Naming the Principles in Democritus: an Epistemological Problem
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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. -
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. -
The Early History of Man and the Uses of Diodorus in Renaissance Scholarship: from Annius of Viterbo to Johannes Boemus
chapter 40 The Early History of Man and the Uses of Diodorus in Renaissance Scholarship: From Annius of Viterbo to Johannes Boemus C. Philipp E. Nothaft Introduction When Diodorus of Sicily took up the stylus during the middle years of the first century bce to write a whole “library” (Bibliotheke) of universal history in forty books, the gap between gods and men had become a narrow one. In a reality deeply shaped by the past conquests of Alexander the Great and the present wars of Julius Caesar, many had begun to think of historical change as a pro- cess bound up with the heroic exploits of powerful and charismatic generals, who covered vast stretches of land, founded and destroyed cities, and created conditions under which inventions, crafts, food crops, and other goods could flow at an unprecedented rate from one end of the known world to the other. Nations and city-states reacted to their dependence on the good will of this new class of Hellenistic kings by showering them with divine honors, which sometimes developed into fully fledged ruler cults. The learned approach to mythology that was most congenial to this dynamic atmosphere of hero worship is forever associated with the name of Euhemerus of Messene (fl. 300 bce), for whom even the deities of the old pantheon had once been mere mortals, who received apotheosis on account of their military and politi- cal achievements.1 In Diodorus’s Bibliotheke, which is incidentally our most important source for Euhemerus’s life and ideas, this mythographic approach is expanded to include the deification of inventors, lawgivers, and pioneers of the arts and 1 On Euhemerism and its afterlife, see Marek Winiarczyk, The “Sacred History” of Euhemerus of Messene (Berlin: De Gruyer, 2013); Jean Seznec, The Survival of the Pagan Gods, trans. -
Proclus and Artemis: on the Relevance of Neoplatonism to the Modern Study of Ancient Religion
Kernos Revue internationale et pluridisciplinaire de religion grecque antique 13 | 2000 Varia Proclus and Artemis: On the Relevance of Neoplatonism to the Modern Study of Ancient Religion Spyridon Rangos Electronic version URL: http://journals.openedition.org/kernos/1293 DOI: 10.4000/kernos.1293 ISSN: 2034-7871 Publisher Centre international d'étude de la religion grecque antique Printed version Date of publication: 1 January 2000 ISSN: 0776-3824 Electronic reference Spyridon Rangos, « Proclus and Artemis: On the Relevance of Neoplatonism to the Modern Study of Ancient Religion », Kernos [Online], 13 | 2000, Online since 21 April 2011, connection on 01 May 2019. URL : http://journals.openedition.org/kernos/1293 ; DOI : 10.4000/kernos.1293 Kernos Kernos, 13 (2000), p. 47-84. Proclus and Artemis: On the Relevance of Neoplatonism to the Modern Study of Andent Religion* Imagine the situation in which contemporary philosophers would find themselves if Wittgenstein introduced, in his Philosophical Investigations, the religious figure of Jesus as Logos and Son of God in order to illuminate the puzzlement ofthe private-language paradox, or if in the second division of Being and Time Heidegger mentioned the archangel Michael to support the argument of 'being toward death'. Similar is the perplexity that a modern reader is bound to encounter when, after a highly sophisticated analysis of demanding metaphysical questions about the relationship of the one and the many, finitude and infinity, mind and body, Proclus, l in ail seriousness and without the slightest touch of irony, assigns to some traditional gods of Greek polytheism a definitive place in the structure of being. -
Sicilian Landscape As Contested Space in the First Century BC: Three Case Studies
