Aristotle's Account of Speusippus' and Xenocrates' Metaphysical and Epistemological Theories
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The Roles of Solon in Plato's Dialogues
The Roles of Solon in Plato’s Dialogues Dissertation Presented in partial fulfillment of the requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By Samuel Ortencio Flores, M.A. Graduate Program in Greek and Latin The Ohio State University 2013 Dissertation Committee: Bruce Heiden, Advisor Anthony Kaldellis Richard Fletcher Greg Anderson Copyrighy by Samuel Ortencio Flores 2013 Abstract This dissertation is a study of Plato’s use and adaptation of an earlier model and tradition of wisdom based on the thought and legacy of the sixth-century archon, legislator, and poet Solon. Solon is cited and/or quoted thirty-four times in Plato’s dialogues, and alluded to many more times. My study shows that these references and allusions have deeper meaning when contextualized within the reception of Solon in the classical period. For Plato, Solon is a rhetorically powerful figure in advancing the relatively new practice of philosophy in Athens. While Solon himself did not adequately establish justice in the city, his legacy provided a model upon which Platonic philosophy could improve. Chapter One surveys the passing references to Solon in the dialogues as an introduction to my chapters on the dialogues in which Solon is a very prominent figure, Timaeus- Critias, Republic, and Laws. Chapter Two examines Critias’ use of his ancestor Solon to establish his own philosophic credentials. Chapter Three suggests that Socrates re- appropriates the aims and themes of Solon’s political poetry for Socratic philosophy. Chapter Four suggests that Solon provides a legislative model which Plato reconstructs in the Laws for the philosopher to supplant the role of legislator in Greek thought. -
Proclus on the Elements and the Celestial Bodies
PROCLUS ON THE ELEMENTS AND THE CELESTIAL BODIES PHYSICAL TH UGHT IN LATE NEOPLAT NISM Lucas Siorvanes A Thesis submitted for the Degree of Doctor of Philosophy to the Dept. of History and Philosophy of Science, Science Faculty, University College London. Deuember 1986 - 2 - ABSTRACT Until recently, the period of Late Antiquity had been largely regarded as a sterile age of irrationality and of decline in science. This pioneering work, supported by first-hand study of primary sources, argues that this opinion is profoundly mistaken. It focuses in particular on Proclus, the head of the Platonic School at Athens in the 5th c. AD, and the chief spokesman for the ideas of the dominant school of thought of that time, Neoplatonism. Part I, divided into two Sections, is an introductory guide to Proclus' philosophical and cosmological system, its general principles and its graded ordering of the states of existence. Part II concentrates on his physical theories on the Elements and the celestial bodies, in Sections A and B respectively, with chapters (or sub-sections) on topics including the structure, properties and motion of the Elements; light; space and matter; the composition and motion of the celestial bodies; and the order of planets. The picture that emerges from the study is that much of the Aristotelian physics, so prevalent in Classical Antiquity, was rejected. The concepts which were developed instead included the geometrization of matter, the four-Element composition of the universe, that of self-generated, free motion in space for the heavenly bodies, and that of immanent force or power. -
PROCLUS and the ANCIENTS Steven K. Strange Emory
