Georg Kreisel Papers SC0136
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“Gödel's Modernism: on Set-Theoretic Incompleteness,” Revisited
“G¨odel'sModernism: on Set-Theoretic Incompleteness," revisited∗ Mark van Atten and Juliette Kennedy As to problems with the answer Yes or No, the con- viction that they are always decidable remains un- touched by these results. —G¨odel Contents 1 Introduction 1.1 Questions of incompleteness On Friday, November 15, 1940, Kurt G¨odelgave a talk on set theory at Brown University.1 The topic was his recent proof of the consistency of Cantor's Con- tinuum Hypothesis, henceforth CH,2 with the axiomatic system for set theory ZFC.3 His friend from their days in Vienna, Rudolf Carnap, was in the audience, and afterward wrote a note to himself in which he raised a number of questions on incompleteness:4 (Remarks I planned to make, but did not) Discussion on G¨odel'slecture on the Continuum Hypothesis, November 14,5 1940 There seems to be a difference: between the undecidable propo- sitions of the kind of his example [i.e., 1931] and propositions such as the Axiom of Choice, and the Axiom of the Continuum [CH ]. We used to ask: \When these two have been decided, is then everything decided?" (The Poles, Tarski I think, suspected that this would be the case.) Now we know that (on the basis of the usual finitary rules) there will always remain undecided propositions. ∗An earlier version of this paper appeared as ‘G¨odel'smodernism: on set-theoretic incom- pleteness', Graduate Faculty Philosophy Journal, 25(2), 2004, pp.289{349. Erratum facing page of contents in 26(1), 2005. 1 1. Can we nevertheless still ask an analogous question? I.e. -
Kreisel and Wittgenstein
Kreisel and Wittgenstein Akihiro Kanamori September 17, 2018 Georg Kreisel (15 September 1923 { 1 March 2015) was a formidable math- ematical logician during a formative period when the subject was becoming a sophisticated field at the crossing of mathematics and logic. Both with his technical sophistication for his time and his dialectical engagement with man- dates, aspirations and goals, he inspired wide-ranging investigation in the meta- mathematics of constructivity, proof theory and generalized recursion theory. Kreisel's mathematics and interactions with colleagues and students have been memorably described in Kreiseliana ([Odifreddi, 1996]). At a different level of interpersonal conceptual interaction, Kreisel during his life time had extended engagement with two celebrated logicians, the mathematical Kurt G¨odeland the philosophical Ludwig Wittgenstein. About G¨odel,with modern mathemat- ical logic palpably emanating from his work, Kreisel has reflected and written over a wide mathematical landscape. About Wittgenstein on the other hand, with an early personal connection established Kreisel would return as if with an anxiety of influence to their ways of thinking about logic and mathematics, ever in a sort of dialectic interplay. In what follows we draw this out through his published essays|and one letter|both to elicit aspects of influence in his own terms and to set out a picture of Kreisel's evolving thinking about logic and mathematics in comparative relief.1 As a conceit, we divide Kreisel's engagements with Wittgenstein into the \early", \middle", and \later" Kreisel, and account for each in successive sec- tions. x1 has the \early" Kreisel directly interacting with Wittgenstein in the 1940s and initial work on constructive content of proofs. -
Georg Kreisel Correspondence with Jean Van Heijenoort
http://oac.cdlib.org/findaid/ark:/13030/c84q7wxh No online items Guide to the Georg Kreisel Correspondence with Jean van Heijenoort Daniel Hartwig Stanford University. Libraries.Department of Special Collections and University Archives Stanford, California October 2010 Copyright © 2015 The Board of Trustees of the Leland Stanford Junior University. All rights reserved. Note This encoded finding aid is compliant with Stanford EAD Best Practice Guidelines, Version 1.0. Guide to the Georg Kreisel SC0233 1 Correspondence with Jean van Heijenoort Overview Call Number: SC0233 Creator: Kreisel, Georg, 1923- Title: Georg Kreisel correspondence with Jean van Heijenoort Dates: 1949-1981 Physical Description: 6 Linear feet Summary: Correspondence, notes, memoranda, articles and