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A Mathematician Reads Plutarch: Plato's Criticism of Geometers of His Time
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Scholarship@Claremont Journal of Humanistic Mathematics Volume 7 | Issue 2 July 2017 A Mathematician Reads Plutarch: Plato's Criticism of Geometers of His Time John B. Little College of the Holy Cross Follow this and additional works at: https://scholarship.claremont.edu/jhm Part of the Ancient History, Greek and Roman through Late Antiquity Commons, and the Mathematics Commons Recommended Citation Little, J. B. "A Mathematician Reads Plutarch: Plato's Criticism of Geometers of His Time," Journal of Humanistic Mathematics, Volume 7 Issue 2 (July 2017), pages 269-293. DOI: 10.5642/ jhummath.201702.13 . Available at: https://scholarship.claremont.edu/jhm/vol7/iss2/13 ©2017 by the authors. This work is licensed under a Creative Commons License. JHM is an open access bi-annual journal sponsored by the Claremont Center for the Mathematical Sciences and published by the Claremont Colleges Library | ISSN 2159-8118 | http://scholarship.claremont.edu/jhm/ The editorial staff of JHM works hard to make sure the scholarship disseminated in JHM is accurate and upholds professional ethical guidelines. However the views and opinions expressed in each published manuscript belong exclusively to the individual contributor(s). The publisher and the editors do not endorse or accept responsibility for them. See https://scholarship.claremont.edu/jhm/policies.html for more information. A Mathematician Reads Plutarch: Plato's Criticism of Geometers of His Time Cover Page Footnote This essay originated as an assignment for Professor Thomas Martin's Plutarch seminar at Holy Cross in Fall 2016. -
A Short History of Greek Mathematics
Cambridge Library Co ll e C t i o n Books of enduring scholarly value Classics From the Renaissance to the nineteenth century, Latin and Greek were compulsory subjects in almost all European universities, and most early modern scholars published their research and conducted international correspondence in Latin. Latin had continued in use in Western Europe long after the fall of the Roman empire as the lingua franca of the educated classes and of law, diplomacy, religion and university teaching. The flight of Greek scholars to the West after the fall of Constantinople in 1453 gave impetus to the study of ancient Greek literature and the Greek New Testament. Eventually, just as nineteenth-century reforms of university curricula were beginning to erode this ascendancy, developments in textual criticism and linguistic analysis, and new ways of studying ancient societies, especially archaeology, led to renewed enthusiasm for the Classics. This collection offers works of criticism, interpretation and synthesis by the outstanding scholars of the nineteenth century. A Short History of Greek Mathematics James Gow’s Short History of Greek Mathematics (1884) provided the first full account of the subject available in English, and it today remains a clear and thorough guide to early arithmetic and geometry. Beginning with the origins of the numerical system and proceeding through the theorems of Pythagoras, Euclid, Archimedes and many others, the Short History offers in-depth analysis and useful translations of individual texts as well as a broad historical overview of the development of mathematics. Parts I and II concern Greek arithmetic, including the origin of alphabetic numerals and the nomenclature for operations; Part III constitutes a complete history of Greek geometry, from its earliest precursors in Egypt and Babylon through to the innovations of the Ionic, Sophistic, and Academic schools and their followers. -
Does Pyrrhonism Have Practical Or Epistemic Value? 49
