The Case of Galileo: a Closed Question?
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Galileo's Assayer
University of Nevada, Reno Galileo's Assayer: Sense and Reason in the Epistemic Balance A thesis submitted in partial fulfillment of the requirements for the degree of Master of Arts in History. by James A Smith Dr. Bruce Moran/Thesis Advisor May 2018 c by James A Smith 2018 All Rights Reserved THE GRADUATE SCHOOL We recommend that the thesis prepared under our supervision by JAMES A. SMITH entitled Galileo's Assayer: Sense and Reason in the Epistemic Balance be accepted in partial fulfillment of the requirements for the degree of MASTER OF ARTS Bruce Moran, Ph.D., Advisor Edward Schoolman, Ph.D., Committee Member Carlos Mariscal, Ph.D., Committee Member Stanislav Jabuka, Ph.D., Graduate School Representative David W. Zeh, Ph.D., Dean, Graduate School May, 2018 i Abstract Galileo's The Assayer, published in 1623, represents a turning point in Galileo's philo- sophical work. A highly polemical \scientific manifesto," The Assayer was written after his astronomical discoveries of the moons of Jupiter and sunspots on a rotating sun, but before his mature Copernican work on the chief world systems (Ptolemaic versus Copernican). The Assayer included major claims regarding the place of math- ematics in natural philosophy and how the objects of the world and their properties can be known. It's in The Assayer that Galileo wades into the discussion about the ultimate constituents of matter and light, namely, unobservable particles and atoms. Galileo stressed the equal roles that the senses and reason served in the discovery of knowledge, in contradistinction to Aristotelian authoritarian dogma that he found to hinder the processes of discovery and knowledge acquisition. -
On the Infinite in Leibniz's Philosophy
On the Infinite in Leibniz's Philosophy Elad Lison Interdisciplinary Studies Unit Science, Technology and Society Ph.D. Thesis Submitted to the Senate of Bar-Ilan University Ramat-Gan, Israel August 2010 This work was carried out under the supervision of Dr. Ohad Nachtomy (Department of Philosophy), Bar-Ilan University. Contents א.……………………………….…………………………………………Hebrew Abstract Prologue…………………………………………………………...………………………1 Part A: Historic Survey Methodological Introduction…………………………………………………………..15 1. Aristotle: Potential Infinite………………………………………………………….16 2. Thomas Aquinas: God and the Infinite………………………………………..…….27 3. William of Ockham: Syncategorematic and Actual Infinite……………………..….32 4. Rabbi Abraham Cohen Herrera: Between Absolute Unity and Unbounded Multitude………………………………………………………………………..….42 5. Galileo Galilei: Continuum Constructed from Infinite Zero's………………………49 6. René Descartes: Infinite as Indefinite…………………………………………….…58 7. Pierre Gassendi: Rejection of the Infinite…………………………………………...69 8. Baruch Spinoza: Infinite Unity…………………………………………………...…73 9. General Background: Leibniz and the History of the Infinite……………………....81 Summary…………………………………………………………………………….…94 Part B: Mathematics Introduction…………………………………………………………………………….99 1. 'De Arte Combinatoria' as a Formal Basis for Thought: Retrospective on Leibniz's 1666 Dissertation………………………………………………………………....102 2. Leibniz and the Infinitesimal Calculus……………………………………….……111 2.1. Mathematical Background: Mathematical Works in 16th-17th Centuries…..111 2.2. Leibniz's Mathematical Development…………………………………….…127 -
A New Vision of the Senses in the Work of Galileo Galilei
