The Classical Quarterly THEOPHRASTUS on PLATONIC
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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. -
Thinking Outside the Sphere Views of the Stars from Aristotle to Herschel Thinking Outside the Sphere
Thinking Outside the Sphere Views of the Stars from Aristotle to Herschel Thinking Outside the Sphere A Constellation of Rare Books from the History of Science Collection The exhibition was made possible by generous support from Mr. & Mrs. James B. Hebenstreit and Mrs. Lathrop M. Gates. CATALOG OF THE EXHIBITION Linda Hall Library Linda Hall Library of Science, Engineering and Technology Cynthia J. Rogers, Curator 5109 Cherry Street Kansas City MO 64110 1 Thinking Outside the Sphere is held in copyright by the Linda Hall Library, 2010, and any reproduction of text or images requires permission. The Linda Hall Library is an independently funded library devoted to science, engineering and technology which is used extensively by The exhibition opened at the Linda Hall Library April 22 and closed companies, academic institutions and individuals throughout the world. September 18, 2010. The Library was established by the wills of Herbert and Linda Hall and opened in 1946. It is located on a 14 acre arboretum in Kansas City, Missouri, the site of the former home of Herbert and Linda Hall. Sources of images on preliminary pages: Page 1, cover left: Peter Apian. Cosmographia, 1550. We invite you to visit the Library or our website at www.lindahlll.org. Page 1, right: Camille Flammarion. L'atmosphère météorologie populaire, 1888. Page 3, Table of contents: Leonhard Euler. Theoria motuum planetarum et cometarum, 1744. 2 Table of Contents Introduction Section1 The Ancient Universe Section2 The Enduring Earth-Centered System Section3 The Sun Takes -
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. -
Platonist Philosopher Hypatia of Alexandria in Amenabar’S Film Agorá
A STUDY OF THE RECEPTION OF THE LIFE AND DEATH OF THE NEO- PLATONIST PHILOSOPHER HYPATIA OF ALEXANDRIA IN AMENABAR’S FILM AGORÁ GILLIAN van der HEIJDEN Submitted in partial fulfilment of the requirement for the degree of MASTER OF ARTS In the Faculty of Humanities School of Religion, Philosophy and Classics at the UNIVERSITY OF KWAZULU-NATAL, DURBAN SUPERVISOR: PROFESSOR J.L. HILTON MARCH 2016 DECLARATION I, Gillian van der Heijden, declare that: The research reported in this dissertation, except where otherwise indicated, is my original research; This dissertation has not been submitted for any degree or examination at any other university; This dissertation does not contain other persons’ data, pictures, graphs or other information, unless specifically acknowledged as being sourced from other persons; The dissertation does not contain other persons’ writing, unless specifically acknowledged as being sourced from other researchers. Where other written sources have been quoted, then: a) their words have been re-written but the general information attributed to them has been referenced; b) where their exact words have been used, their writing has been paragraphed and referenced; c) This dissertation/thesis does not contain text, graphics or tables copied and pasted from the Internet, unless specifically acknowledged, and the source being detailed in the dissertation/thesis and in the References sections. Signed: Gillian van der Heijden (Student Number 209541374) Professor J. L. Hilton ii ABSTRACT The film Agorá is better appreciated through a little knowledge of the rise of Christianity and its opposition to Paganism which professed ethical principles inherited from Greek mythology and acknowledged, seasonal rituals and wealth in land and livestock. -
Max Planck Institute for the History of Science Aristotle And
MAX-PLANCK-INSTITUT FÜR WISSENSCHAFTSGESCHICHTE Max Planck Institute for the History of Science 2012 PREPRINT 422 TOPOI – Towards a Historical Epistemology of Space Pietro Daniel Omodeo, Irina Tupikova Aristotle and Ptolemy on Geocentrism: Diverging Argumentative Strategies and Epistemologies TOPOI – TOWARDS A HISTORICAL EPISTEMOLOGY OF SPACE The TOPOI project cluster of excellence brings together researchers who investigate the formation and transformation of space and knowledge in ancient civilizations and their later developments. The present preprint series presents the work of members and fellows of the research group Historical Epistemology of Space which is part of the TOPOI cluster. The group is based on a cooperation between the Humboldt University and the Max Planck Institute for the History of Science in Berlin and commenced work in September 2008. Contents 1 Introduction 1 2 Aristotle 5 2.1 Aristotle’s confrontation with the cosmologies of his prede- cessors . 