Sicilian Landscape as Contested Space in the First Century BC: Three Case Studies Dustin Leigh McKenzie BA (Hons), Dip. Lang. A thesis submitted for the degree of Master of Philosophy at The University of Queensland in 2018 School of Historical and Philosophical Inquiry ii Abstract Sicily was made the first overseas Roman province between 241 and 212 BC, and became known as the ‘bread-basket’ of the Republic due to the island’s famously fertile farmlands. The island, with its history of pre-Roman conflict, second century slave revolts, and use as a military stronghold in the civil wars of the first century, never dissociated itself from conflict. As such, its construction as a ‘contested space’ was popular in the literature of first-century Rome, employed as a symptomatic topos of the state of Rome – the closer Roman Sicily resembled its pre- annexation state, the greater the perceived threat to the Republic, and vice-versa. This construction of Sicily and its landscape was employed by authors such as Cicero, Diodorus Siculus, and Virgil to great effect, as they engaged with, reinforced, or challenged the major contemporary discourses of imperialism, the impact of civil war, and food security. Cicero’s In Verrem presents its audience with a Sicily that has been purposely constructed to deliver the most damning image of Verres, the infamously corrupt governor of Sicily from 73-71, the most sympathetic and familiar image of the Sicilians, presented as virtuous and stoic farmers, and a Sicily that has been reduced to a war-torn desert under Verres’ rule. Through his construction of Sicily as contested space, Cicero secured his win against Verres in court and demonstrated to his audiences the danger Verres’ actions presented Rome, threatening the stability of the relationship between Sicily and Rome. -
PROCLUS on HESIOD's WORKS and DAYS Patrizia Marzillo
PERFORMING AN ACADEMIC TALK: PROCLUS ON HESIOD’S WORKS AND DAYS Patrizia Marzillo Abstract From Socrates onwards orality was the favoured means of expression for those wholaterlovedtocallthemselves‘Platonic’.Theyusedtodiscussphilosophical issues in debates that turned into academic lectures and seminars. According to Plato’s original teaching, these talks should have not been “fixed” in written compositions, yet Plato himself put most of his doctrine into fictive “written dia- logues”.His followers intensified their connection with writing, above all for the purposes of teaching. On the one hand, they made notes on the lessons of their teachers; on the other, they enlarged their own talks in written compositions. Neoplatonists’ commentaries are often an amplification of their academic talks. The lessons held in the school of Athens or in Platonic circles coalesced into texts that mostly constitute Neoplatonic propaganda intended for the outside world. When Proclus directed the school in Athens, Plato and Aristotle were taught, but also theologian poets such as Homer, Orpheus, Hesiod. As the Suda reports, Proclus wrote commentaries on all of these poets, but the only onepreservedisthecommentaryonHesiod’sWorks and Days.Througha comparison of some passages from this commentary, I show how Proclus’ commentary on Hesiod is not only a good example of an oral lesson that has become a written commentary, but also, importantly, of a text that aimed at the diffusion of Neoplatonic ideas among an audience of non-adherents. As his biographer and disciple Marinus of Neapolis relates, the neo- Platonist Proclus was accustomed to write about lines a day.1 Besides being a very prolific author, he was also an indefatigable teacher since in addition to his writing he held several classes during the day and also gave evening talks.2 What I propose to show in this paper is the profound interaction between the oral communication in his school and the written performance of his commentaries. -
Neoplatonic Asclepius: Science and Religion at the Crossroads of Aristotelian Biology, Hippocratic Medicine and Platonic Theurgy
Studia Antiqua et Archaeologica 23(2): 333–349 Neoplatonic Asclepius: Science and religion at the crossroads of Aristotelian biology, Hippocratic medicine and Platonic theurgy Eugene AFONASIN1 Abstract. In the first part of the paper, I will briefly discuss certain peculiarities of the medical profession in antiquity. In his Philosophical History (fr. 80–84 Athanassiadi) Damascius narrates about a philosopher, named Asclepiodotus, whose interests ranged from Platonic philosophy to Aristotelian natural sciences. Asclepiodotus’ instructor in medical matters, a son of a doctor from the island of Rhodos, Iacobus, is pictured by Damascius as an exemplary figure (fr. 84), who, unlike many of his contemporaries, always tested the opinions of others and gained a reputation of an extremely successful physician, although the methods of treatment, ascribed to him by Damascius, are highly reminiscent of those presented as the Pythagorean by Iamblichus (On the Pythagorean way of life 244). In this respect both Iacobus and Asclepiodotus are conformed to the best standards of medical ethics, and pass the test set by Galen in his “On examination by which the best physicians are recognized”, except perhaps by the fact that they preferred to base their activities on such authorities as Aristotle and the Methodist Soranus rather than on a list of the “dogmatists” proposed by Galen. In the second part of the paper, dedicated to the cult of Asclepius in Late Antiquity, I will look at various kinds of evidence taken from the Neoplatonic philosophers. Having discussed first the principal philosophical interpretations of Asclepius found in Apuleius, Aelianus, Macrobius, Julian, Porphyry, Iamblichus, Proclus, Damascius, etc., we turn to Proclus’ attitude to Athena and Asclepius as reflected in Marinus’ Vita Procli and finally discuss the cult of Eshmun as found in Damascius. -
