Aristotle—And “Why Things Happen” 18
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Stony Brook University
SSStttooonnnyyy BBBrrrooooookkk UUUnnniiivvveeerrrsssiiitttyyy The official electronic file of this thesis or dissertation is maintained by the University Libraries on behalf of The Graduate School at Stony Brook University. ©©© AAAllllll RRRiiiggghhhtttsss RRReeessseeerrrvvveeeddd bbbyyy AAAuuuttthhhooorrr... The Civic Virtue of Women in Quattrocento Florence A Dissertation Presented by Christine Contrada to The Graduate School in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy in History Stony Brook University May 2010 Copyright by Christine Contrada 2010 Stony Brook University The Graduate School Christine Contrada We, the dissertation committee for the above candidate for the Doctor of Philosophy degree, hereby recommend acceptance of this dissertation. Dr. Alix Cooper – Dissertation Advisor Associate Professor, History Dr. Joel Rosenthal – Chairperson of Defense Distinguished Professor Emeritus, History Dr. Gary Marker Professor, History Dr. James Blakeley Assistant Professor, History St. Joseph’s College, New York This dissertation is accepted by the Graduate School. Lawrence Martin Dean of the Graduate School ii Abstract of the Dissertation The Civic Virtue of Women in Quattrocento Florence by Christine Contrada Doctor of Philosophy in History Stony Brook University 2010 Fifteenth century Florence has long been viewed as the epicenter of Renaissance civilization and a cradle of civic humanism. This dissertation seeks to challenge the argument that the cardinal virtues, as described by humanists like Leonardo Bruni and Matteo Palmieri, were models of behavior that only men adhered to. Elite men and women alike embraced the same civic ideals of prudence, justice, fortitude, and temperance. Although they were not feminists advocating for social changes, women like Alessandra Strozzi, Margherita Datini, and Lucrezia Tornabuoni had a great deal of opportunity to actively support their own interests and the interests of their kin within popular cultural models of civic virtue. -
May 2, 2020 Live the Ucf Creed
UNIVERSITY OF CENTRAL FLORIDA COMMENCEMENT MAY 2, 2020 LIVE THE UCF CREED INTEGRITY I will practice and defend academic and personal honesty. SCHOLARSHIP I will cherish and honor learning as a fundamental purpose of my membership in the UCF community. COMMUNITY I will promote an open and supportive campus environment by respecting the rights and contributions of every individual. CREATIVITY I will use my talents to enrich the human experience. EXCELLENCE I will strive toward the highest standards of performance in any endeavor I undertake. UNIVERSITY OF CENTRAL FLORIDA | COMMENCEMENT | MAY 2, 2020 About the University of Central Florida The University of Central Florida is a bold, public research institution that is regularly ranked among the nation’s top 20 most innovative universities by U.S. News & World Report. With more than 69,500 students, UCF is one of the largest universities in the United States and is ranked as one of the best educational values in the nation by Forbes and Kiplinger. The university benefits from a diverse faculty and staff who create a welcoming environment and opportunities for all students to grow, learn, and succeed. A Foundation for Success UCF and its 13 colleges offer more than 220 degrees at UCF’s main campus, hospitality campus, health sciences campus, online and through multiple regional locations. The 1,415-acre main campus is 13 miles east of downtown Orlando and adjacent to one of the top research parks in the nation. Other campuses are located throughout Central Florida and include a fully accredited College of Medicine at Lake Nona. -
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). -
Anaximander's Ἄπειρον
1 Pulished in: Ancient Philosophy Volume 39, Issue 1, Spring 2019 Anaximander’s ἄπειρον: from the Life-world to the Cosmic Event Horizon Norman Sieroka Pages 1-22 https://doi.org/10.5840/ancientphil2019391 1 Current affiliation of author (July 2020): Theoretische Philosophie, Universität Bremen www.uni-bremen.de/theophil/sieroka Abstract Scholars have claimed repeatedly that Anaximander’s notion of the ἄπειρον marks the first metaphysical concept, or even the first theoretical entity, in Western thought. The present paper scrutinizes this claim. Characterizing natural phenomena as ἄπειρος— that is, as being inexhaustible or untraversable by standard human means—was common in daily practice, especially when referring to landmasses and seas but also when referring to vast numbers of countable objects. I will deny the assumption that Anaximander’s notion started off as being a theoretical answer to a specific philosophical question. That said, the aforementioned everyday notion of ἄπειρος could still lead to the development of theoretical concepts. Based on the observations Anaximander did with seasonal sundials, the inexhaustible landmasses and seas just mentioned became depicted on his world map by means of concentric circles. These circles then marked the bounds of experience and, by being fixed and finite, suggested the possibility of traversing beyond what is directly experienced. Evaluating claims from recent Anaximander scholarship, the paper ends with a brief comparison with concepts from modern physics which play an analogous role of demarcating the bounds of experience. Anaximander’s ἄπειρον: from the Life-world to the Cosmic Event Horizon Norman Sieroka Interest in Anaximander (c. 610-c. 547 BC) has increased in recent years. -
