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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. -
Alexander Jones Calendrica I: New Callippic Dates
ALEXANDER JONES CALENDRICA I: NEW CALLIPPIC DATES aus: Zeitschrift für Papyrologie und Epigraphik 129 (2000) 141–158 © Dr. Rudolf Habelt GmbH, Bonn 141 CALENDRICA I: NEW CALLIPPIC DATES 1. Introduction. Callippic dates are familiar to students of Greek chronology, even though up to the present they have been known to occur only in a single source, Ptolemy’s Almagest (c. A.D. 150).1 Ptolemy’s Callippic dates appear in the context of discussions of astronomical observations ranging from the early third century B.C. to the third quarter of the second century B.C. In the present article I will present new attestations of Callippic dates which extend the period of the known use of this system by almost two centuries, into the middle of the first century A.D. I also take the opportunity to attempt a fresh examination of what we can deduce about the Callippic calendar and its history, a topic that has lately been the subject of quite divergent treatments. The distinguishing mark of a Callippic date is the specification of the year by a numbered “period according to Callippus” and a year number within that period. Each Callippic period comprised 76 years, and year 1 of Callippic Period 1 began about midsummer of 330 B.C. It is an obvious, and very reasonable, supposition that this convention for counting years was instituted by Callippus, the fourth- century astronomer whose revisions of Eudoxus’ planetary theory are mentioned by Aristotle in Metaphysics Λ 1073b32–38, and who also is prominent among the authorities cited in astronomical weather calendars (parapegmata).2 The point of the cycles is that 76 years contain exactly four so-called Metonic cycles of 19 years. -
94 Erkka Maula
ORGANON 15 PROBLÊMES GENERAUX Erkka Maula (Finland) FROM TIME TO PLACE: THE PARADIGM CASE The world-order in philosophical cosmology can be founded upon time as well as .space. Perhaps the most fundamental question pertaining to any articulated world- view concerns, accordingly, their ontological and epistemological priority. Is the basic layer of notions characterized by temporal or by spatial concepts? Does a world-view in its development show tendencies toward the predominance of one set of concepts rather than the other? At the stage of its relative maturity, when the qualitative and comparative phases have paved the way for the formation of quantitative concepts: Which are considered more fundamental, measurements of time or measurements of space? In the comparative phase: Is the geometry of the world a geometry of motion or a geometry of timeless order? In the history of our own scientific world-view, there seems to be discernible an oscillation between time-oriented and space-oriented concept formation.1 In the dawn, when the first mathematical systems of astronomy and geography appear, shortly before Euclid's synthesis of the axiomatic thought, there were attempts at a geometry of motion. They are due to Archytas of Tarentum and Eudoxus of Cnidus, foreshadowed by Hippias of Elis and the Pythagoreans, who tend to intro- duce temporal concepts into geometry. Their most eloquent adversary is Plato, and after him the two alternative streams are often called the Heraclitean and the Parmenidean world-views. But also such later and far more articulated distinctions as those between the statical and dynamic cosmologies, or between the formalist and intuitionist philosophies of mathematics, can be traced down to the original Greek dichotomy, although additional concepts entangle the picture. -
Meet the Philosophers of Ancient Greece
Meet the Philosophers of Ancient Greece Everything You Always Wanted to Know About Ancient Greek Philosophy but didn’t Know Who to Ask Edited by Patricia F. O’Grady MEET THE PHILOSOPHERS OF ANCIENT GREECE Dedicated to the memory of Panagiotis, a humble man, who found pleasure when reading about the philosophers of Ancient Greece Meet the Philosophers of Ancient Greece Everything you always wanted to know about Ancient Greek philosophy but didn’t know who to ask Edited by PATRICIA F. O’GRADY Flinders University of South Australia © Patricia F. O’Grady 2005 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, electronic, mechanical, photocopying, recording or otherwise without the prior permission of the publisher. Patricia F. O’Grady has asserted her right under the Copyright, Designs and Patents Act, 1988, to be identi.ed as the editor of this work. Published by Ashgate Publishing Limited Ashgate Publishing Company Wey Court East Suite 420 Union Road 101 Cherry Street Farnham Burlington Surrey, GU9 7PT VT 05401-4405 England USA Ashgate website: http://www.ashgate.com British Library Cataloguing in Publication Data Meet the philosophers of ancient Greece: everything you always wanted to know about ancient Greek philosophy but didn’t know who to ask 1. Philosophy, Ancient 2. Philosophers – Greece 3. Greece – Intellectual life – To 146 B.C. I. O’Grady, Patricia F. 180 Library of Congress Cataloging-in-Publication Data Meet the philosophers of ancient Greece: everything you always wanted to know about ancient Greek philosophy but didn’t know who to ask / Patricia F. -
