Chapter 5 Pythagoras, Alkmaeon and Hippasos 1. the Problem
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King Lfred's Version Off the Consolations of Boethius
King _lfred's Version off the Consolations of Boethius HENRY FROWDE, M A. PUBLISHER TO THE UNIVERSITY OF OF_0RD LONDON, EDINBURGH_ AND NEW YORK Kring e__lfred's Version o_/"the Consolations of Boethius _ _ Z)one into c_gfodern English, with an Introduction _ _ _ _ u_aa Litt.D._ Editor _o_.,I_ing .... i .dlfred_ OM Englis.h..ffgerAon2.' !ilo of the ' De Con.d.¢_onz,o,e 2 Oxford : _4t the Claro_don:,.....: PrestO0000 M D CCCC _eee_ Ioee_ J_el eeoee le e_ZNeFED AT THE_.e_EN_N PI_.._S _ee • • oeoo eee • oeee eo6_o eoee • ooeo e_ooo ..:.. ..'.: oe°_ ° leeeo eeoe ee •QQ . :.:.. oOeeo QOO_e 6eeQ aee...._ e • eee TO THE REV. PROFESSOR W. W. SKEAT LITT.D._ D.C.L._ LL.D.:_ PH.D. THIS _800K IS GRATEFULLY DEDICATED PREFACE THE preparationsfor adequately commemoratingthe forthcoming millenary of King Alfred's death have set going a fresh wave of popularinterest in that hero. Lectares have been given, committees formed, sub- scriptions paid and promised, and an excellent book of essays by eminent specialists has been written about Alfred considered under quite a number of aspects. That great King has himself told us that he was not indifferent to the opinion of those that should come after him, and he earnestly desired that that opinion should be a high one. We have by no means for- gotten him, it is true, but yet to verymany intelligent people he is, to use a paradox, a distinctly nebulous character of history. His most undying attributes in the memory of the people are not unconnected with singed cakes and romantic visits in disguise to the Danish viii Preface Danish camp. -
Plato As "Architectof Science"
Plato as "Architectof Science" LEONID ZHMUD ABSTRACT The figureof the cordialhost of the Academy,who invitedthe mostgifted math- ematiciansand cultivatedpure research, whose keen intellectwas able if not to solve the particularproblem then at least to show the methodfor its solution: this figureis quite familiarto studentsof Greekscience. But was the Academy as such a centerof scientificresearch, and did Plato really set for mathemati- cians and astronomersthe problemsthey shouldstudy and methodsthey should use? Oursources tell aboutPlato's friendship or at leastacquaintance with many brilliantmathematicians of his day (Theodorus,Archytas, Theaetetus), but they were neverhis pupils,rather vice versa- he learnedmuch from them and actively used this knowledgein developinghis philosophy.There is no reliableevidence that Eudoxus,Menaechmus, Dinostratus, Theudius, and others, whom many scholarsunite into the groupof so-called"Academic mathematicians," ever were his pupilsor close associates.Our analysis of therelevant passages (Eratosthenes' Platonicus, Sosigenes ap. Simplicius, Proclus' Catalogue of geometers, and Philodemus'History of the Academy,etc.) shows thatthe very tendencyof por- trayingPlato as the architectof sciencegoes back to the earlyAcademy and is bornout of interpretationsof his dialogues. I Plato's relationship to the exact sciences used to be one of the traditional problems in the history of ancient Greek science and philosophy.' From the nineteenth century on it was examined in various aspects, the most significant of which were the historical, philosophical and methodological. In the last century and at the beginning of this century attention was paid peredominantly, although not exclusively, to the first of these aspects, especially to the questions how great Plato's contribution to specific math- ematical research really was, and how reliable our sources are in ascrib- ing to him particular scientific discoveries. -
15 Famous Greek Mathematicians and Their Contributions 1. Euclid
