DOCSLIB.ORG

ȘCOALA Din ATENA

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
ȘCOALA Din ATENA The SCHOOL of ATHENS The School of Athens, or Scuola di Atene in Italian, is one of the most famous frescoes by the Italian Renaissance artist Raphael. It was painted between 1509 and 1510. "Raphael received a hearty welcome from Pope Julius, and in the chamber of the Segnatura he painted... Aristotle and Plato, with the Ethics and Timaeus respectively, and a group of philosophers in a ring about them. Indescribably fine are those astrologers and geometricians drawing figures and characters with their sextants. $e further adorned his work with a perspective and many figures, so delicately and finely finished that Pope Julius caused all the other wor%s of the other masters, both old and new to be destroyed, that Raphael alone might have the glory of replacing what had been done.“ Giorgio Vasari, The Lives of the Most Excellent Architects, Painters, and Sculptors, 2nd edition, Forence, 1568 The School of Athens represents all the greatest mathematicians, philosophers and scientists from classical anti'uity gathered together sharing their ideas and learning from each other. hese "gures all lived at di(erent times, but here they are gathered together under one roof. The School of Athens is one of a group of four main frescoes on the walls of the Stan)a that depict distinct branches of knowledge. Commentators have suggested that nearly every great Greek philosopher can be found within the painting. Plato = da Vinci Aristotle = Giuliano da Sangallo $eraclit = Michelangelo Apelles = Raphael !n the centre of the fresco, at its architecture/s central vanishing point, are the two undisputed main subjects1 Plato on the left and Aristotle, his student, on the right. Aristotle !" – $$ %&' was a (ree) philosopher. *lato "$!+"$, or "$"+"$ %&– "!+ ", %& His writings cover many subjects – was a philosopher in Classical +reece. including physics, biology, )oology, $e was also a mathematician, student of Socrates, metaphysics, logic, ethics, and founder of the Academy in Athens, aesthetics, poetry, theater, music, the "rst institution of higher learning in the 3estern world. rhetoric, linguistics, politics and government 2 and constitute the "rst comprehensive system of 3estern philosophy. 4oth "gures hold modern 5of the time6, bound copies of their books in their left hands, while gesturing with their right. Plato holds imaeus, Aristotle his 7icomachean Ethics Plato's imaeus was, even in the Renaissance, a very in8uential treatise on the cosmos, whereas Aristotle insisted that the purpose of ethics is "practical" rather than "theoretical" or "speculative&. Sapho din 3esbos Socrate Socrates ",0+"-9 %& – 99 %&. was a classical (ree) (Athenian) philosopher, credited as one of the founders of 0estern philosophy. Socratic thin%ing revolve around self knowledge 9 +nothi se auton. :rom Socrates, the man becomes a problem for himself. 12our person is your soul1 he said. 4ne of the best )nown sayin5s of Socrates is 1I )now that I )now nothin56. Saying he knows nothing, Socrates is not an ignorant or not trying to assert the uselessness of knowledge. This is not an abdication or a cause for resignation, but, on the contrary, is the "rst step to be able to know something. 1I )now that I don7t )now anythin5, but I )now that I )now more than I )now.1 The trial and e8ecution of Socrates too) place in 99 %&. Socrates was tried on two char5es9 corruptin5 the youth and impiety. :ore speci;cally, Socrates7 accusers cited two 1impious1 acts9 1failin5 to ac)nowled5e the 5ods that the city ac)nowled5es1 and 1introducin5 new deities1. After the <ote on Socrates7 5uilt, his prosecutor proposed the death penalty. The =ury <oted for death as the penalty. Apparently in accordance with his philosophy of obedience to law, he carried out his own e8ecution, by drin)in5 the hemloc) provided to him. Socrates died at the a5e of ,0. Socrates was ac'uitted in ;<=; after ;><< years from death, in a new process, symbolically, in +reece. Sappho was a (ree) lyric poet, born on the island of 3esbos. Her birth was sometime between ?@< and ?=; 4*, and it is said that she died around >A< 4C, but little is known for certain about her life. The bulk of her poetry, which was well9%nown and greatly admired through much of anti'uity, has been lost. 4ut, her immense reputation has endured through surviving fragments. Sappho's poetry centers on passion and love for various people and both se#es. The word lesbian derives from the name of the island of her birth, Besbos, while her name is also the origin of the word Sapphic. Heraclitus of Ephesus c. 5 5 # c. ",5 %&' was a pre?Socratic (ree) philosopher. >e was called "The 4bscure" and the 10eepin5 *hilosopher". $eraclitus is famous for his insistence on ever9present change in the universe, as stated in the famous saying, "7o man ever steps in the same river