Perception, 2008, volume 37, pages 1312 ^ 1340 doi:10.1068/p6011 Galileo's eye: A new vision of the senses in the work of Galileo Galilei Marco Piccolino Dipartimento di Biologia, Universita© di Ferrara, I 44100 Ferrara, Italy; e-mail: [email protected] Nicholas J Wade University of Dundee, Dundee DD1 4HN, Scotland, UK Received 4 December 2007 Abstract. Reflections on the senses, and particularly on vision, permeate the writings of Galileo Galilei, one of the main protagonists of the scientific revolution. This aspect of his work has received scant attention by historians, in spite of its importance for his achievements in astron- omy, and also for the significance in the innovative scientific methodology he fostered. Galileo's vision pursued a different path from the main stream of the then contemporary studies in the field; these were concerned with the dioptrics and anatomy of the eye, as elaborated mainly by Johannes Kepler and Christoph Scheiner. Galileo was more concerned with the phenomenology rather than with the mechanisms of the visual process. His general interest in the senses was psychological and philosophical; it reflected the fallacies and limits of the senses and the ways in which scientific knowledge of the world could be gathered from potentially deceptive appearances. Galileo's innovative conception of the relation between the senses and external reality contrasted with the classical tradition dominated by Aristotle; it paved the way for the modern understanding of sensory processing, culminating two centuries later in Johannes Mu« ller's elaboration of the doctrine of specific nerve energies and in Helmholtz's general theory of perception. -
Galileo Galilei by Beatrix Mccrea Galileo Galilei Was an Italian Physicist, Engineer, and Astronomer Bestknown for Disc
3/24/2019 Galileo Galilei - Google Docs Galileo Galilei By Beatrix McCrea Galileo Galilei was an Italian physicist, engineer, and astronomer bestknown for discovering the four largest moons on Jupiter and his theory of gravity. His theory of gravity stated that if a bowling ball and a feather dropped at the same time in space they would land at the same time. He also invented the thermometer and an astronomical telescope. Galileo Galilei was born to Vincenzo Galilei and Giulia Ammanniti in Piza, Italy on February 15, 1564. He was the first of six children. There were two things that happened which led Galileo to find that he loved math and science. On The Famous People the text states “the first incident happened in 1581 when he first noticed that a chandelier despite swinging in small and large arcs took almost the same time to return to the first position.” The other incident was when he accidentally attended a geometry lecture. Both these incidents made Galileo find his love for science. Galileo discovered the four largest moons on Jupiter. On Biography.com it says Galileo Galilei was best known for discovering Jupiter and it’s four biggest moons. The names were Io, Europa, Ganymede, and Callisto. They were discovered by Galileo in January of 1610. Galileo used a better version of the telescope that made him made to see the four moons. Galileo Galilei had a very popular theory of gravity, that if there was no air resistance (like in space) you would drop a bowling ball and a feather and they would land at the exact same time. -
The Oldest Translation of the Almagest Made for Al-Maʾmūn by Al-Ḥasan Ibn Quraysh: a Text Fragment in Ibn Al-Ṣalāḥ’S Critique on Al-Fārābī’S Commentary
Zurich Open Repository and Archive University of Zurich Main Library Strickhofstrasse 39 CH-8057 Zurich www.zora.uzh.ch Year: 2020 The Oldest Translation of the Almagest Made for al-Maʾmūn by al-Ḥasan ibn Quraysh: A Text Fragment in Ibn al-Ṣalāḥ’s Critique on al-Fārābī’s Commentary Thomann, Johannes DOI: https://doi.org/10.1484/M.PALS-EB.5.120176 Posted at the Zurich Open Repository and Archive, University of Zurich ZORA URL: https://doi.org/10.5167/uzh-190243 Book Section Accepted Version Originally published at: Thomann, Johannes (2020). The Oldest Translation of the Almagest Made for al-Maʾmūn by al-Ḥasan ibn Quraysh: A Text Fragment in Ibn al-Ṣalāḥ’s Critique on al-Fārābī’s Commentary. In: Juste, David; van Dalen, Benno; Hasse, Dag; Burnett, Charles. Ptolemy’s Science of the Stars in the Middle Ages. Turnhout: Brepols Publishers, 117-138. DOI: https://doi.org/10.1484/M.PALS-EB.5.120176 The Oldest Translation of the Almagest Made for al-Maʾmūn by al-Ḥasan ibn Quraysh: A Text Fragment in Ibn al-Ṣalāḥ’s Critique on al-Fārābī’s Commentary Johannes Thomann University of Zurich Institute of Asian and Oriental Research [email protected] 1. Life and times of Ibn al-Ṣalāḥ (d. 1154 ce) The first half of the twelfth century was a pivotal time in Western Europe. In that period translation activities from Arabic into Latin became a common enterprise on a large scale in recently conquered territories, of which the centres were Toledo, Palermo and Antioch. This is a well known part of what was called the Renaissance of the Twelfth Century.1 Less known is the situation in the Islamic World during the same period. -