DiegoE.Machuca Does Pyrrhonism HavePractical or Epistemic Value? 1Introduction My purpose in this paper is to examine whether Pyrrhonian scepticism, as this stance is described in Sextus Empiricus’sextant works,has practical or epistemic value. More precisely, Iwould like to consider whether the Pyrrhonist’ssuspension of judg- ment (epochē)and undisturbedness (ataraxia)can be deemed to be of practical or epistemic value. By “practical” value Imean both moral value and prudential value. Moral value refers to moral rightness and wrongness; prudential value to per- sonal or social well-being.Hence, when Iask whether the Pyrrhonist’ssuspension and undisturbedness have practical value, Imean whether they make us behave in amannerthat is morallyright or wrong,and whether they allow us to attain those goals thatwould make it possible to live well. As for “epistemic” value, it ba- sicallyrefers to the values of attaining truth and avoiding error. Hence, when Iask whether the Pyrrhonist’ssuspension has epistemic value, Imean whether it allows us to attain truth and avoid error.Mymain focus will be the practical value of both suspension and undisturbedness, because this is the value thatscholars of an- cient philosophycritical of Pyrrhonism have emphasised. The reason for examining the epistemic value of suspension is thatdoing so will enable afuller assessment of the significance of Pyrrhonism as akind of philosophy, which is my primary concern. Iwill begin by brieflydescribing the states of suspension and undisturbedness and their connection, and by succinctlyconsideringsome objections to the effect that,despite claiming to suspend judgmentacross the board, Pyrrhonists actually hold anumber of beliefs. Thiswill provide the necessary framework for the subse- quent discussions. -
The Influence of Pyrrho of Elis and the Pyrrhonian Praxis of Aporetic
The Influence of Pyrrho of Elis and the Pyrrhonian Praxis of Aporetic Language by © Christopher Craig Dupuis A Thesis submitted to the School of Graduate Studies in partial fulfillment of the requirements for the degree of Master of Arts in Philosophy, Faculty of Arts, Department of Philosophy Memorial University of Newfoundland May, 2014 St. John’s Newfoundland and Labrador 2 Table of Contents Abstract 4 Introduction and Overview 5 Chapter One 1 Pyrrho’s Aporetic Linguistic Praxis 12 1.1 Ataraxia in Epictetus and Epicurus 21 1.2 The Role of Epoche and Ataraxia in Pyrrho 23 1.3 Plato’s Socrates as Pyrrho’s Sage 43 1.4 Pyrrho and Plato’s Phaedo 45 1.5 Pyrrho, the Meno, and The Soul of The Hellenes 48 1.6 Appearances, Customs, and The Soul of the Sceptic 51 1.7 Pyrrho and Plato’s Theaetetus 55 1.8 Chapter One Conclusion 62 Chapter Two 2.1 Introduction: Academic Scepticism 64 2.2 Scepticism up to this Point 65 2.3 Arcesilaus And the Early Academic Sceptics 68 2.4 Carneades And the ‘New’ Academic Sceptics 81 2.5 Connecting with Pyrrho 91 Chapter Three 3.1 Introduction: Later Pyrrhonian Scepticism 95 3.2 Aenesidemus and the Revival of Pyrrhonism 97 3.3 Aenesidemus, Relativity, and Language Practice 107 3.4 Later Pyrrhonism: Sextus Empiricus 112 3.5 Outline of Sextus 118 3.6 Phantasiai 119 3.7 Apprehension 122 3.8 What the Sceptics Do 125 3.9 Ataraxia and Epoche 128 3.10 The Five Ways to Epoche 133 3 3.10.1 The First Trope: Diaphonia 136 3.10.2 The Second Trope: Infinite Regression 138 3.10.3 The Third Trope: Relativity 139 3.10.4 The Fourth -
Boethius the Demiurge
BOETHIUS THE DEMIURGE: TIMAEAN DOUBLE-CIRCLE SPIRAL STRUCTURE IN THE CONSOLATIO by Cristalle N. Watson Submitted in partial fulfilment of the requirements for the degree of Master of Arts at Dalhousie University Halifax, Nova Scotia April 2020 © Copyright by Cristalle N. Watson, 2020 For my Opa, Karl Heinz Hiob 1926-1999 Vir doctissimus & lover of words, who first introduced me to Latin Ars longa, vita brevis ii TABLE OF CONTENTS LIST OF TABLES..............................................................................................................vi LIST OF FIGURES...........................................................................................................vii ABSTRACT.....................................................................................................................viii ACKNOWLEDGEMENTS................................................................................................ix CHAPTER 1: INTRODUCTION........................................................................................1 CHAPTER 2: POETRY AND THE CIRCLE IN THE CONSOLATIO: AN OVERVIEW….............................................................................................................3 2.1 A "MULTIFACETED" CONSOLATIO AND AUTHOR.............................................3 2.2 THE METERS OF THE CONSOLATIO: A NEGLECTED STUDY............................11 2.3 IIIM9: CENTRAL PIVOT, TIMAEAN PARAPHRASE, PRAYER...........................17 2.4 THE CIRCLE IN THE CONSOLATIO AND IN IIIM9.............................................22 -
