Prof. Richard Von Mises
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Von Mises' Frequentist Approach to Probability
Section on Statistical Education – JSM 2008 Von Mises’ Frequentist Approach to Probability Milo Schield1 and Thomas V. V. Burnham2 1 Augsburg College, Minneapolis, MN 2 Cognitive Systems, San Antonio, TX Abstract Richard Von Mises (1883-1953), the originator of the birthday problem, viewed statistics and probability theory as a science that deals with and is based on real objects rather than as a branch of mathematics that simply postulates relationships from which conclusions are derived. In this context, he formulated a strict Frequentist approach to probability. This approach is limited to observations where there are sufficient reasons to project future stability – to believe that the relative frequency of the observed attributes would tend to a fixed limit if the observations were continued indefinitely by sampling from a collective. This approach is reviewed. Some suggestions are made for statistical education. 1. Richard von Mises Richard von Mises (1883-1953) may not be well-known by statistical educators even though in 1939 he first proposed a problem that is today widely-known as the birthday problem.1 There are several reasons for this lack of recognition. First, he was educated in engineering and worked in that area for his first 30 years. Second, he published primarily in German. Third, his works in statistics focused more on theoretical foundations. Finally, his inductive approach to deriving the basic operations of probability is very different from the postulate-and-derive approach normally taught in introductory statistics. See Frank (1954) and Studies in Mathematics and Mechanics (1954) for a review of von Mises’ works. This paper is based on his two English-language books on probability: Probability, Statistics and Truth (1936) and Mathematical Theory of Probability and Statistics (1964). -
The Interpretation of Probability: Still an Open Issue? 1
philosophies Article The Interpretation of Probability: Still an Open Issue? 1 Maria Carla Galavotti Department of Philosophy and Communication, University of Bologna, Via Zamboni 38, 40126 Bologna, Italy; [email protected] Received: 19 July 2017; Accepted: 19 August 2017; Published: 29 August 2017 Abstract: Probability as understood today, namely as a quantitative notion expressible by means of a function ranging in the interval between 0–1, took shape in the mid-17th century, and presents both a mathematical and a philosophical aspect. Of these two sides, the second is by far the most controversial, and fuels a heated debate, still ongoing. After a short historical sketch of the birth and developments of probability, its major interpretations are outlined, by referring to the work of their most prominent representatives. The final section addresses the question of whether any of such interpretations can presently be considered predominant, which is answered in the negative. Keywords: probability; classical theory; frequentism; logicism; subjectivism; propensity 1. A Long Story Made Short Probability, taken as a quantitative notion whose value ranges in the interval between 0 and 1, emerged around the middle of the 17th century thanks to the work of two leading French mathematicians: Blaise Pascal and Pierre Fermat. According to a well-known anecdote: “a problem about games of chance proposed to an austere Jansenist by a man of the world was the origin of the calculus of probabilities”2. The ‘man of the world’ was the French gentleman Chevalier de Méré, a conspicuous figure at the court of Louis XIV, who asked Pascal—the ‘austere Jansenist’—the solution to some questions regarding gambling, such as how many dice tosses are needed to have a fair chance to obtain a double-six, or how the players should divide the stakes if a game is interrupted. -
Einstein and the Development of Twentieth-Century Philosophy of Science