6 2.2 Aristotle’s presentation of his own views . 9 3 Ptolemy 15 3.1 The heavens move like a sphere . 16 3.2 The Earth, taken as a whole, is sensibly spherical . 24 3.3 The Earth is in the middle of the heavens . 24 3.4 The Earth has the ratio of a point to the heavens . 32 3.5 The Earth does not have any motion from place to place . 33 4 Conclusions and perspectives 37 Chapter 1 Introduction This paper aims at a comparison of the different argumentative strategies employed by Aristotle and Ptolemy in their approaches to geocentrism through an analysis of their discussion of the centrality of the Earth in De caelo II, 13-14 and Almagest, I, 3-7. -
Numenius and the Hellenistic Sources of the Central Christian Doctrine
! Numenius and the Hellenistic Sources ! of the Central Christian Doctrine Marian Hillar Center for Philosophy and Socinian Studies Houston, TX 77004 Paper published in A Journal from the Radical Reformation. A testimony to Biblical Unitarianism. Vol. 14, No.! 1, Spring 2007, pp. 3-31. Quis obsecro, nisi penitus amens logomachias has sine risu toleraret? Nec in Thalmud, nec in Alchoran, sunt tam horrendae blasfemiae. Haec nos hactenus audire ita sumus alsuefacti, ut nihil miremur. Futurae vero generationes stupenda haec iudicabunt. Stupenda sunt vere, plusquam ea daemonum inventa, quae Valentinianis tribuit Irenaeus. I implore you, who in his sane mind could tolerate such logomachias without bursting into laughter? Not in the Talmud, nor in the Qu’ran can one find such horrendous blasphemies. But we are accustomed to hear them to the point that nothing astonishes us. Future generations will judge them obscure. Indeed, they are obscure, much more than the diabolic inventions which Irenaeus attributed to the Valentinians. ! Michael Servetus Christianismi Restitutio, De Trinitate, lib. I. p. 46. Si locum mihi aliquem ostendas, quo verbum illud filius olim vocetur, fatebor me victum. Christianismi Restitutio, If you show me a single passage in which the Son was called the Word, I will give up. Michael Servetus, Christianismi Restitutio, De Trinitate, lib. III p. 108. ! Abstract This paper attempts to explain the sources of the central Christian doctrine about the nature of deity. We can trace a continuous line of thought from the Greek philosophy to the development of the doctrine of the Trinity. The first Christian doctrine was developed by Justin Martyr (114-165 C.E.). -
Philoponus on the Nature of the Heavens and the Movement of Elements in Against Aristotle on the Eternity of the World
_full_journalsubtitle: Journal of Patrology and Critical Hagiography _full_abbrevjournaltitle: SCRI _full_ppubnumber: ISSN 1817-7530 (print version) _full_epubnumber: ISSN 1817-7565 (online version) _full_issue: 1 _full_issuetitle: 0 _full_alt_author_running_head (change var. to _alt_author_rh): Varlamova _full_alt_articletitle_running_head (change var. to _alt_arttitle_rh): Philoponus on the Nature of the Heavens _full_alt_articletitle_toc: 0 _full_is_advance_article: 0 446 Scrinium 14 (2018) 446-461 Varlamova www.brill.com/scri Philoponus on the Nature of the Heavens and the Movement of Elements in Against Aristotle on the Eternity of the World Maria Varlamova Saint Petersburg State University of Aerospace Instrumentation [email protected] Abstract This paper deals with the John Philoponus' arguments against the eternity of the heav- ens in context of the dispute against the eternity of the world. The theory of eternity of the heavens was defended by Aristotle in his Physics and in the 1st book On the Heavens. In his treatise On Eternity of the World against Aristotle Philoponus attacks the argu- ments of Aristotle in order to prove the essential finititude of the heavens. The Philoponus' arguments are related to the nature and motion of elements and especially to the nature of fire. In order to explore the Philoponus' arguments against Aristotle I compare his doctrine with the Aristotle's theories of elemental nature and celestial motion. Keywords eternity of the heavens – elements – aether – fire – movement – Philoponus – Aristotle * The present study is a part of the project Nr. 16-03-00047, “Nature and movement in the ‘Commentaryon the Physics of Aristotle’ by Michael Psellos. Study of the influence of the late antique tradition, of the correlation between physics and the Orthodox theology, and of the reception in the later Peripatetic physics”, implemented with a financial support of the Russian Foundation for Basic Research. -