Anaximander and the Problem of the Earth's Immobility
Binghamton University The Open Repository @ Binghamton (The ORB) The Society for Ancient Greek Philosophy Newsletter 12-28-1953 Anaximander and the Problem of the Earth's Immobility John Robinson Windham College Follow this and additional works at: https://orb.binghamton.edu/sagp Recommended Citation Robinson, John, "Anaximander and the Problem of the Earth's Immobility" (1953). The Society for Ancient Greek Philosophy Newsletter. 263. https://orb.binghamton.edu/sagp/263 This Article is brought to you for free and open access by The Open Repository @ Binghamton (The ORB). It has been accepted for inclusion in The Society for Ancient Greek Philosophy Newsletter by an authorized administrator of The Open Repository @ Binghamton (The ORB). For more information, please contact [email protected]. JOHN ROBINSON Windham College Anaximander and the Problem of the Earth’s Immobility* N the course of his review of the reasons given by his predecessors for the earth’s immobility, Aristotle states that “some” attribute it I neither to the action of the whirl nor to the air beneath’s hindering its falling : These are the causes with which most thinkers busy themselves. But there are some who say, like Anaximander among the ancients, that it stays where it is because of its “indifference” (όμοιότητα). For what is stationed at the center, and is equably related to the extremes, has no reason to go one way rather than another—either up or down or sideways. And since it is impossible for it to move simultaneously in opposite directions, it necessarily stays where it is.1 The ascription of this curious view to Anaximander appears to have occasioned little uneasiness among modern commentators. -
Thales of Miletus Sources and Interpretations Miletli Thales Kaynaklar Ve Yorumlar
Thales of Miletus Sources and Interpretations Miletli Thales Kaynaklar ve Yorumlar David Pierce October , Matematics Department Mimar Sinan Fine Arts University Istanbul http://mat.msgsu.edu.tr/~dpierce/ Preface Here are notes of what I have been able to find or figure out about Thales of Miletus. They may be useful for anybody interested in Thales. They are not an essay, though they may lead to one. I focus mainly on the ancient sources that we have, and on the mathematics of Thales. I began this work in preparation to give one of several - minute talks at the Thales Meeting (Thales Buluşması) at the ruins of Miletus, now Milet, September , . The talks were in Turkish; the audience were from the general popu- lation. I chose for my title “Thales as the originator of the concept of proof” (Kanıt kavramının öncüsü olarak Thales). An English draft is in an appendix. The Thales Meeting was arranged by the Tourism Research Society (Turizm Araştırmaları Derneği, TURAD) and the office of the mayor of Didim. Part of Aydın province, the district of Didim encompasses the ancient cities of Priene and Miletus, along with the temple of Didyma. The temple was linked to Miletus, and Herodotus refers to it under the name of the family of priests, the Branchidae. I first visited Priene, Didyma, and Miletus in , when teaching at the Nesin Mathematics Village in Şirince, Selçuk, İzmir. The district of Selçuk contains also the ruins of Eph- esus, home town of Heraclitus. In , I drafted my Miletus talk in the Math Village. Since then, I have edited and added to these notes. -
Meet the Philosophers of Ancient Greece