other materials by Professor Georg Kreisel, sent to his colleague, Professor J. van Heijenoort of Harvard University. Includes some correspondence with other colleagues. Language(s): The materials are in English. Repository: Department of Special Collections and University Archives Green Library 557 Escondido Mall Stanford, CA 94305-6064 Email: [email protected] Phone: (650) 725-1022 URL: http://library.stanford.edu/spc Gift of J. van Heijenoort, 1981. Information about Access This collection is open for research. Ownership & Copyright All requests to reproduce, publish, quote from, or otherwise use collection materials must be submitted in writing to the Head of Special Collections and University Archives, Stanford University Libraries, Stanford, California 94304-6064. Consent is given on behalf of Special Collections as the owner of the physical items and is not intended to include or imply permission from the copyright owner. Such permission must be obtained from the copyright owner, heir(s) or assigns. -
An Interview with Martin Davis
Notices of the American Mathematical Society ISSN 0002-9920 ABCD springer.com New and Noteworthy from Springer Geometry Ramanujan‘s Lost Notebook An Introduction to Mathematical of the American Mathematical Society Selected Topics in Plane and Solid Part II Cryptography May 2008 Volume 55, Number 5 Geometry G. E. Andrews, Penn State University, University J. Hoffstein, J. Pipher, J. Silverman, Brown J. Aarts, Delft University of Technology, Park, PA, USA; B. C. Berndt, University of Illinois University, Providence, RI, USA Mediamatics, The Netherlands at Urbana, IL, USA This self-contained introduction to modern This is a book on Euclidean geometry that covers The “lost notebook” contains considerable cryptography emphasizes the mathematics the standard material in a completely new way, material on mock theta functions—undoubtedly behind the theory of public key cryptosystems while also introducing a number of new topics emanating from the last year of Ramanujan’s life. and digital signature schemes. The book focuses Interview with Martin Davis that would be suitable as a junior-senior level It should be emphasized that the material on on these key topics while developing the undergraduate textbook. The author does not mock theta functions is perhaps Ramanujan’s mathematical tools needed for the construction page 560 begin in the traditional manner with abstract deepest work more than half of the material in and security analysis of diverse cryptosystems. geometric axioms. Instead, he assumes the real the book is on q- series, including mock theta Only basic linear algebra is required of the numbers, and begins his treatment by functions; the remaining part deals with theta reader; techniques from algebra, number theory, introducing such modern concepts as a metric function identities, modular equations, and probability are introduced and developed as space, vector space notation, and groups, and incomplete elliptic integrals of the first kind and required. -
“YOU MUST REMEMBER THIS” Abraham (“Abe”) Edel
MATERIAL FOR “YOU MUST REMEMBER THIS” Abraham (“Abe”) Edel (6 December 1908 – 22 June 2007) “Twenty-Seven Uses of Science in Ethics,” 7/2/67 Abraham Edel, In Memoriam, by Peter Hare and Guy Stroh Abraham Edel, 1908-2007 Abraham Edel was born in Pittsburgh, Pennsylvania on December 6, 1908. Raised in Yorkton, Canada with his older brother Leon who would become a biographer of Henry James, Edel studied Classics and Philosophy at McGill University, earning a BA in 1927 and an MA in 1928. He continued his education at Oxford where, as he recalled, “W.D. Ross and H.A. Prichard were lecturing in ethics, H.W.B. Joseph on Plato, and the influence of G. E. Moore and Bertrand Russell extended from Cambridge. Controversy on moral theory was high. The same was true of epistemology, where Prichard posed realistic epistemology against Harold Joachim who was defending Bradley and Bosanquet against the metaphysical realism of Cook Wilson.” He received a BA in Litterae Humaniores from Oxford in 1930. In that year he moved to New York City for doctoral studies at Columbia University, and in 1931 began teaching at City College, first as an assistant to Morris Raphael Cohen. F.J.E. Woodbridge directed his Columbia dissertation, Aristotle’s Theory of the Infinite (1934). This monograph and two subsequent books on Aristotle were influenced by Woodbridge’s interpretation of Aristotle as a philosophical naturalist. Although his dissertation concerned ancient Greek philosophy, he was much impressed by research in the social sciences at Columbia, and the teaching of Cohen at City College showed him how philosophical issues lay at the root of the disciplines of psychology, sociology, history, as well as the natural sciences. -