5. Hipparchus 6. Ptolemy
introduction | 15 catalogue included into his oeuvre? Our answer is in Hipparchus. The catalogue itself has not survived. the positive. We have developed a method to serve However, it is believed that the ecliptic longitude and this end, tested it on several veraciously dated cata- latitude of each star was indicated there, as well as the logues, and then applied it to the Almagest. The reader magnitude. It is believed that Hipparchus localised the shall find out about our results in the present book. stars using the same terms as the Almagest: “the star Let us now cite some brief biographical data con- on the right shoulder of Perseus”,“the star over the cerning the astronomers whose activities are imme- head of Aquarius” etc ([395], page 52). diately associated with the problem as described above. One invariably ponders the extreme vagueness of These data are published in Scaligerian textbooks. One this star localization method. Not only does it imply must treat them critically, seeing as how the Scaligerian a canonical system of drawing the constellations and version of history is based on an erroneous chronol- indicating the stars they include – another stipulation ogy (see Chron1 and Chron2). We shall consider is that there are enough identical copies of a single star other facts that confirm it in the present book. chart in existence. This is the only way to make the verbal descriptions of stars such as the above work 5. and help a researcher with the actual identification of HIPPARCHUS stars. However, in this case the epoch of the cata- logue’s propagation must postdate the invention of Scaligerian history is of the opinion that astron- the printing press and the engraving technique, since omy became a natural science owing to the works of no multiple identical copies of a single work could be Hipparchus, an astronomer from the “ancient” Greece manufactured earlier. -
Safety Vs. Simulation: a Skeptic's Argument
Aporia vol. 27 no. 2—2017 Safety vs. Simulation: A Skeptic’s Argument BRYAN RAGAN will show that Safety-based theories of knowledge which rely on nearby possible worlds fail to resolve the Brain-in-a-Vat (hereafter BiV) version I of the Skeptic’s Argument. These theories rely on the ideas that being a BiV is not a belief which is credible enough to be sincerely held, and that such a belief has a much lower probability of being true than false. BiV is a more modern evolution of Descartes’ “Deceiver God,” and advances in computer technology have made further evolution of this basic epistemic problem possible. By using the Simulation Hypothesis (hereafter Simulation) as put forward by Nick Bostrom, a new version of the Skeptic’s Argument can be constructed. Simulation not only replaces the BiV framing of the Skeptic’s Argument but goes further in arguing that this is actually more likely to be true than the alternative: that we live in a natural (not simulated) reality. The challenges this presents to epistemological theories are nearly identical to the BiV argument or Descartes’ Deceiver God, but the nature of Simulation is especially problematic for any theory of knowledge based on Safety, such as those presented by Ernest Sosa and Duncan Pritchard. The Skeptic’s Argument The Skeptic’s Argument has persisted in the same general form since its conception. It began properly with Descartes in the 1600s when he wrote, Bryan Ragan is a United States Marine Corps veteran who is attending North Carolina State University on the Post-9/11 GI Bill. -
The Project Gutenberg Ebook #31061: a History of Mathematics
