Doing Hard Time: Is God the Prisoner of the Oldest Dimension?
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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 -
The Search for the Historical Gassendi
The Search for the Historical Gassendi Margaret J. Osler University of Calgary Writing about the history of science and the history of philosophy in- volves assumptions about the role of context and about the relationships between past and present ideas. Some historians emphasize the context, concentrating on the intellectual, personal, and social factors that affect the way earlier thinkers have approached their subject. Analytic philoso- phers take a critical approach, considering the logic and merit of the arguments of past thinkers almost as though they are engaging in contem- porary debates. Some philosophers use the ideas of historical ªgures to support their own philosophical agendas. Scholarly studies of the French natural philosopher Pierre Gassendi (1592–1655) exemplify many of these approaches. What, then, is context? At the most basic level, the context is the text itself. The most acontextual scholars examine only snippets of the text. In- terested in ideas about necessity, arguments for the existence of God, or ideas about matter and gravity, they mine the writings of historical ªgures for their views on these questions without considering the author’s aim for the book or project as a whole. This approach has frequently characterized discussions of Gassendi’s philosophy. His major work, the Syntagma Philo- sophicum, is a massive treatise in difªcult neo-Latin, daunting to all but the hardiest (or most foolish) of scholars. Consequently, of those philosophers and historians who deal with Gassendi at all, many rely on the bits that have been translated into English or French or those that deal with speciªc topics and seldom consider the entirety of his work, but the work as a whole gives the parts their meaning. -
Pierre Gassendi's Animals
[Intellectual History Archive 3, 2018] Begley, Pierre Gassendi’s Animals PIERRE GASSENDI’S ANIMALS: A CASE OF EXCLUSION Justin Begley1 University of Helsinki I. Introduction: A Learned Vegetarian The French priest, professor of mathematics, historian, and philosopher, Pierre Gassendi, was perhaps the most influential and well-respected thinkers of his day. 2 While the linguistic and conceptual complexity of his Latin tomes excluded him from the philosophical canon that was formed during the late eighteenth, historians are now beginning to appreciate just how central his ideas were to the development of early modern intellectual life. But recent studies of Gassendi have consistently bypassed a major component of his thought: his defense of a vegetarian diet.3 Conversely, because it is no small task to identify and translate the relevant passages from Gassendi’s oeuvre, historical surveys of vegetarianism have mostly neglected his arguments. Indeed, in the history of vegetarianism, emphasis has been placed on religious sectarians or intellectual outsiders such as Thomas Bushnell and Roger Crab, while figures such as Gassendi who were, historically speaking, intellectual insiders have paradoxically been neglected. 4 Proponents of vegetarianism have thus been shaped teleologically as progressive or even “radical” thinkers. But Gassendi remained thoroughly embedded in the institutions of his day, and channeled the full gamut of humanist apparatuses in his endeavor to integrate the philosophy of the ancient Greek atomist, Epicurus, into the university curriculum. For this purpose, he sought to cleanse Epicurean philosophy of its popular associations with excess, atheism, and debauchery 1 [email protected] 2 Meric Casaubon, Generall Learning: A Seventeenth-Century Treatise on the Formation of the General Scholar, ed. -
Seventeenth-Century News
131 seventeenth-century news Michael Edwards. Time and The Science of The Soul In Early Modern Philosophy. Brill’s Studies in Intellectual History 224. Leiden: Brill, 2013. x + 224 pp. $128.00. Review by Karin Susan Fester, Independent Scholar. This is a book for philosophers who are not only interested in the concept of time, but who seek new perspectives on this intriguing and problematical philosophical concept as well as appreciate what René Descartes and Thomas Hobbes have to say about it. Michael Edwards’ book is distinctive because it focuses attention on the numerous late Aristotelian thinkers who assumed that the soul’s diverse functions played an active role in the concept of time. More precisely, it is de- voted to the aspects of time which have either not been thoroughly examined or omitted by other historians of early modern philosophy; instead, these other scholars have shown how Aristotelian natural philosophy was concentrated on “space” rather than “time.” Edwards argues that time is somehow intimately connected to the human ra- tional soul—“‘relative’ or as dependent on motion and the soul”—and this, of course, contrasts with Isaac Newton’s (1642–1727) concept of time as something ‘absolute’ (6). The author seems to achieve a persuasive argument, and he invokes elements from early modern commentaries and textbooks concerning Aristotle’s Physics and De Anima and attempts to find connections and influential elements to the natural and political philosophy of Descartes and Hobbes in the seventeenth century. The in-depth Introduction begins with delineating distinct ways of conceptualizing time: absolute and relative. -