PROCLUS AND THE ANCIENTS Steven K. Strange Emory University My title may be somewhat misleading. My subject will not be Pro- clus in general, but only his Parmenides Commentary, and I will only be concerned with those figures whom he calls in this commentary “the ancients” ( ? παλαι ), i.e., the older commentators on the dialogue, a group that certainly includes Porphyry, Amelius Gentilianus, and other early Neoplatonists, and perhaps Iamblichus, and some others whom we might suppose to be Middle Platonists, pre-Plotinian commentators. Who exactly is to be included in this category is, however, a some- what difficult and interesting question, which I wish to take up. I will examine the principal passages in which Proclus uses the expression ? παλαι in his commentary on the Parmenides,inorder,Ihope,topoint to some of the ways that they might be exploited to yield information about the earlier history of Parmenides-interpretation. I will be building throughout on the work of John Dillon in his notes and introductory material to his and Morrow’s translation of the Commentary,butIhope to be able to advance the discussion a little farther than he has done. There would be no difficulty, of course, if only Proclus had named the previous commentators whom he discusses, as he had done throughout his commentary on the Timaeus, which seems to have been among his earliest works. But the targets of his discussions in the Par- menides Commentary, in general, remain anonymous, their positions being introduced only by phrases like “some people say”, “others say”, and so forth: as Dillon argues in his Introduction,1 not naming names appears to have become Proclus’ standard practice in his later commentaries. -
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. -
Theon of Alexandria and Hypatia
CREATIVE MATH. 12 (2003), 111 - 115 Theon of Alexandria and Hypatia Michael Lambrou Abstract. In this paper we present the story of the most famous ancient female math- ematician, Hypatia, and her father Theon of Alexandria. The mathematician and philosopher Hypatia flourished in Alexandria from the second part of the 4th century until her violent death incurred by a mob in 415. She was the daughter of Theon of Alexandria, a math- ematician and astronomer, who flourished in Alexandria during the second part of the fourth century. Information on Theon’s life is only brief, coming mainly from a note in the Suda (Suida’s Lexicon, written about 1000 AD) stating that he lived in Alexandria in the times of Theodosius I (who reigned AD 379-395) and taught at the Museum. He is, in fact, the Museum’s last attested member. Descriptions of two eclipses he observed in Alexandria included in his commentary to Ptolemy’s Mathematical Syntaxis (Almagest) and elsewhere have been dated as the eclipses that occurred in AD 364, which is consistent with Suda. Although originality in Theon’s works cannot be claimed, he was certainly immensely influential in the preservation, dissemination and editing of clas- sic texts of previous generations. Indeed, with the exception of Vaticanus Graecus 190 all surviving Greek manuscripts of Euclid’s Elements stem from Theon’s edition. A comparison to Vaticanus Graecus 190 reveals that Theon did not actually change the mathematical content of the Elements except in minor points, but rather re-wrote it in Koini and in a form more suitable for the students he taught (some manuscripts refer to Theon’s sinousiai). -
Golden Ratio: a Subtle Regulator in Our Body and Cardiovascular System?
See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/306051060 Golden Ratio: A subtle regulator in our body and cardiovascular system? Article in International journal of cardiology · August 2016 DOI: 10.1016/j.ijcard.2016.08.147 CITATIONS READS 8 266 3 authors, including: Selcuk Ozturk Ertan Yetkin Ankara University Istinye University, LIV Hospital 56 PUBLICATIONS 121 CITATIONS 227 PUBLICATIONS 3,259 CITATIONS SEE PROFILE SEE PROFILE Some of the authors of this publication are also working on these related projects: microbiology View project golden ratio View project All content following this page was uploaded by Ertan Yetkin on 23 August 2019. The user has requested enhancement of the downloaded file. International Journal