Una Fundamentaci´On De La Historia De Las Matem´Aticas
UNA FUNDAMENTACION´ DE LA HISTORIA DE LAS MATEMATICAS´ UNA FUNDAMENTACION´ DE LA HISTORIA DE LAS MATEMATICAS´ Jesus Hernando P´erezAlc´azar OSCAR´ ARMANDO IBARRA RUSSI Rector ALEJANDRO ALVAREZ´ GALLEGO Vicerrector Acad´emico MARIO BALLESTEROS MEJ´IA Vicerrector Administrativo y Financiero NOHORA PATRICIA MORENO GARC´IA Vicerrectora de Gesti´onUniversitaria c Universidad Pedag´ogicaNacional c Jes´us Hernando P´erez Alc´azar Profesor investigador Universidad Sergio Arboleda ISBN: Primera edici´on,2007 Preparaci´oneditorial Universidad Pedag´ogicaNacional Fondo Editorial LUIS EDUARDO VASQUEZ´ SALAMANCA Coordinador Impresi´on Bogot´a,Colombia, 2007 Dedicado a: La memoria de mi padre, el educador matem´atico Jos´e Ignacio P´erez, Mi madre Aura Mar´ıaAlc´azar. Contenido Agradecimientos IV Presentaci´on V Prefacio VIII 1. Principios orientadores para la fundamentaci´onde la historia de la matem´aticas 1 1.1. (P1) Principio de Durkheim o de la divisi´onsocial trabajo . 1 1.2. (P2) Principio ´eticoy legal o de las tensiones entre permitido versus prohibido y conveniente versus inconveniente . 2 1.3. (P3) Principio acad´emico o de la dial´ecticaimaginarios versus teor´ıas 4 1.4. (P4) Principio de historicidad . 8 1.5. (P5) Principio de Chomsky o de la tensi´onentre finito e infinito . 10 1.6. (P6) Principio anfibi´oticoo de la tensi´onentre ser y no ser . 14 2. Ejemplos iniciales de documentos historiogr´aficos 19 2.1. Un art´ıculode divulgaci´on. 19 2.2. Un trabajo hist´orico-filos´ofico . 24 2.3. Historia de la historia . 27 2.4. (P7) Principio de Struik o de la dignificaci´onde la especie humana 30 2.4. -
About Logic and Logicians
About Logic and Logicians A palimpsest of essays by Georg Kreisel Selected and arranged by Piergiorgio Odifreddi Volume 2: Mathematics Lógica no Avião ABOUT LOGIC AND LOGICIANS A palimpsest of essays by Georg KREISEL Selected and arranged by Piergiorgio ODIFREDDI Volume II. Mathematics Editorial Board Fernando Ferreira Departamento de Matem´atica Universidade de Lisboa Francisco Miraglia Departamento de Matem´atica Universidade de S~aoPaulo Graham Priest Department of Philosophy The City University of New York Johan van Benthem Department of Philosophy Stanford University Tsinghua University University of Amsterdam Matteo Viale Dipartimento di Matematica \Giuseppe Peano" Universit`adi Torino Piergiorgio Odifreddi, About Logic and Logicians, Volume 2. Bras´ılia: L´ogicano Avi~ao,2019. S´erieA, Volume 2 I.S.B.N. 978-65-900390-1-9 Prefixo Editorial 900390 Obra publicada com o apoio do PPGFIL/UnB. Editor's Preface These books are a first version of Odifreddi's collection of Kreisel's expository papers, which together constitute an extensive, scholarly account of the philo- sophical and mathematical development of many of the most important figures of modern logic; some of those papers are published here for the first time. Odifreddi and Kreisel worked together on these books for several years, and they are the product of long discussions. They finally decided that they would collect those essays of a more expository nature, such as the biographical memoirs of the fellows of the Royal Society (of which Kreisel himself was a member) and other related works. Also included are lecture notes that Kreisel distributed in his classes, such as the first essay printed here, which is on the philosophy of mathematics and geometry. -
Sir Karl Raimund Popper Papers, 1928-1995