Philosophy in Ancient Greek Biography. Turnhout: Brepols, 2016
Revista Classica, v. 30, n. 2, p. 137-142, 2017 137 BONAZZI, Mauro; SCHORN, Stefan. Bios Philosophos: Philosophy in Ancient Greek Biography. Turnhout: Brepols, 2016. 313p. ISBN 978-2-503-56546-0 Gustavo Laet Gomes* * Mestre em Filosofia Bernardo C. D. A. Vasconcelos** pela Universidade Federal de Minas Gerais. guslaet@ gmail.com Bios Philosophos. Philosophy in Ancient Greek Biography (Brepols, 2016), organized by Mauro Bonazzi and Stefan Schorn, delivers a ** Mestre em Filosofia pela both deep and wide tour through the philosophical aspects of Greek Universidade Federal biographical production. On one hand, it does not concentrate only in de Minas Gerais. the later periods of Greek philosophy, when biographical production bernardovasconcelos abounded, but goes all the way back to the fourth century BCE, when @gmail.com biographical texts were fragmentary and mingled with other styles. On the other, it tries to unveil the philosophical motives in the works of authors who tend to be disregarded as historians, biographers, hagiographers or even as mere fans of the most prominent figures of their own schools. In our review, we will attempt to give a brief account of the ten articles that make up this volume, which, in turn, will hopefully provide an overview of the different connections between the biographies and biographers and their philosophical motives. Thomas Bénatouïl’s Pythagore chez Dicéarque: anectodes biographiques et critique de la philosophie contemplative (p. 11-36) proposes an inversion of the traditional interpretation regarding the testimony of Dicaearchus of Messana about the life of Pythagoras. Since antiquity, Dicaearchus’ reports tend to be seen as positive, because they present a Pythagoras devoid of mysticism and apparently more interested in practical matters. -
Assessing Porphyry's Reaction to Plotinus's Doctrine of The
HeyJ LII (2011), pp. 1–10 DOI: 10.1111/j.1468-2265.2011.00686.x PORPHYRY THE APOSTATE: ASSESSING PORPHYRY’S REACTION TO PLOTINUS’S DOCTRINE OF THE ONE SEAMUS O’NEILL Memorial University of Newfoundland St. John’s, Canada In an article in the first volume of Harris’s Studies in Neoplatonism, Patrick Atherton described what he saw as a radical difference between the trinitarian and Neoplatonic first principles. The distinction he draws is seminal: because the first principle, or , produces all things, all that follows from it is determined by its nature. Whereas the unity of what Atherton describes as the ‘Neoplatonic One’ transcends all relation and difference, The trinitarian , by contrast, appears as an attempt to reconcile the requirement of unity with that of difference within the principle itself: is now recognised as a moment within the unity, as belonging to the principle as unity. Such a position requires a very different interpretation of the relation between the principle and its derivatives than that found in Neoplatonism.1 Recent scholarship on Porphyry, however, suggests that the important distinction Atherton adverts to is not resolvable into distinctly Neoplatonic and trinitarian camps. What Atherton describes as ‘Neoplatonism’ is more diverse, as scholars debate the subtle differences between the doctrines of Plotinus, Porphyry, Iamblichus, Augustine, and Proclus, among others. For example, John Dillon and Steven Strange have recently argued that Porphyry’s doctrine of the first principle is in fact – as Atherton describes the two positions – ‘trinitarian’ rather than ‘Neoplatonic’. Atherton’s characterization of the Neoplatonic describes more narrowly the Plotinian One, for Plotinus is the only Neoplatonist who maintains the absolute transcendence of the first principle beyond all relation and difference. -
Democritus and Protagoras