New Perspectives on Galileo the University of Western Ontario Series in Philosophy of Science
NEW PERSPECTIVES ON GALILEO THE UNIVERSITY OF WESTERN ONTARIO SERIES IN PHILOSOPHY OF SCIENCE A SERIES OF BOOKS ON PHILOSOPHY OF SCIENCE, METHODOLOGY, AND EPISTEMOLOGY PUBLISHED IN CONNECTION WITH THE UNIVERSITY OF WESTERN ONTARIO PHILOSOPHY OF SCIENCE PROGRAMME Managing Editor J. 1. LEACH Editorial Board J. BUB, R. E. BUTTS, W. HARPER, J. HINTIKKA, D. J. HOCKNEY, C. A. HOOKER, 1. NICHOLAS, G. PEARCE VOLUME 14 NEW PERSPECTIVES ON GALILEO Papers Deriving from and Related to a Workshop on Gali/eo held at Virginia Polytechnic Institute and State University, 1975 Edited by ROBERT E. BUTTS Department of Philosophy, the University of Western Ontario, London, Canada and JOSEPH C. PITT Department of Philosophy and Religion, Virginia Polytechnic Institute and State University, Blacksburg, Virginia, U.S.A. D. REIDEL PUBLISHING COMPANY DORDRECHT : HOLLAND / BOSTON: U.S.A. Library of Congress Cataloging in Publication Data Main entry under title: New perspectives on Galileo. (The University of Western Ontario series in philosophy of science ; v. 14) Bibliography: p. Includes index. 1. S cience-Methodology -Congresses. 2. Science-Philosophy-Congresses. 3. Galilei, Galileo,1564-1642. I. Butts, Robert E. II. Pitt, JosephC. Q174.N48 509 /.2'4 77-17851 ISBN-I3: 978-90-277-0891-5 e-ISBN: 978-94-009-9799-8 DOl: 10.1007/978-94-009-9799-8 Published by D. Reidel Publishing Company, P.O. Box 17, Dordrecht, Holland Sold and distributed in the U.S.A., Canada, and Mexico by D. Reidel Publishing Company,lnc. Lincoln Building, 160 Old Derby Street, Hingham, Mass. 02043, U.S.A. All Rights Reserved Copyright © 1978 by D. -
A Modern Almagest an Updated Version of Ptolemy’S Model of the Solar System
A Modern Almagest An Updated Version of Ptolemy’s Model of the Solar System Richard Fitzpatrick Professor of Physics The University of Texas at Austin Contents 1 Introduction 5 1.1 Euclid’sElementsandPtolemy’sAlmagest . ......... 5 1.2 Ptolemy’sModeloftheSolarSystem . ..... 5 1.3 Copernicus’sModeloftheSolarSystem . ....... 10 1.4 Kepler’sModeloftheSolarSystem . ..... 11 1.5 PurposeofTreatise .................................. .. 12 2 Spherical Astronomy 15 2.1 CelestialSphere................................... ... 15 2.2 CelestialMotions ................................. .... 15 2.3 CelestialCoordinates .............................. ..... 15 2.4 EclipticCircle .................................... ... 17 2.5 EclipticCoordinates............................... ..... 18 2.6 SignsoftheZodiac ................................. ... 19 2.7 Ecliptic Declinations and Right Ascenesions. ........... 20 2.8 LocalHorizonandMeridian ............................ ... 20 2.9 HorizontalCoordinates.............................. .... 23 2.10 MeridianTransits .................................. ... 24 2.11 Principal Terrestrial Latitude Circles . ......... 25 2.12 EquinoxesandSolstices. ....... 25 2.13 TerrestrialClimes .................................. ... 26 2.14 EclipticAscensions .............................. ...... 27 2.15 AzimuthofEclipticAscensionPoint . .......... 29 2.16 EclipticAltitudeandOrientation. .......... 30 3 Dates 63 3.1 Introduction...................................... .. 63 3.2 Determination of Julian Day Numbers . .... 63 4 Geometric -
If You Were Not Here Last Week... Please Come to The
