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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. -
Mathematical Discourse in Philosophical Authors: Examples from Theon of Smyrna and Cleomedes on Mathematical Astronomy
Mathematical discourse in philosophical authors: Examples from Theon of Smyrna and Cleomedes on mathematical astronomy Nathan Sidoli Introduction Ancient philosophers and other intellectuals often mention the work of mathematicians, al- though the latter rarely return the favor.1 The most obvious reason for this stems from the im- personal nature of mathematical discourse, which tends to eschew any discussion of personal, or lived, experience. There seems to be more at stake than this, however, because when math- ematicians do mention names they almost always belong to the small group of people who are known to us as mathematicians, or who are known to us through their mathematical works.2 In order to be accepted as a member of the group of mathematicians, one must not only have mastered various technical concepts and methods, but must also have learned how to express oneself in a stylized form of Greek prose that has often struck the uninitiated as peculiar.3 Be- cause of the specialized nature of this type of intellectual activity, in order to gain real mastery it was probably necessary to have studied it from youth, or to have had the time to apply oneself uninterruptedly.4 Hence, the private nature of ancient education meant that there were many educated individuals who had not mastered, or perhaps even been much exposed to, aspects of ancient mathematical thought and practice that we would regard as rather elementary (Cribiore 2001; Sidoli 2015). Starting from at least the late Hellenistic period, and especially during the Imperial and Late- Ancient periods, some authors sought to address this situation in a variety of different ways— such as discussing technical topics in more elementary modes, rewriting mathematical argu- ments so as to be intelligible to a broader audience, or incorporating mathematical material di- rectly into philosophical curricula. -
Is Plato a Perfect Idealist?
IOSR Journal Of Humanities And Social Science (IOSR-JHSS) Volume 19, Issue 3, Ver. V (Mar. 2014), PP 22-25 e-ISSN: 2279-0837, p-ISSN: 2279-0845. www.iosrjournals.org Is Plato a Perfect Idealist? Dr. Shanjendu Nath M. A., M. Phil., Ph.D. Associate Professor Rabindrasadan Girls’ College, Karimganj, Assam, India. Abstract: Idealism is a philosophy that emphasizes on mind. According to this theory, mind is primary and objective world is nothing but an idea of our mind. Thus this theory believes that the primary thing that exists is spiritual and material world is secondary. This theory effectively begins with the thought of Greek philosopher Plato. But it is Gottfried Wilhelm Leibniz (1646–1716) who used the term ‘idealism’ when he referred Plato in his philosophy. Plato in his book ‘The Republic’ very clearly stated many aspects of thought and all these he discussed from the idealistic point of view. According to Plato, objective world is not a real world. It is the world of Ideas which is real. This world of Ideas is imperishable, immutable and eternal. These ideas do not exist in our mind or in the mind of God but exist by itself and independent of any mind. He also said that among the Ideas, the Idea of Good is the supreme Idea. These eternal ideas are not perceived by our sense organs but by our rational self. Thus Plato believes the existence of two worlds – material world and the world of Ideas. In this article I shall try to explore Plato’s idealism, its origin, locus etc. -
The Metaphysical Doctrine of Creation
The Metaphysical Doctrine of Creation THOMAS V. MORRIS The majestic introduction to the book of Genesis proclaims that1 In the beginning, God created the heavens and the earth. This is the key to a distinctively theistic perspective on reality. This one statement captures the heart of a theistic world-view: We live in a created universe. For centuries, theists have held that the most important truth about our world is that it is a created world. And it is no exaggeration to add that one of the most important truths about God is that He is the creator of this world. Aquinas once expressed the core of the doctrine of creation quite suc- cinctly with the single sentence: Anything that exists in any way must necessarily have its origin fromGod.2 The philosophical view which is here so crisply and simply conveyed, I shall refer to as the metaphysical doctrine of creation . I understand it as a thesis about the metaphysical or ontological dependence of all things distinct from God on God as their source of being, the ultimate cause of their existence. As a philosophical thesis, the metaphysical doctrine of creation is not to be thought of as necessarily allied to, or as in competition with, any particu- lar scientific theory of physical cosmology or biological development. A few years ago, many religious people enthusiastically welcomed and loudly en- dorsed what is popularly known as the Big Bang Theory of Physical Cosmol- ogy. The physical event which was postulated to have issued in an almost inconceivable, explosive origination of our current cosmos was widely bap- tized as a scientific acknowledgement of the act of divine creation. -