of Cardiology 223 (2016) 143–145 Contents lists available at ScienceDirect International Journal of Cardiology journal homepage: www.elsevier.com/locate/ijcard Review Golden ratio: A subtle regulator in our body and cardiovascular system? Selcuk Ozturk a, Kenan Yalta b, Ertan Yetkin c,⁎ a Abant Izzet Baysal University, Faculty of Medicine, Department of Cardiology, Bolu, Turkey b Trakya University, Faculty of Medicine, Department of Cardiology, Edirne, Turkey c Yenisehir Hospital, Division of Cardiology, Mersin, Turkey article info abstract Article history: Golden ratio, which is an irrational number and also named as the Greek letter Phi (φ), is defined as the ratio be- Received 13 July 2016 tween two lines of unequal length, where the ratio of the lengths of the shorter to the longer is the same as the Accepted 7 August 2016 ratio between the lengths of the longer and the sum of the lengths. -
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. -
Alexandrea Ad Aegyptvm the Legacy of Multiculturalism in Antiquity
Alexandrea ad aegyptvm the legacy of multiculturalism in antiquity editors rogério sousa maria do céu fialho mona haggag nuno simões rodrigues Título: Alexandrea ad Aegyptum – The Legacy of Multiculturalism in Antiquity Coord.: Rogério Sousa, Maria do Céu Fialho, Mona Haggag e Nuno Simões Rodrigues Design gráfico: Helena Lobo Design | www.hldesign.pt Revisão: Paula Montes Leal Inês Nemésio Obra sujeita a revisão científica Comissão científica: Alberto Bernabé, Universidade Complutense de Madrid; André Chevitarese, Universidade Federal, Rio de Janeiro; Aurélio Pérez Jiménez, Universidade de Málaga; Carmen Leal Soares, Universidade de Coimbra; Fábio Souza Lessa, Universidade Federal, Rio de Janeiro; José Augusto Ramos, Universidade de Lisboa; José Luís Brandão, Universidade de Coimbra; Natália Bebiano Providência e Costa, Universidade de Coimbra; Richard McKirahan, Pomona College, Claremont Co-edição: CITCEM – Centro de Investigação Transdisciplinar «Cultura, Espaço e Memória» Via Panorâmica, s/n | 4150-564 Porto | www.citcem.org | [email protected] CECH – Centro de Estudos Clássicos e Humanísticos | Largo da Porta Férrea, Universidade de Coimbra Alexandria University | Cornice Avenue, Shabty, Alexandria Edições Afrontamento , Lda. | Rua Costa Cabral, 859 | 4200-225 Porto www.edicoesafrontamento.pt | [email protected] N.º edição: 1152 ISBN: 978-972-36-1336-0 (Edições Afrontamento) ISBN: 978-989-8351-25-8 (CITCEM) ISBN: 978-989-721-53-2 (CECH) Depósito legal: 366115/13 Impressão e acabamento: Rainho & Neves Lda. | Santa Maria da Feira [email protected] Distribuição: Companhia das Artes – Livros e Distribuição, Lda. [email protected] Este trabalho é financiado por Fundos Nacionais através da FCT – Fundação para a Ciência e Tecnologia no âmbito do projecto PEst-OE/HIS/UI4059/2011 HYPATIA AND THE IDIOSCYNCRASIES OF CHRISTIANITY IN EGYPT – A STUDY OF THE EVENTS OCCURRED AT EASTER 415 A.D. -
Being the Treatises of the First Ennead With
Tufts College Library FROM THE INCOME OF THE SHIPMAN MEMORIAL FUND Digitized by the Internet Archive in 2016 https://archive.org/details/ethicaltreatises01plot I f ; « li s’ I I V Oo dum 5l<5ipe 0(^ i on6fu\ tiA h-6ipe^nn, 1 nDoriin^id-Dpoc t)jiile-^i!;4-CU-iC tioni, Sciopin tTiAC-ennii. TIo'dUaij 1916. LOTINUS: THE ETHICAL TREATISES BEING THE TREATISES OF THE FIRST ENNEAD WITH PORPHYRY’S LIFE OF PLOTINUS, AND THE PRELLER-RITTER EXTRACTS FORMING A CONSPECTUS OF THE PLOTINIAN SYSTEM, TRANSLATED FROM THE GREEK BY STEPHEN MACKENNA CHARLES T. BRANFORD COMPANY BOSTON, MASSACHUSETTS /1>.L % k95 ,E5 ,M-b v.l CONTENTS I'AQP. Porphyry’s Life of Plotinus ....... i THE BOOKS OF THE FIRST ENNEAD I. The Animate and the Man . .29 . II. On Virtue . • 41 III. Dialectic (or The Upward Way) . -.50 IV. On Happiness (or The Authentic Good of Life) . V. On Happiness and Extension of Time . -72 VI. On Beauty . *77 VII. On the Primal Good and its Secondary Forms . .89 VIII. On Evil, Its Nature and Source . .92 IX. On “The Reasoned Dismissal” ...... 