Logical Empiricism (Stanford Encyclopedia of Philosophy)
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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. -
The Delphi Method: Techniques and Applications from the Foreword by Olaf Helmer
The Delphi Method Techniques and Applications Edited by Harold A. Linstone Portland State University Murray Turoff New Jersey Institute of Technology With a Foreword by Olaf Helmer University of Southern California ©2002 Murray Turoff and Harold A. Linstone I. Introduction I. Introduction HAROLD A. LINSTONE and MURRAY TUROFF General Remarks It is common, in a book of this kind, to begin with a detailed and explicit definition of the subject- the Delphi technique. However, if we were to attempt this, the reader would no doubt encounter at least one contribution to this collection which would violate our definition. There is in addition a philosophical perspective that when something has attained a point at which it is explicitly definable, then progress has stopped; such is the view we hold with respect to Delphi. In 1969 the number of Delphi studies that had been done could be counted in three digits; today, in 1974, the figure may have already reached four digits. The technique and its application are in a period of evolution, both with respect to how it is applied and to what it is applied. It is the objective of this book to expose the richness of what may be viewed as an evolving field of human endeavor. The reader will encounter in these pages many different perspectives on the Delphi method and an exceedingly diverse range of applications. For a technique that can be considered to be in its infancy, it would be presumptuous of us to present Delphi in the cloak of a neatly wrapped package, sitting on the shelf and ready to use, Rather, we have adopted the approach, through our selection of contributions, of exhibiting a number of different objects having the Delphi label and inviting you to sculpt from these examples your own view and assessment of the technique. -
How to Train Your Oracle: the Delphi Method and Its Turbulent Youth in Operations Research and the Policy Sciences
SSS0010.1177/0306312718798497Social Studies of ScienceDayé 798497research-article2018 Article Social Studies of Science 1 –23 How to train your oracle: © The Author(s) 2018 Article reuse guidelines: The Delphi method and its sagepub.com/journals-permissions https://doi.org/10.1177/0306312718798497DOI: 10.1177/0306312718798497 turbulent youth in operations journals.sagepub.com/home/sss research and the policy sciences Christian Dayé Department of Sociology, Alpen-Adria-Universität Klagenfurt, Klagenfurt, Austria Abstract Delphi is a procedure that produces forecasts on technological and social developments. This article traces the history of Delphi’s development to the early 1950s, where a group of logicians and mathematicians working at the RAND Corporation carried out experiments to assess the predictive capacities of groups of experts. While Delphi now has a rather stable methodological shape, this was not so in its early years. The vision that Delphi’s creators had for their brainchild changed considerably. While they had initially seen it as a technique, a few years later they reconfigured it as a scientific method. After some more years, however, they conceived of Delphi as a tool. This turbulent youth of Delphi can be explained by parallel changes in the fields that were deemed relevant audiences for the technique, operations research and the policy sciences. While changing the shape of Delphi led to some success, it had severe, yet unrecognized methodological consequences. The core assumption of Delphi that the convergence of expert opinions observed over the iterative stages of the procedure can be interpreted as consensus, appears not to be justified for the third shape of Delphi as a tool that continues to be the most prominent one. -
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. -
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. -
Prof. Richard Von Mises
Professor Richard von Mises (1883 – 1953) From Wikipedia, the free encyclopedia (http://en.wikipedia.org/wiki/Richard_von_Mises ) Richard Edler von Mises ( 19 April 1883, Lwów – 14 July 1953, Boston, Massachusetts) was a scientist and mathematician who worked on solid mechanics, fluid mechanics, aerodynamics, aeronautics, statistics and probability theory. He held the position of Gordon-McKay Professor of Aerodynamics and Applied Mathematics at Harvard University. He described his work in his own words shortly before his death as being on “... practical analysis, integral and differential equations, mechanics, hydrodynamics and aerodynamics, constructive geometry, probability calculus, statistics and philosophy.” Although best known for his mathematical work, he also contributed to the philosophy of science as a neo- positivist, following the line of Ernst Mach. Historians of the Vienna Circle of logical empiricism recognize a "first phase" from 1907 through 1914 with Philipp Frank, Hans Hahn, and Otto Neurath. His older brother, Ludwig von Mises, held an opposite point of view with respect to positivism and epistemology. During his time in Istanbul, von Mises maintained close contact with Philipp Frank, a logical positivist and Professor of Physics in Prague until 1938. His literary interests included the Austrian novelist Robert Musil and the poet Rainer Maria Rilke, on whom he became a recognized expert. Von Mises’ Life: Eighteen months after his brother, the Austrian School economist Ludwig von Mises, Richard von Mises was born in Lemberg, then part of Austria-Hungary, into a Jewish family. His parents were Arthur Edler von Mises, a doctor of technical sciences who worked as an expert for the Austrian State Railways, and Adele Landau. -