Automatic Action in Plotinus
Created on 26 November 2007 at 17.13 hours page 373 AUTOMATIC ACTION IN PLOTINUS JAMES WILBERDING 1. Introduction Plotinus scholars have recently called attention to a kind of action in the sensible world, which one could call ‘spontaneous’ or ‘automatic’ action, that is supposed to result automatically from the contemplation of the intelligible.1 Such action is meant to be opposed to actions that result from reason, calculation, and plan- ning, and has been put to work to provide a way for Plotinus’ sage to act, and in particular to act morally, without compromising his ã James Wilberding 2008 A version of this paper was presented at the Katholieke Universiteit Leuven in 2006, where it received a helpful discussion. For comments and suggestions I am par- ticularly indebted to Peter Adamson, Julie Cassiday, Christoph Helmig, Christoph Horn, Jan Opsomer, David Sedley, and Carlos Steel. I have also profited greatly from a reading group held in autumn 2005 at King’s College London on Ennead 3. 8 with Peter Adamson, Verity Harte, M. M. McCabe, and others. I would like to thank Williams College and the Humboldt-Stiftung for funding the research leave during which this paper was written, and Andreas Speer for welcoming me into the Thomas-Institut for this period. 1 e.g. A. Schniewind, L’Ethique‹ du sage chez Plotin [L’Ethique‹ ] (Paris, 2003), 190 with n. 7: ‘les actions du sage sont l’expression (παρακολοýθηµα) de sa propre con- templation . Plotin evoque‹ deux possibilites:‹ d’une part, les actions par faiblesse (èσθÝνεια) de contemplation, pour ceux qui ne parviennent pas a› l’Un; d’autre part — et c’est la› ce qui correspond au sage — les actions en tant qu’activites‹ secondaires (παρακολοýθηµα), issues de la contemplation’; D. -
The Emergent, Self-Explaining Universe of Paul Davies – a Summary and Christian Response
S & CB (2012), 24, 33–53 0954–4194 PAUL HIMES The Emergent, Self-explaining Universe of Paul Davies – a Summary and christian Response Physicist Paul Davies has emerged as one of the most popular scientists of the twenty-first century, despite his critique of the scientific establishment and its perceived failure to account for the origins and rational nature of the universe. Davies argues that the scientific consensus on cosmology rests on faith, both in its failure to provide an ultimate explanation for the origin of the universe and in its blind acceptance of its rational laws. As an alternative, Davies postulates an ‘emergent’ universe which contains the cause of its own existence and which renders unnecessary any sort of a personal deity. Yet Davies’s alternative falls short of providing a satisfactory cosmic explanation. Davies himself cannot adequately account for the principle of backward causation which creates his universe, and thus his paradigm still relies on a transcendent principle that remains unexplained. Furthermore, Davies’s objections against a personal god can be answered on philosophical grounds. Thus Davies’s hypothesis does not provide a superior alternative to the Christian view of God. key words: Paul Davies, physics, universe, emergent, self-causation, quantum mechanics, cosmology, time, teleology, cosmological argument, fine-tuning introduction Douglas Adams’ classic Hitchhiker’s Guide to the Galaxy tells the story of an advanced civilisation that builds a magnificent supercomputer for the sole purpose of providing the ultimate answer to the meaning of ‘life, the universe, and everything’. After millions of years of calculation, the an- swer, much to the confusion and frustration of the advanced civilisation, turns out to be ‘42’.1 Physicist Paul C. -
INFINITE PROCESSES in GREEK MATHEMATICS by George