twice" 9 Panta rhei, "everything 8ows&. He believed in the unity of opposites, stating that "the path up and down are one and the same", all e#isting entities being characteri)ed by pairs of contrary properties. :or $egel, Heraclitus/s great achievements were to have understood the nature of the in"nite, which for Hegel includes understanding the inherent contradictoriness and negativity of reality, and to have grasped that reality is becoming or process. Epicur >ypatia *armenides *ytha5oras Parmenides of Elea 9 >th century 4CE 9 was an ancient +reek philosopher. He was the founder of the Eleatic school of philosophy. The single known work of Parmenides is a poem, Cn 7ature, which has survived only in fragmentary form. !n this poem, Parmenides describes two views of reality. !n 1the way of truth1 5a part of the poem6, he e#plains how reality 5coined as "what9is"6 is one, change is impossible, and e#istence is timeless, uniform, necessary, and unchanging. !n "the way of opinion,1 he e#plains the world of appearances, in which one/s sensory faculties lead to conceptions which are false and deceitful. These ideas strongly in8uenced the whole of 3estern philosophy. $ypatia /born c. AD 50 # ,0A died "15) was a Greek Alexandrine Neoplatonist philosopher in Egypt who was one of the earliest mothers of mathematics. 7o written wor%, widely recogni)ed by scholars as $ypatia's own, has survived to the present time. A partial list of Hypatia's works as mentioned by other antique and medieval authors or as posited by modern authors: • A commentary on the 1@-volume Arithmetica by Diophantus • A commentary on the Conics of Apollonius. • Edited the existing version of Ptolemy/s Almagest • Edited her father's commentary on Euclid's Elements • She wrote a te#t " he Astronomical Canon". As head of the Platonist school at Ale#andria, she also taught philosophy and astronomy. .athematician, astronomer, educator, inventor, musician, philosopher, Hypathia of Ale#andria is a symbol of reason, science, thinking without dogmas. According to the contemporary source, Hypatia was murdered by a Christian mob. Some of them, therefore, hurried away by a "erce and bigoted )eal, whose ringleader was a reader named Peter, waylaid her returning home and, dragging her from her carriage. They took her to the church called Caesareum, where they completely stripped her, and then murdered her with tiles. After tearing her body in pieces, they took her mangled limbs to a place called Cinaron, and there burnt them. *ytha5oras of Samos /c. 5,0 %& # c. "95 %&. was an Ionian (ree) philosopher, mathematician, and founder of the reli5ious mo<ement called *ytha5oreanism. Pythagoras made in8uential contributions to philosophy and religion in the late ?th century 4*. He is often revered as a great mathematician, mystic, and scientist but is best known for the Pythagorean theorem which bears his name. Epicurus / "1#$,0 %&. was an ancient (ree) philosopher as well as the founder of the school of philosophy called Epicureanism. :or Epicurus, the purpose of philosophy was to attain the happy, tran'uil life, characteri)ed by atara#ia E peace and freedom from fear E and aponia E the absence of pain E and by living a self9suFcient life surrounded by friends. Strabon *tolemeu Euclid Euclid /born un)nown ? died un)nown. was a (ree) mathematician, often referred to as the 1Cather of (eometry". In the 'lements, Euclid deduced the principles of what is now called 'uclidean 5eometry from a small set of a#ioms. His Elements is one of the most in8uential works in the history of mathematics, serving as the main te#tbook for teaching mathematics 5especially geometry) from the time of its publication until the late =Gth or early ;<th century. Strabo /-"+- %& # c. AD $". was a (ree) 5eo5rapher, philosopher and historian. Strabo is most famous for his wor% (eo5raphica, which presented a descriptive history of people and places from di(erent regions of the world known to his era &laudius *tolemy /c. A@ 90 # c. A@ 1-!. was a (reco?Roman writer of Alexandria, )nown as a mathematician, astronomer, 5eo5rapher, astrolo5er. Ptolemy was the author of several scienti"c treatises, three of which were of continuing importance to later !slamic and European science. *tolemy7s model, was 5eocentric and was almost universally accepted until the appearance of simpler heliocentric models during the scienti"c revolution. @io5enes of Sinope was a (ree) philosopher and one of the founders of &ynic philosophy. >e was born in Sinope in "1$ or "0" %&' and died at &orinth in $ %&'. >e embarrassed *lato, disputed his interpretation of Socrates and sabota5ed his lectures. He belie<ed that virtue was better re<ealed in action than in theory. >e used his simple lifestyle and behavior to criticise the social values and institutions of what he saw as a corrupt society. He begged for a living and slept in a large ceramic 0ar in the mar%etplace.