15 Famous Greek Mathematicians and Their Contributions 1. Euclid He was also known as Euclid of Alexandria and referred as the father of geometry deduced the Euclidean geometry. The name has it all, which in Greek means “renowned, glorious”. He worked his entire life in the field of mathematics and made revolutionary contributions to geometry. 2. Pythagoras The famous ‘Pythagoras theorem’, yes the same one we have struggled through in our childhood during our challenging math classes. This genius achieved in his contributions in mathematics and become the father of the theorem of Pythagoras. Born is Samos, Greece and fled off to Egypt and maybe India. This great mathematician is most prominently known for, what else but, for his Pythagoras theorem. 3. Archimedes Archimedes is yet another great talent from the land of the Greek. He thrived for gaining knowledge in mathematical education and made various contributions. He is best known for antiquity and the invention of compound pulleys and screw pump. 4. Thales of Miletus He was the first individual to whom a mathematical discovery was attributed. He’s best known for his work in calculating the heights of pyramids and the distance of the ships from the shore using geometry. 5. Aristotle Aristotle had a diverse knowledge over various areas including mathematics, geology, physics, metaphysics, biology, medicine and psychology. He was a pupil of Plato therefore it’s not a surprise that he had a vast knowledge and made contributions towards Platonism. Tutored Alexander the Great and established a library which aided in the production of hundreds of books. -
THE PHILOSOPHY BOOK George Santayana (1863-1952)
Georg Hegel (1770-1831) ................................ 30 Arthur Schopenhauer (1788-1860) ................. 32 Ludwig Andreas Feuerbach (1804-1872) ...... 32 John Stuart Mill (1806-1873) .......................... 33 Soren Kierkegaard (1813-1855) ..................... 33 Karl Marx (1818-1883).................................... 34 Henry David Thoreau (1817-1862) ................ 35 Charles Sanders Peirce (1839-1914).............. 35 William James (1842-1910) ............................ 36 The Modern World 1900-1950 ............................. 36 Friedrich Nietzsche (1844-1900) .................... 37 Ahad Ha'am (1856-1927) ............................... 38 Ferdinand de Saussure (1857-1913) ............. 38 Edmund Husserl (1859–1938) ....................... 39 Henri Bergson (1859-1941) ............................ 39 Contents John Dewey (1859–1952) ............................... 39 Introduction....................................................... 1 THE PHILOSOPHY BOOK George Santayana (1863-1952) ..................... 40 The Ancient World 700 BCE-250 CE..................... 3 Miguel de Unamuno (1864-1936) ................... 40 Introduction Thales of Miletus (c.624-546 BCE)................... 3 William Du Bois (1868-1963) .......................... 41 Laozi (c.6th century BCE) ................................. 4 Philosophy is not just the preserve of brilliant Bertrand Russell (1872-1970) ........................ 41 Pythagoras (c.570-495 BCE) ............................ 4 but eccentric thinkers that it is popularly Max Scheler -
Stony Brook University
SSStttooonnnyyy BBBrrrooooookkk UUUnnniiivvveeerrrsssiiitttyyy The official electronic file of this thesis or dissertation is maintained by the University Libraries on behalf of The Graduate School at Stony Brook University. ©©© AAAllllll RRRiiiggghhhtttsss RRReeessseeerrrvvveeeddd bbbyyy AAAuuuttthhhooorrr... Heraclitus and the Work of Awakening A Dissertation Presented by Nicolas Elias Leon Ruiz to The Graduate School in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy in Philosophy Stony Brook University August 2007 Copyright by Nicolas Elias Leon Ruiz August 2007 Stony Brook University The Graduate School Nicolas Elias Leon Ruiz We, the dissertation committee for the above candidate for the Doctor of Philosophy degree, hereby recommend acceptance of this dissertation. Dr. Peter Manchester – Dissertation Advisor Associate Professor of Philosophy Dr. David Allison – Chairperson of Defense Professor of Philosophy Dr. Eduardo Mendieta Associate Professor of Philosophy Dr. Gregory Shaw Professor of Religious Studies Stonehill College This dissertation is accepted by the Graduate School Lawrence Martin Dean of the Graduate School ii Abstract of the Dissertation Heraclitus and the Work of Awakening by Nicolas Elias Leon Ruiz Doctor of Philosophy in Philosophy Stony Brook University 2007 Heraclitus is regarded as one of the foundational figures of western philosophy. As such, he is typically read as some species of rational thinker: empiricist, materialist, metaphysician, dialectician, phenomenologist, etc. This dissertation argues that all of these views of Heraclitus and his work are based upon profoundly mistaken assumptions. Instead, Heraclitus is shown to be a thoroughly and consistently mystical writer whose work is organized around the recurring theme of awakening. He is thus much more akin to figures such as Buddha, Lao Tzu, and Empedocles than to Aristotle or Hegel. -