INFINITE PROCESSES IN GREEK MATHEMATICS by George Clarence Vedova Thesis submitted to the Faculty of the Graduate School of the University of Maryland in partial fulfillment of the requirements for the degree of Doctor of Philosophy 1943 UMI Number: DP70209 All rights reserved INFORMATION TO ALL USERS The quality of this reproduction is dependent upon the quality of the copy submitted. In the unlikely event that the author did not send a complete manuscript and there are missing pages, these will be noted. Also, if material had to be removed, a note will indicate the deletion. Dissertation Publishing UMI DP70209 Published by ProQuest LLC (2015). Copyright in the Dissertation held by the Author. Microform Edition © ProQuest LLC. All rights reserved. This work is protected against unauthorized copying under Title 17, United States Code ProQuest ProQuest LLC. 789 East Eisenhower Parkway P.O. Box 1346 Ann Arbor, Ml 48106 - 1346 PREFACE The thesis is a historico-philosophic survey of infinite processes in Greek mathematics* Beginning with the first emergence, in Ionian speculative cosmogony, of the tinder lying concepts of infinity, continuity, infinitesimal and limit, the survey follows the development of infinite processes through the ages as these concepts gain in clarity, -it notes the positive contributions of various schools of thought, the negative and corrective influences of others and, in a broad way, establishes the causal chain that finally led to the more abstract processes of the mathematical schools of Cnidus (Eudoxus) and Syracuse -
The Quantum God: an Investigation of the Image of God from Quantum Science
The Quantum God: An Investigation of the Image of God from Quantum Science By Meaghean H. Richardson A Thesis Submitted to Saint Mary’s University, Halifax, Nova Scotia in Partial Fulfillment of the Requirements for the Degree of Master of Arts in Theology and Religious Studies June, 2015, Halifax, Nova Scotia Copyright Meaghean H. Richardson, 2015. Approved: Dr. Anne Marie Dalton Supervisor Approved: Dr. Mary Hale Reader Approved: Dr. Magi Abdul-Masih Examiner Date: June 5, 2015 2 ABSTRACT The Quantum God: An Investigation of the Image of God from Quantum Science By Meaghean H. Richardson This thesis is an investigation of the image of God arising from understandings of quantum science and argues that it enhances ideas about God. It considers the significance of religious interpretations of quantum science and briefly examines the case of Christian theology and God’s actions in the world. The nature of quantum phenomena requires the use of imagery likened to that used in many mystical and religious traditions. Using a multivalued approach, I give equitable consideration to multiple scientific and theological interpretations to describe the God-concept presented by sources writing on the mystical implications of quantum science. The quantum demands an intellectual and academic openness, requiring the use of resources outside of science, and pushes for a holistic approach and a transition to a postmodern paradigm. Therefore, the quantum is said to be a re-enchanting force, calling for a re-evaluation of the spiritual dimension in our overall understanding of reality. June 5, 2015 3 ACKNOWLEDGEMENTS I must first thank my parents for their support of every kind while I chase my dreams. -
Conditions for Proclus's Allegorical Reading of Plato's Parmenides
"Ciarifications" of Obscurity: Conditions for Proclus's Allegorical Reading of Plato's Parmenides Florin George Cäl ian Exegetical work on philosophical systems requires not only that one give an account of the structure of a system's assumptions and arguments, but also of its forms, such as the form of expression (or genre: dialogue, poem, aphorisms, and so on), or its form of argumentation (clear cut dis cursive exposition, logical forma lization, metaphorical, allegorical dis course, and so forth). These formal considerations may seem to be sec ondary, merely ornamental issues, but they can raise unexpected ques tions. The literal reading of a text has its counter-part in allegorical interpretation. This way of reading, which must have Started with the first readers of Homer and found a fertile ground in Philo's allegorical commentaries on the Bible, was amazingly natural for Proclus (c. 411- 485), whose writings and commentaries represent the last phases of late antique philosophy, and particularly of the relation between philosophy and rhetoric. Proclus was a major systemic philosopher of late Neoplatonism. Be side his fame as one of the last notable heads of the Platonic Academy, he was also known in his youth as a rhetorician with a profound curiosity about divination and theurgy. He was a practitioner of magic and it is said that he knew how to bring rain and that, through a particular rite, he saved Attica from a dreadful drought.1 Proclus was devoted to the Greek gods, especially Athena, whom he invokes at the beginning of his com mentary on the Parmenides: I pray to all the gods and goddesses to guide my mind ...to kindie in me a shining light of truth .. -
Pythagorean, Predecessor, and Hebrew: Philo of Alexandria and the Construction of Jewishness in Early Christian Writings