Mathematics and Cosmology in Plato's Timaeus
apeiron 2021; aop Andrew Gregory* Mathematics and Cosmology in Plato’s Timaeus https://doi.org/10.1515/apeiron-2020-0034 Published online March 18, 2021 Abstract: Plato used mathematics extensively in his account of the cosmos in the Timaeus, but as he did not use equations, but did use geometry, harmony and according to some, numerology, it has not been clear how or to what effect he used mathematics. This paper argues that the relationship between mathematics and cosmology is not atemporally evident and that Plato’s use of mathematics was an open and rational possibility in his context, though that sort of use of mathematics has subsequently been superseded as science has progressed. I argue that there is a philosophically and historically meaningful space between ‘primitive’ or unre- flective uses of mathematics and the modern conception of how mathematics relates to cosmology. Plato’s use of mathematics in the Timaeus enabled the cosmos to be as good as it could be, allowed the demiurge a rational choice (of which planetary orbits and which atomic shapes to instantiate) and allowed Timaeus to give an account of the cosmos (where if the demiurge did not have such a rational choice he would not have been able to do so). I also argue that within this space it is both meaningful and important to differentiate between Pythagorean and Platonic uses of number and that we need to reject the idea of ‘Pythagorean/ Platonic number mysticism’. Plato’s use of number in the Timaeus was not mystical even though it does not match modern usage. -
Aristarchus of Samos and Graeco-Babylonian Astronomy George Huxley
Arfstarchus of Samos and Graeco-Babylonian Astronomy Huxley, George Greek, Roman and Byzantine Studies; Summer 1964; 5, 2; ProQuest pg. 123 Aristarchus of Samos and Graeco-Babylonian Astronomy George Huxley N THE HALF CENTURY following the death of Alexander the Great the I history of astronomy amongst the Greeks is dominated by Aris tarchus the Samian, who is best known for his theory of the earth's revolution about the sun. His life cannot be dated exactly, but it is clear that he was already of mature age by 280 B.C., for Ptolemy states that "the men around Aristarchus," that is to say his pupils, observed the summer solstice in that year, the 50th of the first Callippic period [Ptolemy, Almagest 3.1]. He was a pupil of Strato the Lampsacene, who succeeded Theophrastus as head of the Lyceum in ca. 288/7 B.C. [Apollodorus 244 F 40] and remained in that post for eighteen years till his death not later than 269 B.C. [Apollodorus 244 F 350]. The date of the publication of Aristarchus's heliocentric theory is not known, but the doctrine was attacked by Cleanthes the Stoic land so must have been well known by 232 B.C., when Cleanthes died; but the helio centric hypothesis may have been formulated much earlier than that. Vitruvius spoke highly of the versatility of Aristarchus in geometry, astronomy, and music [De Architectura 1.1.16], and ascribes to him the invention of two kinds of sundial-the hemispherical uKac/>T} and the disc in the plane [9.8.1].2 He perhaps made use of these improved instruments in his observations of the solstices. -
Aristotle and His School Felix Grayeff
ARISTOTLE AND HIS SCHOOL FELIX GRAYEFF Duckworth ARISTOTLE AND HIS SCHOOL An Inquiry into the History of the Peripatos With a Commentary on Metaphysics z, H, A and 0 Felix Grayeff Duckworth CONTENTS Preface 7 List of Abbreviations 8 Introduction 9 Part One 1. Life of Aristotle 13 2. The Peripatos after Aristotle's Death 49 3· The Emergence of New Philosophical Schools during the Fourth and Third Centuries B.C. 57 4· The Library of the Pcripatos and its History 69 Part Two S· The Structure of Metaphysics Z (a) The Parts of z 89 (h) The Composition of Z 1 II 6. Peripatetic Ontology according to Metaphysics H 127 7· Peripatetic Ontology according to Metaphysics A 143 R-xcursus: The Theory of the Proper Place 183 8. A Volume on Potentiality and Actuality: Metaphysics 0 r87 Select Bibliography 213 Index of Passages Cl!Ioted in Text 219 General Index 225 Lift ofAristotle him Regent. So conditions at the Macedonian court were un favourable, even threatening, for a youth of Greek birth and a favourite of the toppled royal house at that. It is therefore possible that Aristotle's premature journey to Athens (for he was still a minor) was partially due to the unrest in Macedonia. It can be assumed that Aristotle joined the Academy as soon as he arrived in Athens, doubtless in accordance with the wishes of his guardian. The choice of the Academy was not a matter of course. At that time there was another famous school, that of !socrates, which engaged in keen rivalry with the Academy. -