Load more

Recommended publications
  • Central Balkans Cradle of Aegean Culture
    ANTONIJE SHKOKLJEV SLAVE NIKOLOVSKI - KATIN PREHISTORY CENTRAL BALKANS CRADLE OF AEGEAN CULTURE Prehistory - Central Balkans Cradle of Aegean culture By Antonije Shkokljev Slave Nikolovski – Katin Translated from Macedonian to English and edited By Risto Stefov Prehistory - Central Balkans Cradle of Aegean culture Published by: Risto Stefov Publications [email protected] Toronto, Canada All rights reserved. No part of this book may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording or by any information storage and retrieval system without written consent from the author, except for the inclusion of brief and documented quotations in a review. Copyright 2013 by Antonije Shkokljev, Slave Nikolovski – Katin & Risto Stefov e-book edition 2 Index Index........................................................................................................3 COMMON HISTORY AND FUTURE ..................................................5 I - GEOGRAPHICAL CONFIGURATION OF THE BALKANS.........8 II - ARCHAEOLOGICAL DISCOVERIES .........................................10 III - EPISTEMOLOGY OF THE PANNONIAN ONOMASTICS.......11 IV - DEVELOPMENT OF PALEOGRAPHY IN THE BALKANS....33 V – THRACE ........................................................................................37 VI – PREHISTORIC MACEDONIA....................................................41 VII - THESSALY - PREHISTORIC AEOLIA.....................................62 VIII – EPIRUS – PELASGIAN TESPROTIA......................................69
    [Show full text]
  • MINEOLA BIBLE INSTITUTE and SEMINARY Philosophy II Radically
    MINEOLA BIBLE INSTITUTE AND SEMINARY Page | 1 Philosophy II Radically, Biblical, Apostolic, Christianity Bishop D.R. Vestal, PhD Larry L Yates, ThD, DMin “Excellence in Apostolic Education since 1991” 1 Copyright © 2019 Mineola Bible Institute Page | 2 All Rights Reserved This lesson material may not be used in any manner for reproduction in any language or use without the written permission of Mineola Bible Institute. 2 Contents Introduction ................................................................................................................................. 7 Alexander the Great (356-323 B.C.) ........................................................................................... 8 Philip II of Macedonia (382-336 B.C.) ....................................................................................... 12 Page | 3 “Olympias the mother of Alexander was an evil woman. .......................................... 13 Philip II (of Macedonia) (382-336 BC) .............................................................................. 13 Aristotle (384-322 BC) ............................................................................................................... 15 Works .................................................................................................................................... 16 Methods ............................................................................................................................... 17 Doctrines ............................................................................................................................