A Presocratics Reader
2. THE MILESIANS Thales, Anaximander, and Anaximenes were all from the city of Miletus in Ionia (now the western coast of Turkey) and make up what is referred to as the Milesian “school” of philosophy. Tradition reports that Thales was the teacher of Anaximander, who in turn taught Anaximenes. Aristotle begins his account of the history of philosophy as the search for causes and principles (in Metaphysics I) with these three. 2.1. Thales Thales appears on lists of the seven sages of Greece, a traditional catalog of wise men. The chronicler Apollodorus suggests that he was born around 625 BCE. We should accept this date only with caution, as Apollodorus usually calculated birthdates by assuming that a man was forty years old at the time of his “acme,” or greatest achievement. Thus, Apollodorus arrives at the date by assuming that Thales indeed predicted an eclipse in 585 BCE, and was forty at the time. Plato and Aristotle tell stories about Thales that show that even in ancient times philosophers had a mixed reputation for practicality. 1. (11A9) They say that once when Thales was gazing upwards while doing astronomy, he fell into a well, and that a witty and charming Thracian serving-girl made fun of him for being eager to know the things in the heavens but failing to notice what was just behind him and right by his feet. (Plato, Theaetetus 174a) 2. (11A10) The story goes that when they were reproaching him for his poverty, supposing that philosophy is useless, he learned from his astronomy that the olive crop would be large. -
Democritus (460-370 BC) on Embryology, Anatomy and Pediatrics: the Unknown Aspects of the Greek Atomic Scientist
IJAE Vol. 117, n. 3: 199-204, 2012 ITALIAN JOURNAL OF ANATOMY AND EMBRYOLOGY Research Article: History Of Anatomy and Embryology Democritus (460-370 BC) on Embryology, Anatomy and Pediatrics: the unknown aspects of the Greek atomic scientist Gregory Tsoucalas, Marianna Karamanou*, Antonis A. Kousoulis, George Androutsos History of Medicine Department, Medical School, University of Athens, Greece Submitted January 29, 2012; accepted June 17, 2012 Abstract Democritus was born in Abdera, Thrace, in the 5th century BC. He travelled to the East while being the student of famous philosophers. His philosophical ideas and the establishment of particles, “the atoms”, gave him a leading position in world history. However, his medical knowledge was vast especially in the field of pediatric pharmacology. Numerous are also the reports of his passion for anatomy. Democritus’ views regarding the issue of Human Nature and Anatomy are depicted in a letter he sent to Hippocrates of Kos. He died in old age, possi- bly of infection after having totally neglected his personal hygiene. Keywords Democritus; philosophy; atom; embryology; pediatrics; anatomy. Note: for ancient authors, citations in the text do not include the year of publication of the original writings; the reference list reports the year of publication of the critical edition which was used for this study. Introductory note and brief biography Democritus of Igisistratos or Athinocratos or Damasippos (Precope, 1961; Marcov- ich, 1999) was born in Abdera, Thrace, Greece, around the 80th Olympic Games, 460- 457 BC (Herodotus; Strabo) or earlier (Anaksagoras Klazomenios). He visited Egypt where, in the sanctuary of Memphis, he was initiated to Jewish spirituality by a sage woman named Maria. -
The Combinatorics of Stoic Conjunction: Hipparchus Refuted, Chrysippus Vindicated
Created on 10 January 2011 at 16.23 hours THECOMBINATORICSOFSTOIC CONJUNCTION:HIPPARCHUS REFUTED,CHRYSIPPUSVINDICATED SUSANNEBOBZIEN Dieser Aufsatz ist dem Andenken von Michael Frede gewid- met — einem wahren Philosophen und wahren Freund. Ohne sein grundlegendes Werk über die stoische Logik und ihre Entwicklung in der Antike wäre dieser Aufsatz nicht möglich. Introduction [Chrysippus] says that the number of conjunctions [constructible] from ten assertibles exceeds one million . Yet many mathematicians have refuted Chrysippus; among them is Hipparchus, who has demonstrated that his error in the calculation is huge, since the affirmative produces , con- joined assertibles, and the negative ,. (Plut. Stoic. repugn. –) Chrysippus says that the number of conjunctions [constructible] from