Henry Mendell Class
Phil/Chem/Hist.380 Ancient and Modern Science Instructor: Henry Mendell Class: SH C255 Work Telephone: (323) 343-4178 Time: MW 10:50-12:30 email: [email protected] Office: E&T 422 Class URL: http://www.calstatela.edu/faculty/hmendel/Classwork/Phil%20380/Phil.380.html Easy path to get there: http://www.calstatela.edu/faculty/hmendel schedule (on the left below the picture) Phil./Hist./Chem. 380 Office Hours (check web site for cancellations): MW 10:00-10:40,1:15-2:15, Th 12:30-1:45 (by appointment) Required Reading: Books Philip Kitcher, Abusing Science (Cambridge: MIT, 1982) G.E.R. Lloyd, Early Greek Science: Thales to Aristotle (New York: W.W. Norton, 1970) G.E.R. Lloyd, Greek Science after Aristotle (New York: W.W. Norton, 1973) Michael Matthews, Scientific Background to Modern Philosophy (Indianapolis: Hackett, 1989) Xerox Packet (presently in the packet) Henry Mendell, Handouts on Babylonian, Egyptian, and Greek Mathematics and Science From Hippocrates of Cos. Hippocratic Writings . Trans. E. Chadwick, W.N. Mann et al. Ed. with intro. G.E.R. Lloyd. Harmondsworth: Penguin, 1978. "The Nature of Man," 260-271. "The Sacred Disease," 237-251. From Plato. Republic . Trans. G.M.A. Grube. Revised Reeve. In Plato, Complete Works (ed. John Cooper; Indianapolis: Hackett, 1997). Republic VI 507B-VII 541B From Plato. Timaeus . Trans. Donald Zeyl. In Plato, Complete Works (ed. John Cooper; Indianapolis: Hackett, 1997). Plato, Timaeus 30E-47E Available from the Library On-Line Reserve: Aristotle, On the Heavens ( De caelo ) II 13-14. The Complete Works of Aristotle . -
A Concise History of the Philosophy of Mathematics
A Thumbnail History of the Philosophy of Mathematics "It is beyond a doubt that all our knowledge begins with experience." - Imannuel Kant ( 1724 – 1804 ) ( However naïve realism is no substitute for truth [1] ) [1] " ... concepts have reference to sensible experience, but they are never, in a logical sense, deducible from them. For this reason I have never been able to comprehend the problem of the á priori as posed by Kant", from "The Problem of Space, Ether, and the Field in Physics" ( "Das Raum-, Äether- und Feld-Problem der Physik." ), by Albert Einstein, 1934 - source: "Beyond Geometry: Classic Papers from Riemann to Einstein", Dover Publications, by Peter Pesic, St. John's College, Sante Fe, New Mexico Mathematics does not have a universally accepted definition during any period of its development throughout the history of human thought. However for the last 2,500 years, beginning first with the pre - Hellenic Egyptians and Babylonians, mathematics encompasses possible deductive relationships concerned solely with logical truths derived by accepted philosophic methods of logic which the classical Greek thinkers of antiquity pioneered. Although it is normally associated with formulaic algorithms ( i.e., mechanical methods ), mathematics somehow arises in the human mind by the correspondence of observation and inductive experiential thinking together with its practical predictive powers in interpreting future as well as "seemingly" ephemeral phenomena. Why all of this is true in human progress, no one can answer faithfully. In other words, human experiences and intuitive thinking first suggest to the human mind the abstract symbols for which the economy of human thinking mathematics is well known; but it is those parts of mathematics most disconnected from observation and experience and therefore relying almost wholly upon its internal, self - consistent, deductive logics giving mathematics an independent reified, almost ontological, reality, that mathematics most powerfully interprets the ultimate hidden mysteries of nature. -
Heavenly Stuff