    [Show full text]
  • 1 the AURIC TIME SCALE and the MAYAN FACTOR Or Demography
    1 THE AURIC TIME SCALE AND THE MAYAN FACTOR or Demography, Seismicity And History Of Great Revelations In The Light Of The Solar-Planetary Synchronism Sergey Smelyakov, Yuri Karpenko 2 Sergey V. Smelyakov, Professor, Ph.D., ISAR’s International Vice-President from Ukraine, Member of the Golden Fund of Cyclic Science of Russia and NIS Yuri Karpenko, M.E., Member of the Astrological Research Society “Hamburg School”, Member of Astrovita THE AURIC TIME SCALE AND THE MAYAN FACTOR: Demography, Seismicity and History of Great Revelations in the Light of the Solar-planetary Synchronism. - Kharkov, 1999 Corrections, 2004. The world is one and indivisible. But what can present its unity in num- ber, or specify the community (or synchronism) between such fundamental fea- tures of this Universe as periods of planetary revolutions and 11-year Solar ac- tivity cycle, trends in demography and the Mayan Calendar, the epochs of com- ing of Great Teachers of humanity, not speaking about geological, economical and other cycles in Nature and society? As it turns out, the historical structure of all these phenomena is syn- chronized by the Golden section number = 1.618 033 9… (or by Fibonacci series, as its integer presentation) and the average period T0 = 11.07 (years) of 11-year Solar activity cycles. This synchronism is described with the use of rather simple object – the Auric series, viz. a geometrical progression F = {… -2, -1, 0=1, 1, 2, …} being infinite to both ends, the unit 0=1 of which corresponds to the Earthy k k ¡ year, or to T0. For this series, the terms ¡ , 2· correspond [6] to most known basic periods in Nature and society (from biology to geology, including eco- nomical cycles), and in this sense the series F defines the Scale of the basic phenomena periods.
    [Show full text]
  • The Wars of the Odrysian Kingdom Against Philip II (352–339
    UDC 930.84 (4— 12) YU ISSN 0350—7653 ACADEMIE SERBE DES SCIENCES ET DES ARTS INSTITUT DES ETUDES BALKANIQUES UDC 930.84 (4— 12) YU ISSN 0350—7653 ACADEMIE SERBE DES SCIENCES ET DES ARTS INSTITUT DES ETUDES BALKANIQUES BALCANICA ANNUAIRE DE L’INSTITUT DES ETUDES BALKANIQUES BALCANICA ANNUAIRE DE L’INSTITUTXXVI DES ETUDES BALKANIQUES XXVI Rédacteur NIKOLA TASIĆ Directeur de l’Institut des Etudes balkaniques SecrétaireRédacteur ALEKSANDARNIKOLA PALAVESTRA TASIĆ Directeur de l’Institut des Etudes balkaniques Membres de la Rédaction MtLUTIN GARAŠANIN,Secrétaire MILKA IVIĆ, ČEDOMIR POPOV, ANTHONY-EMILALEKSANDAR TACHIAOS PALAVESTRA (Thessalonique), DIMITRIJE ĐORĐEVIĆ (Santa Barbara), DRAGOSLAV ANTONIJEVIĆ, VESELIN ĐURETIĆ,Membres MIODRAG de la Rédaction STOJANOVIĆ MtLUTIN GARAŠANIN, MILKA IVIĆ, ČEDOMIR POPOV, ANTHONY-EMIL TACHIAOS (Thessalonique), DIMITRIJE ĐORĐEVIĆ (Santa Barbara),BELGRADE DRAGOSLAV ANTONIJEVIĆ, VESELIN ĐURETIĆ, MIODRAG1995 STOJANOVIĆ BELGRADE 1995 http://www.balcanica.rs UDC 938.1(093)"-03" Original Scholarly Work Kinl JORDANüV Instîtute of Thracology Sofia THE WARS OF THE ODRYSIAN KINGDOM AGAINST PHILIP II 352-339 BC Abstract:, The paper trace the dynamism of the complex military and politi- cćtl relations betvveen the Odrysian State and Philip П, vvhich are often the subject of brisk polemics in historiography. The military campaigns of the Macedonian niler in 352/331, 347/3346 and 342/341 BĆ, which resulted m a considérable weakening of the Odrysian kingdom, are investigated suc- cessively and in detail. The successes of Philip IL however, are not the sought reliable evidence about the existence of a stable Macedonian mili­ tant' and administrative mie in the lands betvveen the Haemus. the Aegean Sea and the Propontis, as some researchers are inchned to believe.