Einstein and the Development of Twentieth-Century Philosophy of Science Don Howard University of Notre Dame Introduction What is Albert Einstein’s place in the history of twentieth-century philosophy of science? Were one to consult the histories produced at mid-century from within the Vienna Circle and allied movements (e.g., von Mises 1938, 1939, Kraft 1950, Reichenbach 1951), then one would find, for the most part, two points of emphasis. First, Einstein was rightly remembered as the developer of the special and general theories of relativity, theories which, through their challenge to both scientific and philosophical orthodoxy made vivid the need for a new kind of empiricism (Schlick 1921) whereby one could defend the empirical integrity of the theory of relativity against challenges coming mainly from the defenders of Kant.1 Second, the special and general theories of relativity were wrongly cited as straightforwardly validating central tenets of the logical empiricist program, such as verificationism, and Einstein was wrongly represented as having, himself, explicitly endorsed those same philosophical principles. As we now know, logical empiricism was not the monolithic philosophical movement it was once taken to have been. Those associated with the movement disagreed deeply about fundamental issues concerning the structure and interpretation of scientific theories, as in the protocol sentence debate, and about the overall aims of the movement, as in the debate between the left and right wings of the Vienna Circle over the role of politics in science and philosophy.2 Along with such differences went subtle differences in the assessment of Einstein’s legacy to logical empiricism. -
Philipp Frank at Harvard University: His Work and His Influence
Philipp Frank at Harvard University: His Work and His Influence The Harvard community has made this article openly available. Please share how this access benefits you. Your story matters Citation Holton, Gerald. 2006. Phillip Frank at Harvard: His Work and his Influence. Synthese 153 (2): 297-311. doi.org/10.1007/ s11229-005-5471-3 Citable link http://nrs.harvard.edu/urn-3:HUL.InstRepos:37837879 Terms of Use This article was downloaded from Harvard University’s DASH repository, and is made available under the terms and conditions applicable to Other Posted Material, as set forth at http:// nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of- use#LAA 10/12/04 Lecture at Philipp Frank Conferences in Prague & Vienna, Sept-Oct. ‘04 Philipp Frank at Harvard: His Work and his Influence by Gerald Holton My pleasant task today is to bring to life Philipp Frank’s work and influence during his last three decades, when he found a refuge and a position in America. In what follows, I hope I may call him Philipp--having been first a graduate student in one of his courses at Harvard, then his teaching assistant sharing his offices, then for many years his colleague and friend in the same Physics Department, and finally, doing research on his archival holdings kept at Harvard. I also should not hide my large personal debt to him, for without his recommendation in the 1950s to the Albert Einstein Estate, I would not have received its warm welcome and its permission, as the first one to do historical research in the treasure trove of unpublished letters and manuscripts, thus starting me on a major part of my career in the history of science. -
Mathematicians Fleeing from Nazi Germany
Mathematicians Fleeing from Nazi Germany Mathematicians Fleeing from Nazi Germany Individual Fates and Global Impact Reinhard Siegmund-Schultze princeton university press princeton and oxford Copyright 2009 © by Princeton University Press Published by Princeton University Press, 41 William Street, Princeton, New Jersey 08540 In the United Kingdom: Princeton University Press, 6 Oxford Street, Woodstock, Oxfordshire OX20 1TW All Rights Reserved Library of Congress Cataloging-in-Publication Data Siegmund-Schultze, R. (Reinhard) Mathematicians fleeing from Nazi Germany: individual fates and global impact / Reinhard Siegmund-Schultze. p. cm. Includes bibliographical references and index. ISBN 978-0-691-12593-0 (cloth) — ISBN 978-0-691-14041-4 (pbk.) 1. Mathematicians—Germany—History—20th century. 2. Mathematicians— United States—History—20th century. 3. Mathematicians—Germany—Biography. 4. Mathematicians—United States—Biography. 5. World War, 1939–1945— Refuges—Germany. 6. Germany—Emigration and immigration—History—1933–1945. 7. Germans—United States—History—20th century. 8. Immigrants—United States—History—20th century. 9. Mathematics—Germany—History—20th century. 10. Mathematics—United States—History—20th century. I. Title. QA27.G4S53 2008 510.09'04—dc22 2008048855 British Library Cataloging-in-Publication Data is available This book has been composed in Sabon Printed on acid-free paper. ∞ press.princeton.edu Printed in the United States of America 10 987654321 Contents List of Figures and Tables xiii Preface xvii Chapter 1 The Terms “German-Speaking Mathematician,” “Forced,” and“Voluntary Emigration” 1 Chapter 2 The Notion of “Mathematician” Plus Quantitative Figures on Persecution 13 Chapter 3 Early Emigration 30 3.1. The Push-Factor 32 3.2. The Pull-Factor 36 3.D. -