Meet the Philosophers of Ancient Greece Everything You Always Wanted to Know About Ancient Greek Philosophy but didn’t Know Who to Ask Edited by Patricia F. O’Grady MEET THE PHILOSOPHERS OF ANCIENT GREECE Dedicated to the memory of Panagiotis, a humble man, who found pleasure when reading about the philosophers of Ancient Greece Meet the Philosophers of Ancient Greece Everything you always wanted to know about Ancient Greek philosophy but didn’t know who to ask Edited by PATRICIA F. O’GRADY Flinders University of South Australia © Patricia F. O’Grady 2005 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise without the prior permission of the publisher. Patricia F. O’Grady has asserted her right under the Copyright, Designs and Patents Act, 1988, to be identi.ed as the editor of this work. Published by Ashgate Publishing Limited Ashgate Publishing Company Wey Court East Suite 420 Union Road 101 Cherry Street Farnham Burlington Surrey, GU9 7PT VT 05401-4405 England USA Ashgate website: http://www.ashgate.com British Library Cataloguing in Publication Data Meet the philosophers of ancient Greece: everything you always wanted to know about ancient Greek philosophy but didn’t know who to ask 1. Philosophy, Ancient 2. Philosophers – Greece 3. Greece – Intellectual life – To 146 B.C. I. O’Grady, Patricia F. 180 Library of Congress Cataloging-in-Publication Data Meet the philosophers of ancient Greece: everything you always wanted to know about ancient Greek philosophy but didn’t know who to ask / Patricia F. -
Hypatia of Alexandria
Hypathia of Alexandria Doina Ionescu Astronomical Institute of the Romanian Academy, E–mail: [email protected] Introduction - Born in 350-355/370; - Lived and learned in Alexandria, Roman Egypt; - The daughter of Theon, the last director of the Museum of Alexandria; - Trained by her father in physical education, mathematics, astronomy, philosophy, arts, literature, the principles of teaching, oratory; - Died in 415, killed by a Christian mob who blamed her for religious turmoil. The Musaeum of Alexandria - Founded in the 3rd century BCE by Ptolemy I Soter or his son Ptolemy II; - Comprised gardens, a room for shared dining, a reading room, lecture halls, meetings rooms and a library; - The Library of Alexandria: an acquisitions department and a cataloguing department; - The Mouseion (“The House of the Muses”) – an institution that brought together the best scholars of the Hellenistic world, a university; - Destruction of the Mouseion and Library of Alexandria: 1. Julius Caesar’s Fire in the Alexandrian War, 48 BC; 2. The attack of Aurelian in the 3rd century AD; 3. The decree of Theophilus in AD 391; 4. The Muslim conquest in AD 642 and thereafter. Theon (b: 335 – d. early 5th century) - Most of the references on him and on Hypathia : Suda, the 10th century Byzantine encyclopedia; - Highly educated scholar, mathematician and astronomer; - A member and possibly the last director of the Alexandrian Museion, on public payroll. - Devoted his scholarship to the study of his predecessors Euclid and Ptolemy; his recensions were designed for students; - Euclid’s Elements; - Thirteen books of Ptolemy’ Almagest ; Handy Tables : The Great Commentary, in five books, and The Little Commentary , in one; - He worked together with scholar and student associates and with his daughter, Hypathia - A treatise “On the Small Astrolabe” ; - On Signs and the examination of Birds and the Croaking of Ravens: two essays on the function of the star Syrius and the influence of the planetary spheres on the Nile; - 364 AD: predicted eclipses of the Sun and Moon in Alexandria. -
1 Anaximander and the Origins of Greek Philosophy
1 Anaximander and the Origins of Greek Philosophy The Problem and the Three Tiers of Explanation ow shall we account for the origins of Greek philoso- phy? To answer the question requires, first of all, that we determine precisely what we are trying to explain. HThis, of course, proves to be a daunting task for it is in large measure a perennial problem for philosophers: What exactly is philosophy, and what did it mean to the ancient Greeks? We can profitably distinguish two kinds of questions in our inquiries: (A) What are the defining characteristics of Greek philosophy in terms of which we can distinguish it from earlier pre- philosophical thought? (B) What explains the rise of this particular type of thinking in Greece? 15 16 Anaximander Naturally, the answer we give to (A) will affect the way we and the approach (B). Reflecting upon the diverse scholarly literature Architects over the course of the last century, the disparate views and approaches suggest, not surprisingly, that there is considerable disagreement about precisely what “Greek philosophy” denotes and connotes.When the variety of opinions have been assem- bled, however, they may be roughly but usefully classified into two groups. On the one hand, we have what might be called first-tier accounts. These accounts answer (A) by identifying epistemological and ontological concerns in the systematic pro- grams of Plato and Aristotle as characteristic of philosophical thought. First-tier approaches offer historical narratives that tend to look backward in time, before the classical period, to determine who should and who should not be included in the story that leads up to them. -
Lecture 4. Pythagoras' Theorem and the Pythagoreans