Euripides” Johanna Hanink
The Life of the Author in the Letters of “Euripides” Johanna Hanink N 1694, Joshua Barnes, the eccentric British scholar (and poet) of Greek who the next year would become Regius Professor at the University of Cambridge, published his I 1 long-awaited Euripidis quae extant omnia. This was an enormous edition of Euripides’ works which contained every scrap of Euripidean material—dramatic, fragmentary, and biographical —that Barnes had managed to unearth.2 In the course of pre- paring the volume, Barnes had got wind that Richard Bentley believed that the epistles attributed by many ancient manu- scripts to Euripides were spurious; he therefore wrote to Bentley asking him to elucidate the grounds of his doubt. On 22 February 1693, Bentley returned a letter to Barnes in which he firmly declared that, with regard to the ancient epistles, “tis not Euripides himself that here discourseth, but a puny sophist that acts him.” Bentley did, however, recognize that convincing others of this would be a difficult task: “as for arguments to prove [the letters] spurious, perhaps there are none that will convince any person that doth not discover it by himself.”3 1 On the printing of the book and its early distribution see D. McKitterick, A History of Cambridge University Press I Printing and the Book Trade in Cambridge, 1534–1698 (Cambridge 1992) 380–392; on Joshua Barnes see K. L. Haugen, ODNB 3 (2004) 998–1001. 2 C. Collard, Tragedy, Euripides and Euripideans (Bristol 2007) 199–204, re- hearses a number of criticisms of Barnes’ methods, especially concerning his presentation of Euripidean fragments (for which he often gave no source, and which occasionally consisted of lines from the extant plays). -
MONEY and the EARLY GREEK MIND: Homer, Philosophy, Tragedy
This page intentionally left blank MONEY AND THE EARLY GREEK MIND How were the Greeks of the sixth century bc able to invent philosophy and tragedy? In this book Richard Seaford argues that a large part of the answer can be found in another momentous development, the invention and rapid spread of coinage, which produced the first ever thoroughly monetised society. By transforming social relations, monetisation contributed to the ideas of the universe as an impersonal system (presocratic philosophy) and of the individual alienated from his own kin and from the gods (in tragedy). Seaford argues that an important precondition for this monetisation was the Greek practice of animal sacrifice, as represented in Homeric epic, which describes a premonetary world on the point of producing money. This book combines social history, economic anthropology, numismatics and the close reading of literary, inscriptional, and philosophical texts. Questioning the origins and shaping force of Greek philosophy, this is a major book with wide appeal. richard seaford is Professor of Greek Literature at the University of Exeter. He is the author of commentaries on Euripides’ Cyclops (1984) and Bacchae (1996) and of Reciprocity and Ritual: Homer and Tragedy in the Developing City-State (1994). MONEY AND THE EARLY GREEK MIND Homer, Philosophy, Tragedy RICHARD SEAFORD cambridge university press Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo Cambridge University Press The Edinburgh Building, Cambridge cb2 2ru, UK Published in the United States of America by Cambridge University Press, New York www.cambridge.org Information on this title: www.cambridge.org/9780521832281 © Richard Seaford 2004 This publication is in copyright. -
Chapter Two Democritus and the Different Limits to Divisibility