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. -
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. -
The Berlin School of Logical Empiricism and Its Legacy
Nicholas Rescher July 6, 2006 THE BERLIN SCHOOL OF LOGICAL EMPIRICISM AND ITS LEGACY 1. BACKGROUND What has become generally known as the Berlin School of Logical Empiricism constitutes a philosophical movement that was based in Berlin’s Gesellschaft fuer empirische Philosophie and erected on foundations laid by Albert Einstein. His revolutionary work in physics had a profound impact on philosophers interested in scientific issues, prominent among them Paul Oppenheim and Hans Reichenbach, the founding fathers of the school, who joined in viewing him as their hero among philosopher-scientists. Overall the membership of this school falls into three groups, as per Display 1.1 The founding generation was linked by the circumstance that both Grelling and Reichenbach were collaborators of Oppenheim; the middle generation by the fact that both Hempel and Helmer were students of Reichenbach’s in Berlin; and the younger generation by the fact that all of its members were students and (at least in their early years) disciples either of Reichenbach or of Hempel in the USA. Three stages are thus at issue: an initial phase in Berlin, a transatlantic migration, and a continuation in the U.S.A.—principally in Pittsburgh. 1 Various other people were involved in the Berlin School in a more peripheral way. A detailed account of its early days in Berlin (roughly 1927 to 1933) is given in Dieter Hoffman’s contribution to Dannenberg et. al. 1994, entitled “Zur Geschichte der Berliner Gesellschaft für empirisch/wissenschaftliche Philosophie.” 2 ___________________________________________________ Display 1 THE BERLIN SCHOOL I. THE FOUNDING GENERATION • Paul Oppenheim (1885-1977) • Kurt Grelling (1886-1942) • Hans Reichenbach (1891-1953) • Walter Dubislav (1895-1937) II. -
On the Exchanges Between Wolfgang Doeblin and Bohuslav Hostinský
On the exchanges between Wolfgang Doeblin and Bohuslav Hostinsky´ Laurent MAZLIAK1 October 30, 2007 Action must always be the daughter of rigor before being the sister of dream G.Canguilhem2 Abstract: In this paper, we present the letters sent by Wolfgang Doeblin to Bohuslav Hostinsky´ between 1936 and 1938. They concern some aspects of the general theory of Markov chains and solutions of Chapman-Kolmogorov equation that Doeblin was then establishing for his PhD thesis. Resum´ e´: Nous presentons´ ici les lettres envoyees´ par Wolfgang Doeblin a` Bohuslav Hostinsky´ entre 1936 et 1938. Elles presentent´ des aspects de la theorie´ gen´ erale´ des chaˆınes de Markov que Doeblin mettait en forme pour sa these` ainsi que des considerations´ sur la resolution´ de l’equation´ de Chapman-Kolmogorov. Key-Words: Markov Chains, Markov Processes, Chapman-Kolmogorov Equation, History of Probability calculus AMS Classification : 01A60, 60J10, 60J27, 60J35 INTRODUCTION On June 17th, 1936, Maurice Frechet´ (1878-1973), one of the most prominent representatives of the French mathematical school as well as a creator of the modern school of probability calculus, wrote to his col- league and friend Bohuslav Hostinsky´ (1884-1951), Professor of Theoretical Physics at Brno University in Czechoslovakia: I have a new pupil named Doblin¨ who is studying probabilities in chains and will soon 3 (n) publish in the C.R. some results that I feel are interesting. He has much extended the results for the pik obtained by M.Hadamard at the Bologna conference and those of Romanovsky in his last memoir in the Acta. Since the beginning of the 1990s, there has been a resurgence of interest in Wolfgang Doeblin (1915- 1940), an amazing and engaging character, and above all in his magnificent mathematical achievements. -
Ludwig Von Mises: Scholar, Creator, Hero
Murray N. Rothbard Ludwig von Mises: Scholar, Creator, Hero Introduction The purpose of this essay is to discuss and celebrate the life and work of one of the great creative minds of our century. Ludwig von Mises was born on September 29, 1881, in the city of Lemberg (now Lvov), in Galicia, in the Austro-Hungarian Empire. His father, Arthur Edler von Mises, a Viennese construction engineer working for the Austrian railroads, was stationed in Lemberg at the time. Ludwig’s mother, Adele Landau, also came from a prominent family in Vienna: her uncle, Dr. Joachim Landau, was a deputy from the Liberal Party in the Austrian Parliament. The Young Scholar Though the pre-eminent theorist of our time, Mises’s interest, as a teenager, centered in history, particularly economic and administrative history. But even while still in high school, he reacted against the relativism and historicism rampant in the German-speaking countries, dominated by the Historical School. In his early historical work, he was frustrated to find historical studies virtually consisting of paraphrases from official government reports. Instead, he yearned to write genuine economic history. He early disliked the State orientation of historical studies. Thus, in his memoirs, Mises writes: “It was my intense interest in historical knowledge that enabled me to perceive readily the inadequacy of German historicism. It did not deal with scientific problems, but with the glorification and justification of Prussian policies and Prussian authoritarian government. The German universities were state institutions and the instructors were civil servants. The professors were aware of this civil-service status, that is, they saw themselves as servants of the Prussian king”.[1] Ludwig von Mises entered the University of Vienna at the turn of the twentieth century and his major professor was the economic historian Karl Grünberg, a member of the German Historical School and a statist who was interested in labor history, agricultural history, and Marxism.