    [Show full text]
  • Doc < Parmenides (Dodo Press) \\ Read
    Parmenides (Dodo Press) / PDF \\ 8YW5QL2UKY Parmenides (Dodo Press) By Plato Dodo Press, United Kingdom, 2007. Paperback. Book Condition: New. 229 x 152 mm. Language: English . Brand New Book ***** Print on Demand *****.Plato (428/427 BC-348/347 BC), whose original name was Aristocles, was an ancient Greek philosopher, the second of the great trio of ancient Greeks - succeeding Socrates and preceding Aristotle - who between them laid the philosophical foundations of Western culture. Plato was also a mathematician, writer of philosophical dialogues, and founder of the Academy in Athens, the first institution of higher learning in the western world. Plato is widely believed to have been a student of Socrates and to have been deeply influenced by his teacher s unjust death. Plato s brilliance as a writer and thinker can be witnessed by reading his Socratic dialogues. Some of the dialogues, letters, and other works that are ascribed to him are considered spurious. Plato is thought to have lectured at the Academy, although the pedagogical function of his dialogues, if any, is not known with certainty. They have historically been used to teach philosophy, logic, rhetoric, mathematics, and other subjects about which he wrote. READ ONLINE [ 4.48 MB ] Reviews Good electronic book and valuable one. It generally is not going to charge an excessive amount of. Its been developed in an remarkably straightforward way and is particularly simply following i finished reading this ebook through which really transformed me, change the way i think. -- Mr. Domenic Eichmann This created ebook is wonderful. I am quite late in start reading this one, but better then never.
    [Show full text]
  • Innovation and Conceptual Innovation in Ancient Greece Benoît Godin
    Innovation and Conceptual Innovation in Ancient Greece Benoît Godin with the collaboration of Pierre Lucier INRS Chaire Fernand Dumont sur la Culture Project on the Intellectual History of Innovation Working Paper No. 12 2012 Previous Papers in the Series 1. B. Godin, Innovation: the History of a Category. 2. B. Godin, In the Shadow of Schumpeter: W. Rupert Maclaurin and the Study of Technological Innovation. 3. B. Godin, The Linear Model of Innovation (II): Maurice Holland and the Research Cycle. 4. B. Godin, National Innovation System (II): Industrialists and the Origins of an Idea. 5. B. Godin, Innovation without the Word: William F. Ogburn’s Contribution to Technological Innovation Studies. 6. B. Godin, ‘Meddle Not with Them that Are Given to Change’: Innovation as Evil. 7. B. Godin, Innovation Studies: the Invention of a Specialty (Part I). 8. B. Godin, Innovation Studies: the Invention of a Specialty (Part II). 9. B. Godin, καινοτομία: An Old Word for a New World, or the De-Contestation of a Political and Contested Concept. 10. B. Godin, Innovation and Politics: The Controversy on Republicanism in Seventeenth Century England. 11. B. Godin, Social Innovation: Utopias of Innovation from circa-1830 to the Present. Project on the Intellectual History of Innovation 385 rue Sherbrooke Est, Montréal, Quebec H2X 1E3 Telephone: (514) 499-4074; Facsimile: (514) 499-4065 www.csiic.ca 2 Abstract The study of political thought and the history of political ideas are concerned with concepts such as sovereignty, liberty, virtue, republic, democracy, constitution, state and revolution. “Innovation” is not part of this vocabulary. Yet, innovation is a political concept, first of all in the sense that it is a preoccupation of statesmen for centuries: innovation is regulated by Kings, forbidden by law and punished.
    [Show full text]
  • Plato's Philosophy of Education and the Common Core Debate
    Plato’s Philosophy of Education and the Common Core debate Conference Paper Association for the Development of Philosophy Teaching (ADOPT) Spring Conference, Chicago, IL. De Paul University April 25, 2015 Madonna Murphy, Ph.D., University of St. Francis EDUCATION IN ANCIENT GREECE In Greece we find the origins of many of our educational policies and systems as it is the originating sources of Western civilization. Greek ideas about education and their educational practices have been very influential to other cultures. One of Rome's greatest service to mankind is that it carried the Greek tradition to all the Western lands. Greek civilization developed between 1200 and 490 B.C. It is in the Age of Pericles, around 500 B.C., that we see the first organized effort in a Western society for formal education. 1 The study of ancient Greek civilization provides valuable lessons on citizenship and civic education that illustrates the important role of education in shaping good citizens. Textual analysis of his various dialogues reveals Plato’s views on the purpose of education, what it is that should be taught to others and how the teacher should impart this knowledge. Plato’s educational thought illuminates many problems today’s educators face: Who are worthy models for children to imitate? How does education help to shape good citizenship? How does education serve humankind’s search for truth? In particular we will extrapolate Plato’s response the current common core debate. PLATO’S LIFE AND FAMILY We know about Plato and his family from the comments he makes in his dialogues.