CHAPTER TWO DEMOCRITUS AND THE DIFFERENT LIMITS TO DIVISIBILITY § 0. Introduction In the previous chapter I tried to give an extensive analysis of the reasoning in and behind the first arguments in the history of philosophy in which problems of continuity and infinite divisibility emerged. The impact of these arguments must have been enormous. Designed to show that rationally speaking one was better off with an Eleatic universe without plurality and without motion, Zeno’s paradoxes were a challenge to everyone who wanted to salvage at least those two basic features of the world of common sense. On the other hand, sceptics, for whatever reason weary of common sense, could employ Zeno-style arguments to keep up the pressure. The most notable representative of the latter group is Gorgias, who in his book On not-being or On nature referred to ‘Zeno’s argument’, presumably in a demonstration that what is without body and does not have parts, is not. It is possible that this followed an earlier argument of his that whatever is one, must be without body.1 We recognize here what Aristotle calls Zeno’s principle, that what does not have bulk or size, is not. Also in the following we meet familiar Zenonian themes: Further, if it moves and shifts [as] one, what is, is divided, not being continuous, and there [it is] not something. Hence, if it moves everywhere, it is divided everywhere. But if that is the case, then everywhere it is not. For it is there deprived of being, he says, where it is divided, instead of ‘void’ using ‘being divided’.2 Gorgias is talking here about the situation that there is motion within what is. -
6 X 10. Three Lines .P65
Cambridge University Press 978-0-521-83746-0 - Archytas of Tarentum: Pythagorean, Philosopher and Mathematician King Carl A. Huffman Excerpt More information part one Introductory essays © Cambridge University Press www.cambridge.org Cambridge University Press 978-0-521-83746-0 - Archytas of Tarentum: Pythagorean, Philosopher and Mathematician King Carl A. Huffman Excerpt More information chapter i Life, writings and reception sources (The original texts and translations of the testimonia for Archytas’ life are found in Part Three, Section One) Archytas did not live the life of a philosophical recluse. He was the leader of one of the most powerful Greek city-states in the first half of the fourth century bc. Unfortunately he is similar to most important Greek intellec- tuals of the fifth and fourth centuries bc, in that we have extremely little reliable information about his activities. This dearth of information is all the more frustrating since we know that Aristoxenus wrote a biography of Archytas, not long after his death (A9). Two themes bulk large in the bits of evidence that do survive from that biography and from other evidence for Archytas’ life. First, there is Archytas’ connection to Plato, which, as we will see, was more controversial in antiquity than in most modern scholarship. The Platonic Seventh Letter, whose authenticity continues to be debated, portrays Archytas as saving Plato from likely death, when Plato was visit- ing the tyrant Dionysius II at Syracuse in 361 bc. Second, for Aristoxenus, Archytas is the paradigm of a successful leader. Elected general (strat¯egos) repeatedly, he was never defeated in battle; as a virtuous, kindly and demo- cratic ruler, he played a significant role in the great prosperity of his native Tarentum, located on the heel of southern Italy. -
Anaximander and the Problem of the Earth's Immobility
Binghamton University The Open Repository @ Binghamton (The ORB) The Society for Ancient Greek Philosophy Newsletter 12-28-1953 Anaximander and the Problem of the Earth's Immobility John Robinson Windham College Follow this and additional works at: https://orb.binghamton.edu/sagp Recommended Citation Robinson, John, "Anaximander and the Problem of the Earth's Immobility" (1953). The Society for Ancient Greek Philosophy Newsletter. 