The Project Gutenberg EBook of A History of Mathematics, by Florian Cajori This eBook is for the use of anyone anywhere at no cost and with almost no restrictions whatsoever. You may copy it, give it away or re-use it under the terms of the Project Gutenberg License included with this eBook or online at www.gutenberg.org Title: A History of Mathematics Author: Florian Cajori Release Date: January 24, 2010 [EBook #31061] Language: English Character set encoding: ISO-8859-1 *** START OF THIS PROJECT GUTENBERG EBOOK A HISTORY OF MATHEMATICS *** Produced by Andrew D. Hwang, Peter Vachuska, Carl Hudkins and the Online Distributed Proofreading Team at http://www.pgdp.net transcriber's note Figures may have been moved with respect to the surrounding text. Minor typographical corrections and presentational changes have been made without comment. This PDF file is formatted for screen viewing, but may be easily formatted for printing. Please consult the preamble of the LATEX source file for instructions. A HISTORY OF MATHEMATICS A HISTORY OF MATHEMATICS BY FLORIAN CAJORI, Ph.D. Formerly Professor of Applied Mathematics in the Tulane University of Louisiana; now Professor of Physics in Colorado College \I am sure that no subject loses more than mathematics by any attempt to dissociate it from its history."|J. W. L. Glaisher New York THE MACMILLAN COMPANY LONDON: MACMILLAN & CO., Ltd. 1909 All rights reserved Copyright, 1893, By MACMILLAN AND CO. Set up and electrotyped January, 1894. Reprinted March, 1895; October, 1897; November, 1901; January, 1906; July, 1909. Norwood Pre&: J. S. Cushing & Co.|Berwick & Smith. -
Pyrrhonian Skepticism in Diogenes Laertius
SAPERE Scripta Antiquitatis Posterioris ad Ethicam REligionemque pertinentia Schriften der späteren Antike zu ethischen und religiösen Fragen Herausgegeben von Rainer Hirsch-Luipold, Reinhard Feldmeier und Heinz-Günther Nesselrath unter der Mitarbeit von Natalia Pedrique und Andrea Villani Band XXV Pyrrhonian Skepticism in Diogenes Laertius Introduction, Text, Translation, Commentary and Interpretative Essays by Katja Maria Vogt, Richard Bett, Lorenzo Corti, Tiziano Dorandi, Christiana M. M. Olfert, Elisabeth Scharffenberger, David Sedley, and James Warren edited by Katja Maria Vogt Mohr Siebeck SAPERE is a Project of the Göttingen Academy of Sciences and Humanities within the programme of the Union of the German Academies funded by the Federal Republic of Germany and the State of Lower Saxony. e-ISBN PDF 978-3-16-156430-7 ISBN 978-3-16-153336-5 The Deutsche Nationalbibliothek lists this publication in the Deutsche Natio nal- bibliographie; detailed bibliographic data are available in the Internet at http:// dnb.dnb.de. © 2015 by Mohr Siebeck, Tübingen, Germany. www.mohr.de This book may not be reproduced, in whole or in part, in any form (beyond that permitted by copyright law) without the publisher’s written permission. This ap- plies particularly to reproductions, translations, microfilms and storage and pro- cessing in electronic systems. This book was supervised by Heinz-Günther Nesselrath (representing the SAPERE Editors) and typeset by Magdalena Albrecht, Janjenka Szillat and Andrea Villani at the SAPERE Research Institute, Göttingen. Printed by Gulde Druck in Tübin- gen on non-aging paper and bound by Buchbinderei Spinner in Ottersweier. Printed in Germany. SAPERE Greek and Latin texts of Later Antiquity (1st–4th centuries AD) have for a long time been overshadowed by those dating back to so-called ‘classi- cal’ times. -
The Ears of Hermes
The Ears of Hermes The Ears of Hermes Communication, Images, and Identity in the Classical World Maurizio Bettini Translated by William Michael Short THE OHIO STATE UNIVERSITY PRess • COLUMBUS Copyright © 2000 Giulio Einaudi editore S.p.A. All rights reserved. English translation published 2011 by The Ohio State University Press. Library of Congress Cataloging-in-Publication Data Bettini, Maurizio. [Le orecchie di Hermes. English.] The ears of Hermes : communication, images, and identity in the classical world / Maurizio Bettini ; translated by William Michael Short. p. cm. Includes bibliographical references and index. ISBN-13: 978-0-8142-1170-0 (cloth : alk. paper) ISBN-10: 0-8142-1170-4 (cloth : alk. paper) ISBN-13: 978-0-8142-9271-6 (cd-rom) 1. Classical literature—History and criticism. 2. Literature and anthropology—Greece. 3. Literature and anthropology—Rome. 4. Hermes (Greek deity) in literature. I. Short, William Michael, 1977– II. Title. PA3009.B4813 2011 937—dc23 2011015908 This book is available in the following editions: Cloth (ISBN 978-0-8142-1170-0) CD-ROM (ISBN 978-0-8142-9271-6) Cover design by AuthorSupport.com Text design by Juliet Williams Type set in Adobe Garamond Pro Printed by Thomson-Shore, Inc. The paper used in this publication meets the minimum requirements of the American Na- tional Standard for Information Sciences—Permanence of Paper for Printed Library Materials. ANSI Z39.48–1992. 9 8 7 6 5 4 3 2 1 CONTENTS Translator’s Preface vii Author’s Preface and Acknowledgments xi Part 1. Mythology Chapter 1 Hermes’ Ears: Places and Symbols of Communication in Ancient Culture 3 Chapter 2 Brutus the Fool 40 Part 2. -