E D I T O R I a L
E D I T O R I A L “RETRO-PROGRESSING” As one browses through the history section of a library, one of the volumes that is likely to catch one’s attention is The Discoverers by Daniel Boorstin.1 It is an impressive, 700-page volume. Published in 1983, it chronicles in a semi-popular style selected aspects of man’s discoveries. Two chapters entitled “The Prison of Christian Dogma” and “A Flat Earth Returns” deal with the outlandish con- cept of an earth that is flat instead of spherical. Boorstin has impressive academic credentials from Harvard and Yale, and has held prestigious positions such as the Librarian of Congress, Director of the National Museum of History and Tech- nology, and Senior Historian of the Smithsonian Institution. In The Discoverers he reflects the popular view that the ancient Greeks, including Aristotle and Plato, believed Earth to be a sphere; however, after the rise of Christianity a period of “scholarly amnesia” set in which lasted from around 300 to 1300 A.D. During this time, according to Boorstin, “Christian faith and dogma replaced the useful [spherical] image of the world that had been so slowly, so painfully, and so scrupulously drawn by ancient geographers.” The “spherical” view was replaced by the concept of a flat earth, which Boorstin characterizes as “pious caricatures.”2 Boorstin bolsters his case by mentioning a couple of minor writers — Lactantius and Cosmas — who believed in a flat earth and lived during this “dark age.” He also implicates the powerful authority of St. Augustine of Hippo (354-430), who “heartily agreed” that antipodes “could not exist.”3 Antipodes represented lands on the opposite side of a spherical earth where trees and men, if present, would be upside down, with their feet above their heads; hence, the “antipodes” (opposite-feet) designation. -
Nominalism and Constructivism in Seventeenth-Century Mathematical Philosophy
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Elsevier - Publisher Connector Historia Mathematica 32 (2005) 33–59 www.elsevier.com/locate/hm Nominalism and constructivism in seventeenth-century mathematical philosophy David Sepkoski Department of History, Oberlin College, Oberlin, OH 44074, USA Available online 27 November 2003 Abstract This paper argues that the philosophical tradition of nominalism, as evident in the works of Pierre Gassendi, Thomas Hobbes, Isaac Barrow, and Isaac Newton, played an important role in the history of mathematics during the 17th century. I will argue that nominalist philosophy of mathematics offers new clarification of the development of a “constructivist” tradition in mathematical philosophy. This nominalist and constructivist tradition offered a way for contemporary mathematicians to discuss mathematical objects and magnitudes that did not assume these entities were real in a Platonic sense, and helped lay the groundwork for formalist and instrumentalist approaches in modern mathematics. 2003 Elsevier Inc. All rights reserved. Résumé Cet article soutient que la tradition philosophique du nominalisme, évidente dans les travaux de Pierre Gassendi, Thomas Hobbes, Isaac Barrow et Isaac Newton, a joué un rôle important dans l’histoire des mathématiques pendant le dix-septième siècle. L’argument princicipal est que la philosophie nominaliste des mathématiques est à la base du développement d’une tradition « constructiviste » en philosophie mathématique. Cette tradition nominaliste et constructiviste a permis aux mathématiciens contemporains de pouvoir discuter d’objets et quantités mathématiques sans présupposer leur réalité au sens Platonique du terme, et a contribué au developpement desétudes formalistes et instrumentalistes des mathématiques modernes. -
Introduction
Cambridge University Press 978-0-521-86613-2 - Pierre Gassendi and the Birth of Early Modern Philosophy Antonia Lolordo Excerpt More information Introduction This book is bothaninterpretation of Gassendi’s central metaphysical, epistemological, and natural philosophical views and an advertisement for their philosophical and historical interest. Historians of seventeenth- century philosophy can usually tell you that Gassendi was an atomist, an empiricist,oramitigated skeptic, as well as an opponent of Aristotle and Descartes. They might add that he attempted to revive Epicureanism. However, few are likely to have any clear conception ofthe theses Gassendi articulates, the argumentsheoffers in their defense, or the systematic connections between them. This is an unfortunatesituation, and I aim to remedy it. There are at leasttwo reasons why those of us who are interested in early modern philosophy and natural philosophy need to know more about Gassendi. The first is widely recognized. Gassendi’s influence and the importance he was accorded by his peers and close contemporaries is unquestionable. Gassendi was a central figure in seventeenth-century philosophy and, as such, very importantfor the development of mod- ern philosophical thought. He knew and was known by such figures as Descartes and Hobbes and is importantfor understanding Leibniz, Locke, and Newton. Were one a seventeenth-century intellectual who found Cartesianism unacceptable, Gassendi’s philosophy was the obvi- ous alternative. Less well known, however, is the philosophical interest -