    [Show full text]
  • A Social and Historical Commentary on Demosthenes' Against
    A Social and Historical Commentary on Demosthenes’ Against Euboulides Kerry Louise Phelan A major thesis presented in fulfilment of the requirements for the degree of Doctor of Philosophy Supervisor and Head of Department: Dr. Kieran McGroarty Department of Ancient Classics Faculty of Arts, Celtic Studies and Philosophy National University of Ireland, Maynooth February, 2016 Table of Contents Abstract .......................................................................................................................... iv Acknowledgements ......................................................................................................... v Abbreviations ............................................................................................................... vii Note on the text ............................................................................................................. vii 1. Introduction 1.1: Introducing Demosthenes’ Against Euboulides .................................................... 1 1.2: Demosthenes and his speech-writing career ......................................................... 2 1.3: Libanios’ Hypothesis for Against Euboulides ..................................................... 15 1.4: The re-enactment of Pericles’ citizenship law in 403/2 BC ................................ 21 1.5: Demophilos’ decree and the extraordinary διαψήφισις of 346/5 BC ................... 25 1.6: Slavery as the penalty of a failed appeal against expulsion ................................ 43 1.7: Concluding remarks
    [Show full text]
  • Late Classical Period 404 to 338 B.C
    LATE CLASSICAL PERIOD 404 TO 338 B.C. THIRTY TYRANTS IN ATHENS TO BATTLE OF CHAERONEA ERA SUMMARY – LATE CLASSICAL After the defeat of Athens at the end of the Peloponnesian War, Sparta became the undisputed first power among the Greek city-states. The walls of Athens were pulled down and the Spartan general Lysander appointed thirty men who were loyal to Sparta to run the city. The leaders were called the "thirty tyrants" and they put many of their political opponents, including Socrates to death. Plato was a student of Socrates and witnessed these oppressions and they greatly influenced his later writings. The period immediately after the Peloponnesian war is called the "Spartan Hegemony" because, although Sparta did not collect tribute, it allowed only governments which were friendly to Sparta to exist throughout Greece. The major figure of this period was Agesilaus, a brave and noble Spartan king who came very near to freeing all of the Greek Colonies in Asia Minor before he was recalled to deal with a political crisis at home. While Agesilaus was off fighting Persians in the east, the Spartan government had fallen into a great deal of trouble. The spoils from the successful wars had done much to corrupt Sparta; there was intrigue and infighting and wars with Corinth and Thebes. These problems combined with a significantly reduced population led to the disaster the Battle of Leuctra in 371 BC. Only 33 years after they prevailed in the Peloponnesian War, the Spartans suffered a humiliating defeat against Thebes, the first major land battle that the Spartans had lost to another Greek city-state in 500 years.
    [Show full text]
  • The Ancient Eurasian World and the Celestial Pivot
    SINO-PLATONIC PAPERS Number 192 September, 2009 In and Outside the Square: The Sky and the Power of Belief in Ancient China and the World, c. 4500 BC – AD 200 Volume I: The Ancient Eurasian World and the Celestial Pivot by John C. Didier Victor H. Mair, Editor Sino-Platonic Papers Department of East Asian Languages and Civilizations University of Pennsylvania Philadelphia, PA 19104-6305 USA [email protected] www.sino-platonic.org SINO-PLATONIC PAPERS is an occasional series edited by Victor H. Mair. The purpose of the series is to make available to specialists and the interested public the results of research that, because of its unconventional or controversial nature, might otherwise go unpublished. The editor actively encourages younger, not yet well established, scholars and independent authors to submit manuscripts for consideration. Contributions in any of the major scholarly languages of the world, including Romanized Modern Standard Mandarin (MSM) and Japanese, are acceptable. In special circumstances, papers written in one of the Sinitic topolects (fangyan) may be considered for publication. Although the chief focus of Sino-Platonic Papers is on the intercultural relations of China with other peoples, challenging and creative studies on a wide variety of philological subjects will be entertained. This series is not the place for safe, sober, and stodgy presentations. Sino-Platonic Papers prefers lively work that, while taking reasonable risks to advance the field, capitalizes on brilliant new insights into the development of civilization. The only style-sheet we honor is that of consistency. Where possible, we prefer the usages of the Journal of Asian Studies.