http://oac.cdlib.org/findaid/ark:/13030/tf8c60064j No online items Register of the Sir Karl Raimund Popper Papers, 1928-1995 Finding aid prepared by Hoover Institution staff and David Jacobs Hoover Institution Archives Stanford, CA, 94305-6010 (650) 723-3563 © 1998 Register of the Sir Karl Raimund 86039 1 Popper Papers, 1928-1995 Title: Sir Karl Raimund Popper papers Collection Number: 86039 Contributing Institution: Hoover Institution Archives Language of Material: In English Date (inclusive): 1928-1995 Abstract: Speeches and writings, correspondence, notes, printed matter, phonotapes, phonorecords, and photographs, relating to philosophy, the nature of knowledge, the philosophy of culture, the philosophy and methodology of science, and the philosophy of history and the social sciences. Deacribed in two groups, original collection (boxes 1-463) and the incremental materials acquired at a later date (boxes 464-583). Physical location: Hoover Institution Archives Collection Size: 575 manuscript boxes, 6 oversize boxes, 2 card file boxes, 28 envelopes, 47 phonotape reels, 4 phonotape cassettes, 11 phonorecords (248 linear feet) Creator: Popper, Karl Raimund, Sir, 1902- Access The collection is open for research. Use copies of sound recordings are available for immediate use. Publication Rights For copyright status, please contact the Hoover Institution Archives Acquisition Information Acquired by the Hoover Institution Archives in 1986 with increments added at a later date. Accruals Materials may have been added to the collection since this finding aid was prepared. To determine if this has occurred, find the collection in Stanford University's online catalog Socrates at http://library.stanford.edu/webcat . Materials have been added to the collection if the number of boxes listed in Socrates is larger than the number of boxes listed in this finding aid. -
Association for Symbolic Logic
Association for Symbolic Logic Business Office: Box 742, Vassar College 124 Raymond Avenue, Poughkeepsie, New York 12604, USA Fax: 1-845-437-7830; email: [email protected] Web: http://www.aslonline.org ASL NEWSLETTER April 2016 • In Memoriam: Georg Kreisel. Georg Kreisel died in Salzburg on March 1, 2015, aged 91. Born on September 15, 1923 in Graz, he came to England before the outbreak of World War II to escape Nazi persecution. He completed his secondary education at Dulwich College, in London, and then studied mathematics at Trinity College Cambridge, where A.S. Besicovitch was his director of studies. During this time, and again in 1946-47, in addition to studying mathematics, Kreisel also discussed philosophy of mathematics with Ludwig Wittgenstein, a Fellow of Trinity College (who in 1944 said of Kreisel that he was the most able philosopher he had ever met who was also a mathematician). Kreisel took his B.A. in Mathematics in 1944 (and was in contention to be Senior Wrangler). He then used his training as a mathematician, particularly in fluid dynamics, for war service as an Experimental Officer in the British Admiralty, and continued in that post until 1946, when he returned to Cambridge. He submitted a dissertation for a Research Fellowship at Trinity College but was not elected. Kreisel never took a Ph.D., though in 1962 he was awarded the Cambridge degree of Sc.D., a `higher doctorate' given on the basis of published research. In 1949 he was appointed Lecturer in Mathematics at the University of Reading, a post he held until 1960, during which time and thereafter he also held visiting positions at the University of Paris (intermittently throughout the 1950s, 60s, and 70s), at the Institute for Advanced Study in Princeton (1955-7 and 1962-3)|where he was closely associated with Kurt G¨odel,who had invited him, Stanford University (1958-9 and 1962-3), All Souls College Oxford (1967), and the University of California at Los Angeles (1968). -
You Do the Math. the Newton Fellowship Program Is Looking for Mathematically Sophisticated Individuals to Teach in NYC Public High Schools
AMERICAN MATHEMATICAL SOCIETY Hamilton's Ricci Flow Bennett Chow • FROM THE GSM SERIES ••. Peng Lu Lei Ni Harryoyrn Modern Geometric Structures and Fields S. P. Novikov, University of Maryland, College Park and I. A. Taimanov, R ussian Academy of Sciences, Novosibirsk, R ussia --- Graduate Studies in Mathematics, Volume 71 ; 2006; approximately 649 pages; Hardcover; ISBN-I 0: 0-8218- 3929-2; ISBN - 13 : 978-0-8218-3929-4; List US$79;AII AMS members US$63; Order code GSM/71 Applied Asymptotic Analysis Measure Theory and Integration Peter D. Miller, University of Michigan, Ann Arbor, MI Graduate Studies in Mathematics, Volume 75; 2006; Michael E. Taylor, University