Palingenesia 96 Heavenly Stuff The constitution of the celestial objects and the theory of homocentric spheres in Aristotle's cosmology Bearbeitet von Theokritos Kouremenos 1. Auflage 2010. Buch. 150 S. Hardcover ISBN 978 3 515 09733 8 Format (B x L): 17 x 24 cm Weitere Fachgebiete > Philosophie, Wissenschaftstheorie, Informationswissenschaft > Philosophie: Allgemeines > Antike Philosophie Zu Inhaltsverzeichnis schnell und portofrei erhältlich bei Die Online-Fachbuchhandlung beck-shop.de ist spezialisiert auf Fachbücher, insbesondere Recht, Steuern und Wirtschaft. Im Sortiment finden Sie alle Medien (Bücher, Zeitschriften, CDs, eBooks, etc.) aller Verlage. Ergänzt wird das Programm durch Services wie Neuerscheinungsdienst oder Zusammenstellungen von Büchern zu Sonderpreisen. Der Shop führt mehr als 8 Millionen Produkte. 1. ARISTOTLE’S COSMOLOGY 1.1. PLANTS AND ANIMALS VS. CELESTIAL OBJECTS In Cael . B 5 Aristotle sets out to answer the surprising question why the direction of the diurnal rotation is from east to west, not the other way around.1 Since he be- lieves that, in contrast to what is the case with plants and animals, substances com- ing into being and passing away, nothing occurs randomly in the eternal realm of celestial objects, there cannot but be some reason why the diurnal rotation is from east to west (287b24–28). His brief explanation is prefaced by some words of cau- tion, betokening understandable distress at his raising and trying to settle, albeit tentatively, the issue at hand. To try to pronounce an opinion on intractable matters, such as the one Aris- totle himself is looking into here, and the unwillingness to circumvent any subject might be considered a symptom of excessive eagerness to investigate or, worse, simple-mindedness. -
Pythagorean Philolaus' Pyrocentric Universe
PYTHAGOREAN PHILOLAUS’ PYROCENTRIC UNIVERSE: ITS SIGNIFICANCE AND CONTRIBUTION TO ASTRONOMY AND ASTROPHYSICS YIORGO N. MANIATIS Hellenic Open University [email protected] ABSTRACT. In this work, first, I reexamine the pyrocentric universe of the Pythagorean, Phi- lolaus, who emphatically propounded that the center of the cosmos is neither the earth nor the sun, but a central fiery hearth that stands in the middle of the spherical universe. Second, I attempt to demonstrate the value and significance of this pyrocentric cosmic model by elaborating its novel revolutionary elements and its contribution to astronomy. Third, by underlining the diachroneity and timeliness of this cosmic model, I try to establish as to how the model served as a precursor to not only the ancient and modern heliocentric models, as widely believed, but also as much to the contemporary cosmic models and theories of astro- physics. KEYWORDS. Philolaus, Pythagoreanism, cosmology, universe, astronomy, astrophysics Introduction Pythagoreans were the first, in the history of philosophy and science, to conceive that the earth does not form the center of the universe, but is an orbiting planet, a fact that is closer to the scientific truth. However, most of the historical accounts of science today wrongly project that astronomical revolution started from the 17th cen- tury onwards with the Copernican Revolution, by pioneers like Copernicus, Brahe, Kepler, Galileo, Newton, and others. Only when there is a reference to other associ- ated ancient Greeks, the names of a few astronomers such as Aristarchus and Ptolemy are mentioned. The true pioneers of the astronomical revolution — Py- thagoreans and the other Presocratics — find little or no mention in these accounts. -
Ovid, the Fasti and the Stars 1
Ovid, the Fasti and the Stars 1 Ovid, the Fasti and the Stars This is a pre-print of an article accepted for publication in the Bulletin of the Institute of Classical Studies ©, vol. 50 (2007) Ovid, the Fasti and the Stars 2 Ovid, the Fasti and the Stars Abstract : In the Fasti , Ovid provides dates for a number of astronomical phenomena. For many years these were dismissed by scholars as wildly inaccurate; and this assumption of inaccuracy has formed the basis for a number of literary approaches to the Fasti . Some recent studies have challenged this view of Ovid’s accuracy, claiming that his dates are mostly accurate. This article examines the different conceptions of accuracy at work in these two positions, and explores the implication for literary approaches to the poem. By comparing Ovid’s accuracy with those of other ancient authors, and providing the first detailed exploration in Fasti scholarship of the problems inherent in modern calculations, ancient observations, and the ancient sources, I conclude that a focus on accuracy is not the most helpful methodology, and that a focus on the choice of constellation is a more productive tool for literary criticism. Ovid, the Fasti and the Stars 3 Ovid, the Fasti and the Stars. nec si rationem siderum ignoret poetas [grammatice] intellegat, qui, ut alia mittam, totiens ortu occasuque signorum in declarandis temporibus utuntur... Quintilian, Inst. Orat. 1.4.4 According to Quintilian, poetry cannot be fully understood without a good knowledge of the stars. As one example he cites the fact