --Arthur C. Clarke, "Profiles of The Future", 1961 (Clarke's third law) English physicist & science fiction author (1917 – 2008) “The Bible shows the way to go to heaven, not the way the heavens go.” --Galileo Galilei “By denying scientific principles, one may maintain any paradox.” --Galileo Galilei http://www.physics.smu.edu/pseudo The Scientific Method (continued) Supplementary Material for CFB3333/PHY3333 Professors John Cotton and Stephen Sekula January 23, 2012 Based on the following information on the web: http://www.physics.smu.edu/pseudo/SciMeth http://www.physics.smu.edu/pseudo But first . some MAGIC! http://www.physics.smu.edu/pseudoAA roundround ofof applauseapplause forfor .. .. .. SCALISE,SCALISE, ILIL MAGNIFICO!MAGNIFICO! Wonder at his powers of levitation! Gasp as he commands the elements of nature! http://www.physics.smu.edu/pseudo GLOSSARY OF CRITICAL DEFINITIONS http://www.physics.smu.edu/pseudo FACT ● The National Academy of Sciences definition of fact: ● An observation that has been repeatedly confrmed and for all practical purposes is accepted as true. "In science, 'fact' can only mean 'confirmed to such a degree that it would be perverse to withhold provisional assent.' I suppose that apples might start to rise tomorrow, but the possibility does not merit equal time in physics classrooms." --Stephen Jay Gould EXAMPLE: At Standard Temperature and Pressure, lead is more dense than water.
[Show full text]