7. Mathematical Revival in Western Europe
7. Mathematical revival in Western Europe (Burton , 6.2 – 6.4, 7.1 ) Mathematical studies and discoveries during the early Dark Ages in Europe were extremely limited . One illustration of this fact is the chronology of the highly esteemed English scholar Bede (The Venerable Bede , 672 /673 – 735) , which set the convention that the year 1 B.C.E. immediately precedes the year 1 A.D. ; this remains unchanged even though 0 is now generally accepted to be part of the number system . However , there were contributors to the subject during the period from the Latin commentator Boëthius (Anicius Manlius Severinus Boëthius , c. 475 – 524) shortly after the fall of the Western Roman Empire and continuing through to the end of the 12 th century ; Boëthius has been described as the last of the Romans and the first of the scholastic philosophers (predating the latter by many centuries) , and his mathematical texts of were still widely used 600 years after they were written . Several other names from this period are mentioned in Sections 5.4 and 6.1 of Burton , and the latter ’s exercises also mention Alcuin of York (735 – 804) and Gerbert d ’Aurillac (940 – 1003) , who later became Pope Sylvester I I (997 – 1003) . During the second half of the 11 th century some important political developments helped raise European ’s consciousness of ancient Greek mathematical work and the more recent advances by Indian and Arabic mathematicians. Many of these involved Christian conquests of territory that had been in Muslim hands for long periods of time . Specific examples of particular importance for mathematics were the Norman conquest of Sicily in 1072 , the Spanish reconquista during which extensive and important territories in the Iberian Peninsula changed from Muslim to Christian hands , and the start of the Crusades in 1095 . -
Semiotic Reflections on Medieval and Contemporary Graphic Representations of Motion
Working paper, presented at the History and Pedagogy of Mathematics Conference, 14-18 July 2008, Mexico City. SEMIOTIC REFLECTIONS ON MEDIEVAL AND CONTEMPORARY GRAPHIC REPRESENTATIONS OF MOTION Luis Radford Université Laurentienne Ontario, Canada Introduction In this paper I will present an ongoing semiotic investigation of motion and some 14th century attempts at representing it in geometrical terms. The semiotic approach that I will follow focuses on the manner in which time, space and velocity were signified in certain historical periods. I take as my starting point the idea that the conceptualisation of motion and its key conceptual elements—speed, time and velocity— can only be understood within the scope of the epistemological configurations that make motion thinkable in a certain way. In other words, any attempt at investigating conceptualizations of time, speed, and velocity needs to take into account the cultural mental structures that underpin them. These cultural mental structures, or épistèmes, to use Michel Foucault’s term, are not mere spiritual or intellectual forms evolving on their own. They arise, acquire shape and evolve under the evolution of social practices, as well as their material conditions, forms of production and social relations. Thus, in the perspective that I am advocating here, to ask questions about time, speed and velocity is also to ask questions about the cultural and social conditions that made these theoretical constructs possible. Time, Speed and Velocity in the Middle Ages It is very well known that the investigation of motion became a prominent field of research only in the early years of modernity. However, that does not mean that motion was not an object of reflection in previous historical periods. -
Oelze (Humboldt University of Berlin)