Passmore, J. (1967). Logical Positivism. in P. Edwards (Ed.). the Encyclopedia of Philosophy (Vol. 5, 52- 57). New York: Macmillan
Passmore, J. (1967). Logical Positivism. In P. Edwards (Ed.). The Encyclopedia of Philosophy (Vol. 5, 52- 57). New York: Macmillan. LOGICAL POSITIVISM is the name given in 1931 by A. E. Blumberg and Herbert Feigl to a set of philosophical ideas put forward by the Vienna circle. Synonymous expressions include "consistent empiricism," "logical empiricism," "scientific empiricism," and "logical neo-positivism." The name logical positivism is often, but misleadingly, used more broadly to include the "analytical" or "ordinary language philosophies developed at Cambridge and Oxford. HISTORICAL BACKGROUND The logical positivists thought of themselves as continuing a nineteenth-century Viennese empirical tradition, closely linked with British empiricism and culminating in the antimetaphysical, scientifically oriented teaching of Ernst Mach. In 1907 the mathematician Hans Hahn, the economist Otto Neurath, and the physicist Philipp Frank, all of whom were later to be prominent members of the Vienna circle, came together as an informal group to discuss the philosophy of science. They hoped to give an account of science which would do justice -as, they thought, Mach did not- to the central importance of mathematics, logic, and theoretical physics, without abandoning Mach's general doctrine that science is, fundamentally, the description of experience. As a solution to their problems, they looked to the "new positivism" of Poincare; in attempting to reconcile Mach and Poincare; they anticipated the main themes of logical positivism. In 1922, at the instigation of members of the "Vienna group," Moritz Schlick was invited to Vienna as professor, like Mach before him (1895-1901), in the philosophy of the inductive sciences. Schlick had been trained as a scientist under Max Planck and had won a name for himself as an interpreter of Einstein's theory of relativity. -
The Emergence of French Statistics. How Mathematics Entered the World of Statistics in France During the 1920S
The emergence of French statistics. How mathematics entered the world of statistics in France during the 1920s. Rémi Catellier, Laurent Mazliak To cite this version: Rémi Catellier, Laurent Mazliak. The emergence of French statistics. How mathematics entered the world of statistics in France during the 1920s.. 2009. hal-00397750v1 HAL Id: hal-00397750 https://hal.archives-ouvertes.fr/hal-00397750v1 Preprint submitted on 23 Jun 2009 (v1), last revised 21 Feb 2011 (v2) HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. The emergence of French statistics How mathematics entered the world of statistics in France during the 1920s Remi´ CATELLIER1 and Laurent MAZLIAK2 Abstract This paper concerns the emergence of modern mathematical statistics in France after First World War. Emile Borel’s achievements are presented, and especially his creation of two institutions where mathematical statistics were developed, the Statistical Institute of Paris University, (ISUP) in 1922 and above all the Henri Poincar´eInstitute (IHP) in 1928. At the IHP, a new journal Annales de l’Institut Henri Poincar was created in 1931. We present the first papers dealing with mathematical statistics. INTRODUCTION The important transformations in the field of the mathematics of randomness between around 1910 and 1930 are now rather well listed. -
The Law of Causality and Its Limits Vienna Circle Collection