of North Carolina, 467 pages; Hardcover; ISBN-I 0: 0-82 18-4078-9; ISBN -1 3: 978-0- Chapel H ill, NC 8218-4078-8; List US$69;AII AMS members US$55; Order Graduate Studies in Mathematics, Volume 76; 2006; code GSM/75 319 pages; Hardcover; ISBN- I 0: 0-8218-4180-7; ISBN- 13 : 978-0-8218-4180-8; List US$59;AII AMS members US$47; Order code GSM/76 Linear Algebra in Action Harry Dym, Weizmann Institute of Science, Rehovot, Hamilton's Ricci Flow Israel Graduate Studies in Mathematics, Volume 78; 2006; Bennett Chow, University of California, San Diego, 518 pages; Hardcover; ISBN-I 0: 0-82 18-38 13-X; ISBN- 13: 978-0- La Jolla, CA, Peng Lu, University of Oregon, Eugene, 8218-3813-6; Li st US$79;AII AMS members US$63; O rder OR , and Lei Ni, University of California, San Diego, code GSM/78 La ] olla, CA Graduate Studies in Mathematics, Volume 77; 2006; 608 pages; Hardcover; ISBN-I 0: -
Kreisel's 'Shift of Emphasis' and Contemporary Proof Mining
Kreisel's `shift of emphasis' and contemporary proof mining Ulrich Kohlenbach Department of Mathematics Technische Universit¨atDarmstadt Schlossgartenstraße 7, 64289 Darmstadt, Germany [email protected] October 30, 2018 1 Introduction `The story above began and ended with shifts away from traditional logical aims' ([77], p.401) `A price paid by those (of us) later pursuing proof theory has been to discover suitable ideas for adapting consistency proofs to aims rewarding for a broader view, naturally, not an unduly high price for those (of us) attracted by such activity' ([85], pp.43-44) Starting in the early 50's, Kreisel argued that proof-theoretic methods that had been devel- oped in the course of Hilbert's consistency program could be used for concrete mathematical goals different and independent from their original foundational motivation. Kreisel's writ- ings on this topic, in particular in connection with his concept of `unwinding of proofs', span over a period of 60 years and contain numerous important insights and suggestions on how such a reorientation of traditional proof theory from foundational aims to applications in core mathematics could be achieved. In this paper, we revisit some of Kreisel's main themes from the perspective of the current `proof mining' program which has been pursued e.g. by the present author and many collaborators as a modern and more systematic version of Kreisel's original `unwinding' program and which has the area of nonlinear analysis as its prominent field for applications (see [57] for a recent survey). As we will see, the impor- tance of Kreisel's insights for the development of the proof mining paradigm can hardly be overstated. -
11 May 2012 −− Fritz Joseph Ursell. 28 April 1923
Downloaded from rsbm.royalsocietypublishing.org on October 24, 2013 Fritz Joseph Ursell. 28 April 1923 −− 11 May 2012 I. D. Abrahams and P. A. Martin Biogr. Mems Fell. R. Soc. 2013 59 , doi: 10.1098/rsbm.2013.0005 first published online 10 April 2013 Supplementary data "Data Supplement" http://rsbm.royalsocietypublishing.org/content/suppl/2013/04/0 8/rsbm.2013.0005.DC1.html Receive free email alerts when new articles cite this article - sign up Email alerting service in the box at the top right-hand corner of the article or click here To subscribe to Biogr. Mems Fell. R. Soc. go to: http://rsbm.royalsocietypublishing.org/subscriptions FRITZ JOSEPH URSELL 28 April 1923 — 11 May 2012 Biogr. Mems Fell. R. Soc. 59 , 407–421 (2013) FRITZ JOSEPH URSELL 28 April 1923 — 11 May 2012 Elected FRS 1972 BY I. D. A BRAHAMS 1 AND P. A. M ARTIN 2 1School of Mathematics, University of Manchester, Manchester M13 9PL, UK 2Department of Applied Mathematics and Statistics, Colorado School of Mines, Golden, CO 80401, USA Fritz Ursell was a singular and influential applied mathematician. He made seminal contribu- tions to research in the mathematical analysis of linear water waves. This required the develop- ment of new techniques for the asymptotic evaluation of integrals, especially uniformly valid approximations. He made numerous contributions to the field; for example, he constructed a family of solutions for edge waves on a sloping beach that extended Stokes’s original result, he gave a detailed analysis of the Kelvin ship-wave pattern, and he was the first to prove the existence of trapped modes in water-wave problems.