Summary of Talk Given at the Conference “Immateriality, Thinking, and the Self in the Long Middle Ages” University of Cambridge, Philosophy Faculty, 14 July, 2015 Material Souls, Material Thoughts? Some Medieval Views on Rational Operations in Non-Rational Animals Anselm Oelze (Humboldt University of Berlin) Introductory Remarks Medieval theories of animal cognition by and large start from the assumption that only human animals are endowed with intellect (intellectus) and reason (ratio). That is, ac- cording to the standard medieval view, dogs, cats, donkeys, and other nonhuman anim- als have souls, yet their souls are not immaterial intellectual souls but material sensory souls (including usually five external senses as well as a number of so-called internal senses, e.g., common sense, imagination, estimation, and memory). Consequently, they are incapable of engaging in rational operations such as concept formation, judging, reasoning, and thinking, for only the intellect has access to the realm of universals (or concepts) which are the building blocks of judgments, syllogisms, and thoughts. Nevertheless, on various occasions medieval philosophers do note that in many cases nonhuman animals seem to judge (iudicare), to reason (ratiocinari, sillogizari), or to think (cogitare), too, insofar as their behaviour seems to be brought about by rational processes. In the following, an overview will be given of what six (later) medieval au- thors, namely Thomas Aquinas, Gregory of Rimini, Roger Bacon, Albertus Magnus, John Buridan, and Nicole Oresme, say on how there can be rational processes in non-ra- tional animals, especially reasoning and thinking (note that ʻreasoningʼ and ʻthinkingʼ are not necessarily synonymous here; rather, reasoning is taken to be some type of thinking; for more on that see Section III). -
Polish Translation of Gassendi's Polemic with Descartes
http://dx.doi.org/10.12775/szhf.2018.035 Joanna Usakiewicz University of Białystok, Białystok, Poland e-mail: [email protected] Jerzy Kopania e-mail: [email protected] Polish Translation of Gassendi’s Polemic with Descartes. Description of the Completed Research Project The completion of the following research project involved translating into Polish the work by Pierre Gassendi Disquisitio metaphysica, which is a po- lemic with René Descartes’ Meditations on First Philosophy.1 The description consists of the aim of the project, translation methodology as well as the con- tent summary and the major theses of the introduction to the translation. The project was financed by the National Science Centre under the de- cision DEC-2013/09/B/HS1/01994. The Centre, based in Cracow, finances original research, i.e. experimental or theoretical research which is to pro- duce new knowledge without aiming at immediate commercial application. This project was completed within the years 2014-2017. 1 This work has been carried out thanks to the support of the National Science Centre (Poland), grant: DEC-2013/09/B/HS1/01994. 157 JOA NNA USAKIewICZ, JERZY KOPANIA 1. Origin and aim of translation I n the Polish humanities Pierre Gassendi (1592–1655) is associated pri- marily with his polemic against René Descartes’ Meditations on First Philoso- phy. Of all prolific lifework only a small portion was translated into Polish in 1964, namely a modest part of the treatise Syntagma philosophicum – the introduction (devoted to philosophy) and the first part (devoted to the the- ory of cognition and logic).2 The edition contains the introduction by Leszek Kołakowski3 which has so far been the only overall discussion of Gassendi’s philosophy in Polish. -
The Earliest Translations of Aristotle's Politics and The
ECKART SCHÜTRUMPF THE EARLIEST TRANSLATIONS OF ARISTOTle’S POLITICS AND THE CREATION OF POLITICAL TERMINOLOGY 8 MORPHOMATA LECTURES COLOGNE MORPHOMATA LECTURES COLOGNE 8 HERAUSGEGEBEN VON GÜNTER BLAMBERGER UND DIETRICH BOSCHUNG ECKART SCHÜTRUMPF THE EARLIEST TRANSLATIONS OF ARISTOTLe’s POLITICS AND THE CREATION OF POLITICAL TERMINOLOGY WILHELM FINK unter dem Förderkennzeichen 01UK0905. Die Verantwortung für den Inhalt der Veröffentlichung liegt bei den Autoren. Bibliografische Informationen der Deutschen Nationalbibliothek: Die Deutsche Nationalbibliothek verzeichnet diese Publikation in der Deutschen National biblio grafie; detaillierte Daten sind im Internet über www.dnb.dnb.de abrufbar. Alle Rechte, auch die des auszugweisen Nachdrucks, der fotomechanischen Wieder gabe und der Übersetzung vorbehalten. Dies betrifft auch die Vervielfälti gung und Übertragung einzelner Textabschnitte, Zeichnungen oder Bilder durch alle Verfahren wie Speicherung und Übertragung auf Papier, Transparente, Filme, Bänder, Platten und andere Medien, soweit es nicht § 53 und 54 UrhG ausdrücklich gestatten. © 2014 Wilhelm Fink, Paderborn Wilhelm Fink GmbH & Co. VerlagsKG, Jühenplatz 1, D33098 Paderborn Internet: www.fink.de Lektorat: Sidonie Kellerer, Thierry Greub Gestaltung und Satz: Kathrin Roussel, Sichtvermerk Printed in Germany Herstellung: Ferdinand Schöningh GmbH & Co. KG, Paderborn ISBN 978-3-7705-5685-4 CONTENT 1. The earliest Latin translations of Aristotle— William of Moerbeke 9 2. Nicole Oresme 25 3. Leonardo Bruni’s principles of translation 28 4. Bruni’s translation of Aristotle’s Politics 33 5. The political terminology in Bruni’s translation— a new Humanist concept of res publica? 39 6. The controversy over Bruni’s translation— contemporary and modern 65 Appendix 77 Bibliography 78 This study goes back ultimately to a response I gave on two pa pers presented on “Translating Aristotle’s Politics in Medieval and Renaissance Europe” at the “International Conference on Translation.