THE LAW OF CAUSALITY AND ITS LIMITS VIENNA CIRCLE COLLECTION lIENK L. MULDER, University ofAmsterdam, Amsterdam, The Netherlands ROBERT S. COHEN, Boston University, Boston, Mass., U.SA. BRIAN MCGUINNESS, University of Siena, Siena, Italy RUDOLF IlALLER, Charles Francis University, Graz, Austria Editorial Advisory Board ALBERT E. BLUMBERG, Rutgers University, New Brunswick, N.J., U.SA. ERWIN N. HIEBERT, Harvard University, Cambridge, Mass., U.SA JAAKKO HiNTIKKA, Boston University, Boston, Mass., U.S.A. A. J. Kox, University ofAmsterdam, Amsterdam, The Netherlands GABRIEL NUCHELMANS, University ofLeyden, Leyden, The Netherlands ANTH:ONY M. QUINTON, All Souls College, Oxford, England J. F. STAAL, University of California, Berkeley, Calif., U.SA. FRIEDRICH STADLER, Institute for Science and Art, Vienna, Austria VOLUME 22 VOLUME EDITOR: ROBERT S. COHEN PHILIPP FRANK PHILIPP FRANK THELAWOF CAUSALITY AND ITS LIMITS Edited by ROBERT s. COHEN Boston University Translated by MARIE NEURATH and ROBERT S. COHEN 1Ii.. ... ,~ SPRINGER SCIENCE+BUSINESS MEDIA, B.V. Library of Congress Cataloging-in-Publication data Frank, Philipp, 1884-1966. [Kausalgesetz und seine Grenzen. Englishl The law of causality and its limits / Philipp Frank; edited by Robert S. Cohen ; translation by Marie Neurath and Robert S. Cohen. p. cm. -- (Vienna Circle collection ; v. 22) Inc I udes index. ISBN 978-94-010-6323-4 ISBN 978-94-011-5516-8 (eBook) DOI 10.1007/978-94-011-5516-8 1. Causation. 2. Science--Phi losophy. I. Cohen, R. S. (Robert Sonne) 11. Title. 111. Series. BD543.F7313 -
Physics and the Philosophy of Science at the Turn of the Twentieth Century
Physics and the Philosophy of Science at the Turn of the Twentieth Century (Forthcoming in the Enciclopedia Italiana di Storia della Scienza under the title, “Fisica e Filosofia della Scienza all’Alba del XX Secolo”) I believe that philosophy can be helped to its feet again only if it devotes itself seriously and fervently to investigations of cognitive processes and the methods of science. There it has a real and legitimate task . Philosophy has obviously come to a standstill because it . still has taken no new life from the vigorous development of the natural sciences. — Hermann von Helmholtz to Adolf Fick, ca. 1875 (as quoted in Koenigsberger 1902–1903, 243) Introduction: Disciplinary Symbiosis Theoretical physics and the philosophy of science are among the most important fields of research in the twentieth century, this as gauged both by their prominence within their respective disciplines and by their broader social and intellectual impact. Yet in 1850 neither field, as we know it today, would have been recognized in the academy or elsewhere as constituting an autonomous mode of inquiry with associated institutional structures. With hindsight, each might be glimpsed in germ. Some would read Hermann von Helmholtz’s 1847 lecture, Über die Erhaltung der Kraft (Helmholtz 1848) as marking the advent of the search for generalizable explanatory structures whose deployment is a distinguishing mark of theoretical physics. Some would read Auguste Comte’s Cours de philosophie positive (1830–1842) or William Whewell’s The Philosophy of the Inductive Sciences (1840) as inaugurating the systematic study of those general questions about scientific method, the nature and limits of scientific knowledge, and the structure and interpretation of scientific theories whose focal significance later defined the field in the form made famous by the members of the Vienna Circle. -
Modernism, Fiction and Mathematics
MODERNISM, FICTION AND MATHEMATICS JOHANN A. MAKOWSKY July 15, 2019 Review of: Nina Engelhardt, Modernism, Fiction and Mathematics, Edinburgh Critical Studies in Modernist Culture, Edinburgh University Press, Published June 2018 (Hardback), November 2019 (Paperback) ISBN Paperback: 9781474454841, Hardback: 9781474416238 1. The Book Under Review Nina Engelhardt's book is a study of four novels by three authors, Hermann Broch's trilogy The Sleepwalkers [2, 3], Robert Musil's The Man without Qualities [21, 23, 24], and Thomas Pynchon's Gravity's Rainbow and Against the Day [27, 28]. Her choice of authors and their novels is motivated by the impact the mathe- matics of the interwar period had on their writing fiction. It is customary in the humanities to describe the cultural ambiance of the interwar period between World War I and World War II as modernism. Hence the title of Engelhardt's book: Mod- ernism, Mathematics and Fiction. Broch and Musil are indeed modernist authors par