Lecture 4. Pythagoras' Theorem and the Pythagoreans Figure 4.1 Pythagoras was born on the Island of Samos Pythagoras Pythagoras (born between 580 and 572 B.C., died about 497 B.C.) was born on the island of Samos, just off the coast of Asia Minor1. He was the earliest important philosopher who made important contributions in mathematics, astronomy, and the theory of music. Pythagoras is credited with introduction the words \philosophy," meaning love of wis- dom, and \mathematics" - the learned disciplines.2 Pythagoras is famous for establishing the theorem under his name: Pythagoras' theorem, which is well known to every educated per- son. Pythagoras' theorem was known to the Babylonians 1000 years earlier but Pythagoras may have been the first to prove it. Pythagoras did spend some time with Thales in Miletus. Probably by the suggestion of Thales, Pythagoras traveled to other places, including Egypt and Babylon, where he may have learned some mathematics. He eventually settled in Groton, a Greek settlement in southern Italy. In fact, he spent most of his life in the Greek colonies in Sicily and 1Asia Minor is a region of Western Asia, comprising most of the modern Republic of Turkey. 2Is God a mathematician ? Mario Livio, Simon & Schuster Paperbacks, New York-London-Toronto- Sydney, 2010, p. 15. 23 southern Italy. In Groton, he founded a religious, scientific, and philosophical organization. It was a formal school, in some sense a brotherhood, and in some sense a monastery. In that organization, membership was limited and very secretive; members learned from leaders and received education in religion. -
A Vector Approach to Ptolemy's Theorem a Vector Approach To
386 MATHEMATICSMAGAZINE In the revolutionof a graphy = f(xl) aboutthe y-axis, we let F(l X2, X3) = f (x + X2 + X) . Using sphericalcoordinates the integralbecomes I jlv/1 + (f/(p))2 p2 sin 0 dpdqds= 47rp2 + ( (p))2p dO O a a Formula(4) follows. For revolution aboutthe x-axis, the surface y2 + y2 + y2 = f2(X) can be parame- terizedusing sphericalcoordinates as x = t, Y = f(t) sin cos , Y2 = f(t) sin sin0, 3 = f(t) cos for a < t < b, 0 < 0 < r, 0 < 0 < 2r. Formula(4) follows aftera straightforward calculationof the determinantin (5). Epilogue Now thatwe have extendedthe resultsto fourdimensions, we mightcon- sider extendingthem furtherto n dimensions.In fact, in higherdimensions there are otherways to revolvegraphs about axes. For example,in four dimensionswe could considerthe doublerotation, where the graphis firstrevolved about the y-axis in three dimensionsand thenthe resultingsurface is revolvedabout the x-axis in four dimen- sions. REFERENCES 1. E. A. Abbott,Flatland, Harperand Row Publishers,NY, 1983. 2. D. Davis, TheNature and Power of Mathematics,Princeton University Press, Princeton,NJ, 1993. 3. J. H. Hubbardand B. B. Hubbard,Vector Calculus, Linear Algebra, and Differential Forms, Prentice Hall, Upper Saddle River,NJ, 1999. 4. G. J. Porter,k-volume in ln and the GeneralizedPythagorean Theorem, Amer. Math. Monthly 103 (1996), 252-256. A VectorApproach to Ptolemy'sTheorem ERWIN JUST NORMAN SCHAUMBERGER Bronx Community College of the City University of New York Bronx, NY 10453 [email protected] Ptolemy'sTheorem [1] statesthat the productof the diagonalsof a cyclic quadrilateral (a quadrilateralthat can be inscribedin a circle) is equalto the sum of the productsof its oppositesides. -
The Covid Correspondent
The 13 Covid-19 Correspondent Published by The Inchmarlo Social Forum Proprietor: Della Russell Editor: Phil Allen Issue 13: 17 June 2020 Special Edition: Scotland in Lockdown Dolphins have returned to Italy! Meanwhile in Scotland… Scotland in Spring Scotland in Summer Scotland in Autumn Scotland in Lockdown Scottish kids return to school after home-taught history lessons Lockdown Requiem Mr and Mrs Skene’s Cure for Lockdown Blues Sitting, thinking, watching, waiting, (Entertainment Video of the Week) Day of week and month of year, Instructions: Copy & paste the blue text below into your browser’s address Twelve weeks in with more impending, bar. Alternatively place the curser over the blue text and hold down the Brave Scotland's lockdown, Requiem. control key whilst clicking with the mouse. (This could avoid the ads.) https://www.youtube.com/watch?v=KTlMj9EgFDM Do`s and don'ts with `S` all starting Amazing! A new meaning to the phrase “opera glasses” Stay at home, away, apart, Thank you, Alison and Charles Skene. I hope you approve this version. Social distance, pole dependent, `S` word for living, nowhere now. Scottish Banter: • I was out for a walk in Crathes Castle gardens and saw the Coronavirus New friends discovered, neighbours helping, heading towards me. Thanks to the government advice of staying Disciplined folk, bonding, proud, alert, I hid behind a tree and it totally missed me. Thanks Boris. Old friends appear in weekly shopping, • Two people found sunbathing in Scotland today have tested for Remy, Gordon, Jack et. al. hypothermia. • An Englishman, an Irishman and a Scotsman walk into a bar.