108 BIBLIOGRAPHY AND EXPLANATORY MATTER Text, Previous Tr.\nslations . -113 Method of this Translation . .114 Commentaries ......... 116 Terminology ......... 117 The Divine Names ........ 118 The One .......... n8 The Intellectual-Principle ....... 119 The All-Soul ......... 120 The Divine-Triad as a Unity ....... 120 The Gods and Daimones ....... 121 • Man ; His Nature, Powers and Destiny ..... 121 Evil and Matter ........ 123 Morality ......... 123 The Term and the Way ....... 124 Minor Points of Terminology ....... 124 THE PRELLER-RITTER CONSPECTUS OF THE PLOTINIAN SYSTEM I. -
Murphy Ch1&2
ffiw&wwffiKK Educationin the Early Cultures ducation is, in its broadestsense, the processof transmissionof culture from one generationto the next.l what is culture but the way the membersof the group think, believe,and live; what they do, say,and hold as values.There has been some sort of education ever since human beings existecl.First was the qreat human achieve- ment of spoken language,followed by learning how to muke anJ use rools. hunt and gather food, and make fire. Then the first societiesdeveloped and humans lived in yil- lages,farming, and making pottery and things from copper and bronze.2 Education in primitive society was informal. It consisted of teaching the young to survive by hunting for food and (eventually) by planting crops; to secureshelter; to ,ouk. tools and other utensils; and to learn the tribes' values and rules. Boys learned to make tools, to hunt, and fish. Girls learned to gather and prepare foocl. primitive education knew nothing of books and schools.It was motivated by the ,reedfor self,preservation;it was direct and effective;and it was carried on by the active participation of the learner as he imitated adult activities or was shown how to make tooli, engagein the hunt, or fish. Parents were, from the beginning, the primary educators of theli children. They were helped by other members of their tribe who taughr children the practical skills needed, , and who told them stories that explained the customs (mores) of the tribe.r Moral educa- tion was thus an integral part of the educativeprocess from the beginning. -
Apollonius of Pergaconics. Books One - Seven
APOLLONIUS OF PERGACONICS. BOOKS ONE - SEVEN INTRODUCTION A. Apollonius at Perga Apollonius was born at Perga (Περγα) on the Southern coast of Asia Mi- nor, near the modern Turkish city of Bursa. Little is known about his life before he arrived in Alexandria, where he studied. Certain information about Apollonius’ life in Asia Minor can be obtained from his preface to Book 2 of Conics. The name “Apollonius”(Apollonius) means “devoted to Apollo”, similarly to “Artemius” or “Demetrius” meaning “devoted to Artemis or Demeter”. In the mentioned preface Apollonius writes to Eudemus of Pergamum that he sends him one of the books of Conics via his son also named Apollonius. The coincidence shows that this name was traditional in the family, and in all prob- ability Apollonius’ ancestors were priests of Apollo. Asia Minor during many centuries was for Indo-European tribes a bridge to Europe from their pre-fatherland south of the Caspian Sea. The Indo-European nation living in Asia Minor in 2nd and the beginning of the 1st millennia B.C. was usually called Hittites. Hittites are mentioned in the Bible and in Egyptian papyri. A military leader serving under the Biblical king David was the Hittite Uriah. His wife Bath- sheba, after his death, became the wife of king David and the mother of king Solomon. Hittites had a cuneiform writing analogous to the Babylonian one and hi- eroglyphs analogous to Egyptian ones. The Czech historian Bedrich Hrozny (1879-1952) who has deciphered Hittite cuneiform writing had established that the Hittite language belonged to the Western group of Indo-European languages [Hro].