excellence. Pynchon is a contemporary American author, usually classified by the literary experts as postmodern. arXiv:1907.05787v1 [math.HO] 12 Jul 2019 Hermann Broch in 1909 Robert Musil in 1900 1 2 JOHANN A. MAKOWSKY Thomas Pynchon ca. 1957 Works produced by employees of the United States federal government in the scope of their employment are public domain by statute. Engelhard's book is interesting for the literary minded mathematician for two reasons: First of all it draws attention to three authors who spent a lot of time and thoughts in studying the mathematics of the interwar period and used this experience in the shaping of their respective novels. -
Biographical Notes
Appendix Biographical Notes Bursian, Viktor Robertovich (1886–1945), a Russian and Soviet theoretical physi- cist. He worked on a range of physical problems, firstly using classical, then later quantum physics from 1918 to 1932 under Joffe at the Physico-Technical Insti- tute in Leningrad (LFTI). From 1932 until his arrest in 1936 “for participation in a fascist-Trotskyite-Zinovievite organization” he was professor then director of the Scientific-Research Institute of Physics at Leningrad University. He carried out work in mineral prospecting in the 1920s, one of the founders of the technique of electrical geo-exploration. For more details see Bursian (1988). Bursian was sentenced in 1937 by the Supreme Military Court to 10 years in a labor camp, which he spent in the technical special office of the NKVD carrying out thermal calculations. Egorshin, Vasilii Petrovich (1898–1985), born into a peasant family, joined the Russian Social Democratic Labor Party in 1915. After the revolution in 1921 he taught courses at Moscow University and from 1924 taught physics at the Communist University. Like Hessen he then studied at the IKP. He also joined the Deborin group, but turned against them in the late 1920s. Fock, Vladimir Aleksandrovich (1898–1974), a major Soviet theoretical physicist, known internationally for his foundational work in quantum mechanics and QED, where he introduced key mathematical concepts such as Fock space. Graduating from Petrograd University where he was a postgraduate, becoming a professor there in 1932. He collaborated with the Physico-Technical Institute in Leningrad (LFTI) from 1924 to 1936 and had periods of collaboration with the Vavilov State Optical Institute in Petrograd (now St. -
The Law of Causality and Its Limits Series: Vienna Circle Collection
springer.com Philipp Frank, Robert S. Cohen (Ed.) The Law of Causality and Its Limits Series: Vienna Circle Collection The Law of Causality and its Limits was the principal philosophical work of the physicist turned philosopher, Philipp Frank. Born in Vienna on March 20, 1884, Frank died in Cambridge, Massachusetts on July 21, 1966. He received his doctorate in 1907 at the University of Vienna in theoretical physics, having studied under Ludwig Boltzmann; his sub• sequent research in physics and mathematics was represented by more than 60 scientific papers. Moreover his great success as teacher and expositor was recognized throughout the scientific world with publication of his collaborative Die Differentialgleichungen der Mechanik und Physik, with Richard von Mises, in 1925-27. Frank was responsible for the second volume, on physics, and especially noted for his authoritative article on classical Hamiltonian mechanics and optics. Among his earliest papers were those, beginning in 1908, devoted to special relativity, which together with general relativity and physical cosmology occupied him throughout his life. 1998, XIII, 302 p. Already in 1907, Frank published his seminal paper 'Kausalgesetz und Erfahrung' ('Experience and the Law of Causality'), much later collected with a splendid selection of his essays on Printed book philosophy of science, in English (1941c and 1949g, in our Bibliography). Joining the first Hardcover 'Vienna Circle' in the first decade of the 20th century, with Hans Hahn, mathematician, and Otto 129,99 € | £109.99 | $159.99 Neurath, sociologist and economist, and deeply influenced by studies of Ernst Mach's critical [1] 139,09 € (D) | 142,99 € (A) | CHF conceptual histories of science and by the striking challenge of Poincare and Duhem, Frank 153,50 continued his epistemological investigations.