http://www.physics.smu.edu/pseudo IF YOU WERE NOT HERE LAST WEEK... PLEASE COME TO THE FRONT OF THE CLASS AND SEE PROF. COTTON. http://www.physics.smu.edu/pseudo “Any sufficiently advanced technology is indistinguishable from magic.” --Arthur C. Clarke, "Profiles of The Future", 1961 (Clarke's third law) English physicist & science fiction author (1917 – 2008) “The Bible shows the way to go to heaven, not the way the heavens go.” --Galileo Galilei “By denying scientific principles, one may maintain any paradox.” --Galileo Galilei http://www.physics.smu.edu/pseudo The Scientific Method (continued) Supplementary Material for CFB3333/PHY3333 Professors John Cotton and Stephen Sekula January 23, 2012 Based on the following information on the web: http://www.physics.smu.edu/pseudo/SciMeth http://www.physics.smu.edu/pseudo But first . some MAGIC! http://www.physics.smu.edu/pseudoAA roundround ofof applauseapplause forfor .. .. .. SCALISE,SCALISE, ILIL MAGNIFICO!MAGNIFICO! Wonder at his powers of levitation! Gasp as he commands the elements of nature! http://www.physics.smu.edu/pseudo GLOSSARY OF CRITICAL DEFINITIONS http://www.physics.smu.edu/pseudo FACT ● The National Academy of Sciences definition of fact: ● An observation that has been repeatedly confrmed and for all practical purposes is accepted as true. "In science, 'fact' can only mean 'confirmed to such a degree that it would be perverse to withhold provisional assent.' I suppose that apples might start to rise tomorrow, but the possibility does not merit equal time in physics classrooms." --Stephen Jay Gould EXAMPLE: At Standard Temperature and Pressure, lead is more dense than water. -
John Wallis (1616–1703), Oxford's Savilian Professor
John Wallis (1616–1703), Oxford’s Savilian Professor of Geometry from 1649 to 1703, was the most influential English mathematician before the rise of Isaac Newton. His most important works were his Arithmetic of Infinitesimals and his treatise on Conic Sections, both published in the 1650s. It was through studying the former that Newton came to discover his version of the binomial theorem. Wallis’s last great mathematical work A Treatise of Algebra was published in his seventieth year. John Wallis Wallis’ time-line “In the year 1649 I removed to 1616 Born in Ashford, Kent Oxford, being then Publick 1632–40 Studied at Emmanuel College, Professor of Geometry, of the Cambridge Foundation of Sr. Henry Savile. 1640 Ordained a priest in the And Mathematicks which Church of England had before been a pleasing 1642 Started deciphering secret codes diversion, was now to be for Oliver Cromwell’s intelligence my serious Study.” service during the English Civil Wars John Wallis 1647 Inspired by William Oughtred’s Clavis Mathematicae (Key to Mathematics) which considerably extended his mathematical knowledge 1648 Initiated mathematical correspondence with continental scholars (Hevelius, van Schooten, etc.) 1649 Appointed Savilian Professor of Geometry at Oxford 31 October: Inaugural lecture 1655–56 Arithmetica Infinitorum (The Arithmetic of Infinitesimals) and De Sectionibus Conicis (On Conic Sections) 1658 Elected Oxford University Archivist 1663 11 July: Lecture on Euclid’s parallel postulate 1655–79 Disputes with Thomas Hobbes 1685 Treatise of Algebra 1693–99 Opera Mathematica 1701 Appointed England’s first official decipherer (alongside his grandson William Blencowe) 1703 Died in Oxford John Wallis (1616–1703) Savilian Professor During the English Civil Wars John Wallis was appointed Savilian Professor of Geometry in 1649. -
The Project Gutenberg Ebook #31061: a History of Mathematics
The Project Gutenberg EBook of A History of Mathematics, by Florian Cajori This eBook is for the use of anyone anywhere at no cost and with almost no restrictions whatsoever. You may copy it, give it away or re-use it under the terms of the Project Gutenberg License included with this eBook or online at www.gutenberg.org Title: A History of Mathematics Author: Florian Cajori Release Date: January 24, 2010 [EBook #31061] Language: English Character set encoding: ISO-8859-1 *** START OF THIS PROJECT GUTENBERG EBOOK A HISTORY OF MATHEMATICS *** Produced by Andrew D. Hwang, Peter Vachuska, Carl Hudkins and the Online Distributed Proofreading Team at http://www.pgdp.net transcriber's note Figures may have been moved with respect to the surrounding text. Minor typographical corrections and presentational changes have been made without comment. This PDF file is formatted for screen viewing, but may be easily formatted for printing. Please consult the preamble of the LATEX source file for instructions. A HISTORY OF MATHEMATICS A HISTORY OF MATHEMATICS BY FLORIAN CAJORI, Ph.D. Formerly Professor of Applied Mathematics in the Tulane University of Louisiana; now Professor of Physics in Colorado College \I am sure that no subject loses more than mathematics by any attempt to dissociate it from its history."