263. https://orb.binghamton.edu/sagp/263 This Article is brought to you for free and open access by The Open Repository @ Binghamton (The ORB). It has been accepted for inclusion in The Society for Ancient Greek Philosophy Newsletter by an authorized administrator of The Open Repository @ Binghamton (The ORB). For more information, please contact [email protected]. JOHN ROBINSON Windham College Anaximander and the Problem of the Earth’s Immobility* N the course of his review of the reasons given by his predecessors for the earth’s immobility, Aristotle states that “some” attribute it I neither to the action of the whirl nor to the air beneath’s hindering its falling : These are the causes with which most thinkers busy themselves. But there are some who say, like Anaximander among the ancients, that it stays where it is because of its “indifference” (όμοιότητα). For what is stationed at the center, and is equably related to the extremes, has no reason to go one way rather than another—either up or down or sideways. And since it is impossible for it to move simultaneously in opposite directions, it necessarily stays where it is.1 The ascription of this curious view to Anaximander appears to have occasioned little uneasiness among modern commentators. -
Parmenides B6.1–2 Without a Modal Fallacy
Aporia vol. 21 no. 1—2011 Parmenides B6.1–2 without a Modal Fallacy MICHAEL J. HANSEN n all accounts, Parmenides makes a marvelous argument in the Way of Truth. However, there is no clear consensus among inter- Opreters about how to read it. The only noncontroversial point in interpreting the work seems to be that in it, Parmenides did something pro- found to philosophy. Despite this collective obligation to acknowledge Par- menides’ unique innovation (whatever it may be), it has become popular to read Parmenides as relying on a modal fallacy to make his argument. This would be an embarrassing mistake for such an influential work, especially given the argument’s deductive appearance. In this paper, I will outline the modal fallacy that Parmenides is accused of and argue for an interpretation that is free of the fallacy. I. The Alleged Modal Fallacy The critical fragment we must examine to decide the question is B6.1–2, in which the fallacy is supposed to occur: crhV toV levgein te noei`n t' ejoVn e!mmenai e!sti gaVr ei^nai, mhdeVn d' oujk e!otin . (Graham 214) Michael J. Hansen is a senior majoring in philosophy at Brigham Young University. He is interested in ancient philosophy, the philosophy of mind, epistemology, and metaphysics. In the fall, he will be pursuing a PhD in philosophy at the University of California–Los Angeles. This essay placed first in the 2011 David H. Yarn Philosophical Essay Contest. 2 MICHAEL J. HANSEN As usual, Parmenides’ language admits of many permissible translations for interpreters to quibble over, but this fragment is exceptionally difficult to render. -
Lucan's Natural Questions: Landscape and Geography in the Bellum Civile Laura Zientek a Dissertation Submitted in Partial Fulf
Lucan’s Natural Questions: Landscape and Geography in the Bellum Civile Laura Zientek A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy University of Washington 2014 Reading Committee: Catherine Connors, Chair Alain Gowing Stephen Hinds Program Authorized to Offer Degree: Classics © Copyright 2014 Laura Zientek University of Washington Abstract Lucan’s Natural Questions: Landscape and Geography in the Bellum Civile Laura Zientek Chair of the Supervisory Committee: Professor Catherine Connors Department of Classics This dissertation is an analysis of the role of landscape and the natural world in Lucan’s Bellum Civile. I investigate digressions and excurses on mountains, rivers, and certain myths associated aetiologically with the land, and demonstrate how Stoic physics and cosmology – in particular the concepts of cosmic (dis)order, collapse, and conflagration – play a role in the way Lucan writes about the landscape in the context of a civil war poem. Building on previous analyses of the Bellum Civile that provide background on its literary context (Ahl, 1976), on Lucan’s poetic technique (Masters, 1992), and on landscape in Roman literature (Spencer, 2010), I approach Lucan’s depiction of the natural world by focusing on the mutual effect of humanity and landscape on each other. Thus, hardships posed by the land against characters like Caesar and Cato, gloomy and threatening atmospheres, and dangerous or unusual weather phenomena all have places in my study. I also explore how Lucan’s landscapes engage with the tropes of the locus amoenus or horridus (Schiesaro, 2006) and elements of the sublime (Day, 2013).