Pythagorean, Predecessor, and Hebrew: Philo of Alexandria and the Construction of Jewishness in Early Christian Writings Jennifer Otto Faculty of Religious Studies McGill University, Montreal March, 2014 A thesis submitted to McGill University in partial fulfillment of the requirements of the degree of Doctor of Philosophy © Jennifer Otto, 2014 ii Table of Contents Abstracts v Acknowledgements vii Abbreviations viii Introduction 1 Method, Aims and Scope of the Thesis 10 Christians and Jews among the nations 12 Philo and the Wisdom of the Greeks 16 Christianity as Philosophy 19 Moving Forward 24 Part I Chapter 1: Philo in Modern Scholarship 25 Introducing Philo 25 Philo the Jew in modern research 27 Conclusions 48 Chapter 2: Sects and Texts: The Setting of the Christian Encounter with Philo 54 The Earliest Alexandrian Christians 55 The Trajanic Revolt 60 The “Catechetical School” of Alexandria— A Continuous 63 Jewish-Christian Institution? An Alternative Hypothesis: Reading Philo in the Philosophical Schools 65 Conclusions 70 Part II Chapter 3: The Pythagorean: Clement’s Philo 72 1. Introducing Clement 73 1.1 Clement’s Life 73 1.2 Clement’s Corpus 75 1.3 Clement’s Teaching 78 2. Israel, Hebrews, and Jews in Clement’s Writings 80 2.1 Israel 81 2.2 Hebrews 82 2.3 Jews 83 3. Clement’s Reception of Philo: Literature Review 88 4. Clement’s Testimonia to Philo 97 4.1 Situating the Philonic Borrowings in the context of Stromateis 1 97 4.2 Stromateis 1.5.31 102 4.3 Stromateis 1.15.72 106 4.4 Stromateis 1.23.153 109 iii 4.5 Situating the Philonic Borrowings in the context of Stromateis 2 111 4.6 Stromateis 2.19.100 113 5. -
Illinois Classical Studies
View metadata, citation and similar papers at core.ac.ukbrought to you by CORE provided by Illinois Digital Environment for... 12 Old Comedy, Menippean Satire, and Philosophy's Tattered Robes in Boethius' Consolation JOEL C. RELIHAN If one is convinced that Boethius' Consolation of Philosophy presents, in the face of death, a philosopher's heartfelt belief in the truths of the study to which he devoted his brief lifetime, then one is inclined, with Helm and Courcelle, to regard the Menippean form of the Consolation as something essentially irrelevant to its themes.^ The work would merely exemplify a prosimetric form, and not participate actively in the traditions of Menippus and Varro.2 But I am not convinced of this, and think that the Consolation questions the value of Classical philosophy in a debate that is inconclusive, never reaching its promised goal of telling the narrator, otherwise quite an adept in the definition of persons, who he really is.^ The Middle Ages, 'R. Helm, "Menippos 10." RE XV. 1 (1931) 893; P. Courcelle. La consolation de philosophie dans la tradition Utteraire: Antecedents et posterite de Boece (Paris 1967) 17-28. Courcelle relates the Consolation to the genre of the apocalypse; but F. Klingner. De Boethii Consolatione Philosophiae, Philologische Untersuchungen 27 (Berlin 1927) 155 is, I think, right when he suggests that apocalyptic became intertwined with the genre of Menippean satire before Boethius' time, so as to account for similarities between Julian's Caesares, Marlianus' De Nuptiis, and Boethius. I would claim that apocalypse has always been part of the genre, which relies heavily upon supernatural revelations of truth; consider Menippus* vision of judgement in iMcizn' s Necyomantia. -
Harmonica Membra Disjecta Fabio Acerbi and Anna Gioffreda
Harmonica Membra Disjecta Fabio Acerbi and Anna Gioffreda HE AIM of the present note is to provide the details of a palaeographic finding and to work out some con- T sequences of it.1 The finding amounts to reassembling two membra disjecta of one of the most important manuscript witnesses of ancient Greek harmonic theory. The dismembered portions (which we shall call Mo and Va, and accordingly their reassembly MoVa) presently belong to the composite manu- scripts München, Bayerische Staatsbibliothek, Cod.graec. 361a, and Città del Vaticano, Biblioteca Apostolica Vaticana, Vat.gr. 2338. As we shall see, Mo and Va are both to be dated to the second half of the thirteenth century. The palaeographic analyisis will also reveal the presence of a common reviser to whom we may give a name. This fact will allow us to reconstruct the early history of MoVa to some extent. Again, palaeographic analysis, this time applied to MoVa and to another fundamental witness to Greek harmonics, Venezia, Biblioteca Nazionale Marciana, gr. VI.3 (eleventh century),2 will provide a first step towards eliminating a long-standing draw- 1 Frequently cited items are abbreviated as follows: AEH = R. Da Rios, Aristoxeni Elementa Harmonica (Rome 1954); EOO = J. L. Heiberg and H. Menge, Euclidis Opera omnia I–VIII (Leipzig 1883–1916); MSG = C. von Jan, Musici Scriptores Graeci (Leipzig 1895); PtH = I. Düring, Die Harmonielehre des Klaudios Ptolemaios (Göteborg 1930). Online reproductions of all relevant manuscripts mentioned in this article can be found through the website https://pinakes.irht.cnrs.fr/. Fabio Acerbi is responsible for parts 1, 2, and Appendix 2, Anna Gioffreda for Appendix 1.