|J. W. L. Glaisher New York THE MACMILLAN COMPANY LONDON: MACMILLAN & CO., Ltd. 1909 All rights reserved Copyright, 1893, By MACMILLAN AND CO. Set up and electrotyped January, 1894. Reprinted March, 1895; October, 1897; November, 1901; January, 1906; July, 1909. Norwood Pre&: J. S. Cushing & Co.|Berwick & Smith. -
Quaternions: a History of Complex Noncommutative Rotation Groups in Theoretical Physics
QUATERNIONS: A HISTORY OF COMPLEX NONCOMMUTATIVE ROTATION GROUPS IN THEORETICAL PHYSICS by Johannes C. Familton A thesis submitted in partial fulfillment of the requirements for the degree of Ph.D Columbia University 2015 Approved by ______________________________________________________________________ Chairperson of Supervisory Committee _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ Program Authorized to Offer Degree ___________________________________________________________________ Date _______________________________________________________________________________ COLUMBIA UNIVERSITY QUATERNIONS: A HISTORY OF COMPLEX NONCOMMUTATIVE ROTATION GROUPS IN THEORETICAL PHYSICS By Johannes C. Familton Chairperson of the Supervisory Committee: Dr. Bruce Vogeli and Dr Henry O. Pollak Department of Mathematics Education TABLE OF CONTENTS List of Figures......................................................................................................iv List of Tables .......................................................................................................vi Acknowledgements .......................................................................................... vii Chapter I: Introduction ......................................................................................... 1 A. Need for Study ........................................................................................ -
Beyond Aristotle: Indivisibles and Infinite Divisibility in the Later Middle Ages
BEYOND ARISTOTLE: INDIVISIBLES AND INFINITE DIVISIBILITY IN THE LATER MIDDLE AGES John E. Murdoch The basic text for late medieval Latin atomism and its critics was Aristotle’s Physics, especially Book VI. Here the atoms or indivisibles he considered and combatted were extensionless, a conception that can be found in scholastic debate about atoms all the way to Galileo and his atomi non quanti.1 The medieval atomists were clustered in the fourteenth-century,2 as were their Aristotelian critics. Figure 1 provides the basic dramatis personae of the fourteenth-century atomists and their critics. The list of atomists is nearly complete, save for the followers of Wyclif. The list of their critics is naturally less complete, being made up of chiefl y those who name their atomist opponents. Yet even without such identifi cation, we can often tell other critics, such as John Buridan and his school, because they oppose specifi c identifi able atomist arguments. The question of the motives for the late medieval atomism is pretty murky. The motives for Greek atomism are, at least to some extent, an answer to Parmenides’s monism and center in attempts to explain natural phenomena (if not always totally successfully). Equally clear are the motives for the Arabic atomism of the Mutakallimun: namely, to put all causal relations into the hands of God through the mechanism of the doctrine of continuous creation. However, in the case of late medieval atomism there is not such a wholesale application to nature or to a God who creates the universe anew at every instant.