“Man is the measure of cosmos” Democritus and Protagoras: Values and Beliefs on Naturalism By Anastasia Theologou Submitted to Central European University Department of Philosophy In partial fulfillment of the requirements for the degree of Master of Arts Supervisor: Istvan Bodnar CEU eTD Collection Budapest, Hungary 2015 Table of contents ABSTRACT ....................................................................................................................................... iii ACKNOWLEDGEMENTS ................................................................................................................ iv Introduction .......................................................................................................................................... 1 1. Democritus’ philosophy in Diodorus Siculus .......................................................................... 4 1.1. Democritus’ cosmogony ................................................................................................. 6 1.2. The primary state of human beings ................................................................................. 8 1.3. Living the bestial life .................................................................................................... 10 1.4. Fear................................................................................................................................ 10 1.5. Language ....................................................................................................................... 11 -
MATH 520 Fall 2007 Historical Background
MATH 520 – Foundations of Geometry Historical Background The word geometry is derived from the Greek words meaning “earth measure” implying that geometry involves measuring earthly things. Ancient geometry in part has its beginnings in the practical need necessary for the agriculture of the Babylonians (modern region is southern Iraq from around Baghdad to the Persian Gulf) and Egyptians, civilizations “known for their engineering prowess in marsh drainage, irrigation, flood control, and the erection of great edifices and structures” (Eves, 1969). There is evidence from clay tablets that the Babylonians (~ 1900 BC) were familiar with Pythagorean Triples long before Pythagoras lived. 1 The Egyptians used the formula ++= dbcaA ))(( to calculate the area of an arbitrary quadrilateral with 4 successive sides a, b, c, and d. This formula proves correct for rectangles but not for quadrilaterals in general. Not until the 6th century B.C. did mathematicians begin to question whether such empirical results were always true. The contemporary study of geometry bears little resemblance to its historical beginnings in that it does not necessarily require that we measure anything or even restrict ourselves to the earth. People/Characters Thales of Miletus (ca. 640 – 546 B.C.) Greek Most often credited with initiating the formal study of demonstrative geometry as a discipline – The Father of Demonstrative Geometry; A Wise Man of Antiquity Well traveled throughout Babylonia, Egypt, and the Middle East. Thales knew the work and culture of the regions. He began to generalize and demonstrate geometric propositions by using logical reasoning to argue in favor of propositions rather than simply going with the “it works so use it” method. -
Diodorus Siculus and the World of the Late Roman Republic Ii Iii
i Diodorus Siculus and the World of the Late Roman Republic ii iii Diodorus Siculus and the World of the Late Roman Republic z CHARLES E. MUNTZ 1 iv 1 Oxford University Press is a department of the University of Oxford. It furthers the University’s objective of excellence in research, scholarship, and education by publishing worldwide. Oxford is a registered trade mark of Oxford University Press in the UK and certain other countries. Published in the United States of America by Oxford University Press 198 Madison Avenue, New York, NY 10016, United States of America. © Oxford University Press, 2017 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, without the prior permission in writing of Oxford University Press, or as expressly permitted by law, by license, or under terms agreed with the appropriate reproduction rights organization. Inquiries concerning reproduction outside the scope of the above should be sent to the Rights Department, Oxford University Press, at the address above. You must not circulate this work in any other form and you must impose this same condition on any acquirer. Library of Congress Cataloging- in- Publication Data Names: Muntz, Charles Edward, 1980– author. Title: Diodorus Siculus and the world of the late Roman republic / Charles E. Muntz. Description: New York, NY : Oxford University Press, [2017] | Includes bibliographical references and index. | Description based on print version record and CIP data provided by publisher; resource not viewed. Identifiers: LCCN 2016018875 (print) | LCCN 2016017895 (ebook) | ISBN 9780190498726 (hardback) | ISBN 9780190498733 (ebook) | ISBN 9780190498740 (online) Subjects: LCSH: Diodorus, Siculus.