only ten assertibles exceeds one million. However, Hipparchus refuted this, demonstrating that the affirmative encompasses , conjoined assert- ibles and the negative ,. (Plut. Quaest. conv. – ) Chrysippus, third head of the Stoa and one of the two greatest lo- gicians in antiquity, made his statement about the number of con- junctions in the third century . Hipparchus, famous astronomer and writer of a work in which he discussed combinatorics, flour- ished in the second half of the second century . The claims of © Susanne Bobzien This paper has profited greatly from detailed written comments by Fabio Acerbi and István Bodnár. An early version was presented at the Seminar ‘Hellenistic Science and Scholarship’ at the Radcliffe Institute, Harvard, in May , and I am grateful to the participants for their helpful remarks, in particular to Alexander Jones and the late Ian Mueller. Thanks go also to my brother Matthias Bobzien for first bringing the tree-structure method to my attention. -
A Reading of Porphyry's on Abstinence From
UNIVERSITY OF CALIFORNIA Los Angeles Justice Purity Piety: A Reading of Porphyry’s On Abstinence from Ensouled Beings A dissertation submitted in partial satisfaction of the requirements for the degree Doctor of Philosophy in Classics by Alexander Press 2020 © Copyright by Alexander Press 2020 ABSTRACT OF THE DISSERTATION Justice Purity Piety: A Reading of Porphyry’s On Abstinence from Ensouled Beings by Alexander Press Doctor of Philosophy in Classics University of California, Los Angeles, 2020 Professor David Blank, Chair Abstract: Presenting a range of arguments against meat-eating, many strikingly familiar, Porphyry’s On Abstinence from Ensouled Beings (Greek Περὶ ἀποχῆς ἐµψύχων, Latin De abstinentia ab esu animalium) offers a sweeping view of the ancient debate concerning animals and their treatment. At the same time, because of its advocacy of an asceticism informed by its author’s Neoplatonism, Abstinence is often taken to be concerned primarily with the health of the human soul. By approaching Abstinence as a work of moral suasion and a work of literature, whose intra- and intertextual resonances yield something more than a collection of propositions or an invitation to Quellenforschung, I aim to push beyond interpretations that bracket the arguments regarding animals as merely dialectical; cast the text’s other-directed principle of justice as wholly ii subordinated to a self-directed principle of purity; or accept as decisive Porphyry’s exclusion of craftsmen, athletes, soldiers, sailors, and orators from his call to vegetarianism. -
Face to Face and One Face Reflected in Many Mirrors
Irina Kolbutova Moscow [email protected] FACE TO FACE AND ONE FACE REFLECTED IN MANY MIRRORS In this article I would like to demonstrate how a very ancient theo- logical concept emerged unexpectedly through the mediation of the Platonic tradition almost simultaneously in the twelfth-century Latin West and in a remote oriental context, and how these two later devel- opments of the same set of ideas can clarify each other and their com- mon roots. At the outset it is worth making some observations concerning the use of the early Christian writings in this study, which scholars of the previous generations almost indiscriminately called “gnostic” thus us- ing the term by which, as was noted by A. DeConick, they att empted to reconstruct “an umbrella religion called ‘Gnosticism,’ a religion which in fact did not exist.”1 Furthermore, as R. G. Hall indicated, “the terms ‘Jewish,’ ‘Christian,’ and ‘gnostic’ are notoriously slippery when ap- plied to texts from early in the second century. The Odes of Solomon, with their close relationship to the Hodayot from Qumran, on the one hand, and to later gnostic literature, on the other, would belong equal- ly in studies of ancient Jewish hymnody, early Christian prophecy, and the origin of gnosticism. The Gospel of John belongs as clearly in a study of Gnostic origins as in a study of Christian origins and is Jew- ish to such an extent that one of the biggest issues it faces is being put out of the synagogue.”2 Finally, A. Golitz in highlighted the problem noting the “re-evaluation of apocalyptic literature, Christian origins, and the analysis of Gnosticism” for which scholars “had begun to look to more proximate (as opposed to distant Iranian), Jewish sources.” As this scholar observed, “we can fi nd a striking instance of this shift in the respective — and stunningly diff erent — analyses of the Acts of (1) A.