    [Show full text]
  • Origins of Logic
    Origins of Logic Greek mathematics Rhetoric: “Eristic” and “Sophistry” Core Logic – 2007/08-1ab – p. 2/46 Greek mathematics. Pre-greek mathematics was not primarily concerned with proof, but more with computation. (Egyptians, Babylonians) Geometry = measurement of the earth Jens Høyrup, Lengths, widths, surfaces. A portrait of old Babylonian algebra and its kin. New York 2002 Jens Høyrup, Bronze age formal science? in: B. Löwe, V. Peckhaus, T. Räsch ( eds. ), Foundations of the formal sciences IV, London 2006 [Studies in Logic 3], p. 81–102 Core Logic – 2007/08-1ab – p. 3/46 Greek mathematics. Pre-greek mathematics was not primarily concerned with proof, but more with computation. (Egyptians, Babylonians) Geometry = measurement of the earth Thales of Miletus (c.625-c.546 BC): the first proof Dmitri Panchenko , Thales and the Origin of Theoretical Reasoning, Configurations 1 (1993), p. 387-414 Core Logic – 2007/08-1ab – p. 3/46 Greek mathematics. Pre-greek mathematics was not primarily concerned with proof, but more with computation. (Egyptians, Babylonians) Geometry = measurement of the earth Thales of Miletus (c.625-c.546 BC): the first proof Dmitri Panchenko , Thales and the Origin of Theoretical Reasoning, Configurations 1 (1993), p. 387-414 Pythagoras (c.569-c.475 BC) Mathematics built on proof: Theaetetus (c.417-c.369 BC); student of Socrates Euclid (c.325-c.265 BC); compilation of mathematical knowledge Core Logic – 2007/08-1ab – p. 3/46 Mathematical techniques. Proof by contradiction Claim. √2 is not a fraction of integers. Suppose it were, then there are integers n and m without common divisor such that n √2 = .
    [Show full text]
  • World History Egypt(3000 BC) India(2500
    World History Egypt(3000 BC) Early ancient Egypt was the first empire; it socio-politically tradition-bound and extremely conservative. Egyptians were the most tradition-bound people in the history of the world. They preferred tradition over change thinking that change for the sake of change is a principle of dubious merit. The Pharaohs agreed because that allowed them to keep their power. Egyptian society was organized hierarchically, with gods at the top, the Pharaohs beneath, humanity next, and the dead at the bottom. Pharaoh was a god-man. Egyptians excelled at agriculture and at immense construction projects such as the Great Pyramids. They spent their lives and fortunes preparing for death. India(2500 BC) The ten centuries about 2500 BC saw the rise and fall of an ancient river valley culture based on the Indus River. Classes of society in India dominated by the caste system to maintain order. Indian civilization is best known for the caste system, it hierarchical ordering of civilization. The caste system was helpful for controlling a massive society with vastly different socioeconomic classes. The caste system of: Brahmans (priests), Barons (warriors), Commoners (merchants), and Sudras (artisans and laborers). Mesopotamia(3500 BC) Mesopotamia is earliest human civilization; first to use written language. The Sumerians lived in lower Mesopotamia (Iraq) during the fourth and third millennia BC. Mesopotamia was placed between the rivers, Tigris river and Euphrates river. in lower Mesopotamia (Iraq) during the fourth and third millennia BC. China(221 BC) China built the Great Wall and employed Confucian doctrine in their governance. China unified in 221 BC.
    [Show full text]