Epistemology from Passivity: an Argument Against the Position of Complete Skepticism of an External World
Aporia vol. 28 no. 2—2018 Epistemology from Passivity: An Argument against the Position of Complete Skepticism of an External World LUKAS MYERS he problems of Epistemological Solipsism are present in the minds of all those beginning philosophical inquiry as, perhaps, the most Tintriguing and difficult of questions—directly mystifying the universe and making panic stretch across the psyches of young philosophers in fear that they may be the only thing that exists. For those who continue on with philosophy for any period of time, such a problem likely never loses its difficulties, but maintaining that same level of ferocious intrigue seems unlikely. It is such a problem that many contemporary philosophers, so that they can actually do any productive philosophy, suspend their judgement or hold that the idea of Epistemological Solipsism whatsoever is redundant.1 Many hold that the idea is incredulous, or they reason that there is no ‘good enough’ positive evidence in favor of such a viewpoint as Epistemological Solipsism and so, if such a view desires to be taken seriously, it must pass a high burden of proof for a positive argument in its favor. The idea that radically skeptical positions of epistemology are simply lacking in utility or likelihood is a common one and often comes in two forms: the soft criticism and the hard criticism. In Bertrand Russell’s work, Our Knowledge of the External World, Russell states a similarly pragmatic view of extreme skepticism saying: 1Insofar as if we choose to maintain it seriously, there can be no more important reflection past that specific point. -
Alexander on Aporia 15Iii16
Edinburgh Research Explorer Aporia and exegesis Citation for published version: Kupreeva, I 2017, Aporia and exegesis: Alexander of Aphrodisias. in G Karamanolis & V Politis (eds), The Aporetic Tradition in Ancient Philosophy. Cambridge University Press, Cambridge; New York, pp. 228-247. https://doi.org/10.1017/9781316274293.013 Digital Object Identifier (DOI): 10.1017/9781316274293.013 Link: Link to publication record in Edinburgh Research Explorer Document Version: Peer reviewed version Published In: The Aporetic Tradition in Ancient Philosophy Publisher Rights Statement: This material has been published in "The Aporetic Tradition in Ancient Philosophy" edited by George Karamanolis, Vasilis Politis. This version is free to view and download for personal use only. Not for re- distribution, re-sale or use in derivative works. © Kupreeva . General rights Copyright for the publications made accessible via the Edinburgh Research Explorer is retained by the author(s) and / or other copyright owners and it is a condition of accessing these publications that users recognise and abide by the legal requirements associated with these rights. Take down policy The University of Edinburgh has made every reasonable effort to ensure that Edinburgh Research Explorer content complies with UK legislation. If you believe that the public display of this file breaches copyright please contact [email protected] providing details, and we will remove access to the work immediately and investigate your claim. Download date: 27. Sep. 2021 Aporia and exegesis: Alexander of Aphrodisias Aporetic reasoning features in Alexander’s work throughout - in the Aristotelian commentaries, opuscula, and school treatises (two of which have words aporia and problêma in their manuscript titles).1 Much of Alexander’s use of aporia is prompted by Aristotle’s texts he comments on, and very often aporetic framework is developed in following upon the earlier school discussions and philosophical polemic against other philosophers - both practices going back to Aristotle himself.