DOCSLIB.ORG

History and Philosophy of Logic

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
History and Philosophy of Logic This article was downloaded by:[Universidad Granada] [Universidad Granada] On: 22 May 2007 Access Details: [subscription number 773444453] Publisher: Taylor & Francis Informa Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK History and Philosophy of Logic Publication details, including instructions for authors and subscription information: http://www.informaworld.com/smpp/title~content=t713812075 Book Review To cite this Article: , 'Book Review', History and Philosophy of Logic, 27:2, 200 - 203 To link to this article: DOI: 10.1080/01445340600563135 URL: http://dx.doi.org/10.1080/01445340600563135 PLEASE SCROLL DOWN FOR ARTICLE Full terms and conditions of use: http://www.informaworld.com/terms-and-conditions-of-access.pdf This article maybe used for research, teaching and private study purposes. Any substantial or systematic reproduction, re-distribution, re-selling, loan or sub-licensing, systematic supply or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The accuracy of any instructions, formulae and drug doses should be independently verified with primary sources. The publisher shall not be liable for any loss, actions, claims, proceedings, demand or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material. © Taylor and Francis 2007 200 Book Reviews (IV) Topics and persons loosely related to Becker. The relation of the remaining three articles to Oskar Becker’s philosophy of mathematics is only slim. After correcting Becker’s translations of Archimedes twice (p. 18), Knobloch (pp. 15–34) discusses the reception of Archimedes’ works by the two Renaissance mathemati- cians Kepler and Guldin, focusing on their views on heuristics and proof methods. Peckhaus (pp. 79–99) takes Becker’s critique of Hilbert’s formalism and a paper in which this position was uncritically accepted, published in the first volume on Becker’s philosophy (Gethmann-Siefert and Mittelstraß 2002), as the occasion for clarifying Hilbert’s position. Despite the title, ‘Impliziert Widerspruchsfreiheit Existenz? Oskar Beckers Kritik am formalistischen Existenzbegriff’, Becker’s views are presented only in the first of the five main sections of the paper. The remainder is devoted to a careful interpretation of Hilbert’s views, according to which mathematical freedom is restricted by logical (consistency), metaphysical (the thinking subject), and pragmatic (given mathematical results) considerations. Finally, in Stekeler-Weithofer’s ‘prototheoretic’ reflections on classical set theory (pp. 299–324), which aim at elucidating the introduction of a set-theoretic language, a set-theoretic ontology, and axiomatic set theory as a basis for mathematical proof, Becker is mentioned in only four footnotes (pp. 302, 304, 316, and 322) in relation to his discussions of Dedekind, Bolzano, and Cantor, and is quoted in the concluding section (p. 322). Downloaded By: [Universidad Granada] At: 11:20 22 May 2007 Certainly with merit in their own right, the three papers presented in (IV), however, do not seem to add much to our understanding of Oskar Becker. On the other hand, although some of the papers present certain aspects of Becker’s biography, his sympathies for Nazism are mentioned nowhere. Nevertheless, this collection is highly informative and interesting. Becker’s correspondence gives us an insight into the unpolished ideas and questions that occupied him, as well as Mahnke, Heyting, and Weyl. Together with the reflections on Becker’s work, this volume is a valuable contribution for enhancing our appreciation of Oskar Becker, a deep and original, but still rather unknown, thinker on the philosophy of mathematics. References Gethmann-Siefert, A. and Mittelstraß, J. eds, 2002. Die Philosophie und die Wissenschaften. Zum Werk Oskar Beckers, Munich: Wilhelm Fink Verlag. Mancosu, P. and Ryckman, Th.A. 2002. ‘Mathematics and Phenomenology. The correspondence between Oskar Becker and Hermann Weyl’, Philosophia Mathematica, 10, 130–202. Poser, H. 1996. ‘Ontologie der Mathematik im Anschluß an Oskar Becker’, Acta Analytica 16/17, 125–146. DOI: 10.1080/01445340600601091 H. LILLEHAMMER and D. H. MELLOR (eds.), Ramsey’s Legacy. Oxford: Clarendon Press, 2005. x þ 182 pp. £40.00. ISBN 0-19-927955-1. Reviewed by MARI´ A J. FRA´ POLLI, Departamento de Filosofia, Universidad de Granada, 18071 Granada, Spain Ramsey’s Legacy is Mellor’s latest contribution to Ramsey scholarship. His previous editions include two collections of works of Ramsey, Foundations: essays in Book Reviews 201 philosophy, logic, mathematics and economics (Routledge and Kegan Paul, 1978), Philosophical papers (Cambridge University Press, 1980), and a volume of works on Ramsey, Prospects for pragmatism (Cambridge University Press, 1980). Edited this time in cooperation with Hallvard Lillehammer, the volume provides evidence of the growing interest that Ramsey’s work is rousing nowadays. Ramsey has been a philosopher severely misinterpreted, probably because his insights were too revolutionary for his lifetime. A century after his birth, we are still trying to understand the background and scope of much of what he had to say. If one compares the relative amount of scholarship on Wittgenstein and Ramsey, two philosophers who were contemporaries and both worked in Cambridge and had a manifest mutual influence, one is shocked at the unbalance attention they have received. Still, I would dare to say, Ramsey’s genius resists the comparison, and his ideas are not in the least less groundbreaking, less profound, than those of Wittgenstein. Ramsey wrote on subjects apparently very distant from one another, and his views touched, always imaginatively, always insightfully, the foundations of economics, philosophy of mind, philosophy of logic, philosophy of language, epistemology, the foundations of mathematics and philosophy of science. Ramsey’s scholarship is still in its initial stages. This is one reason for which this book is warmly greeted, but not the only reason; for it is a valuable collection of serious work. It opens with Lillehammer’s Introduction, in Downloaded By: [Universidad Granada] At: 11:20 22 May 2007 which the co-editor explains the content of the subsequent chapters, which range over all aspects of Ramsey’s thought. There are four papers on topics related to philosophy of language and of logic, one on the philosophy of mathematics, one on metaphysics, two papers on epistemology and philosophy of science, one on subjective decision theory, and one on economics. Jeroˆ me Dokic and Pascal Engel are responsible for the first chapter, entitled ‘Ramsey’s principle resituated’. Here, the authors defend Ramsey’s Principle, that the content of a belief is constituted of those features of the world that would guarantee success to those actions that were based on it. This principle has often been misunderstood, Dokic and Engel assert, and the core of the chapter is devoted to explain it and to defend it from some standard objections. The best argument for Ramsey’s Principle, according to the authors, is transcendental, as it should be understood as stating the possibility conditions of intentional action. They conclude that the objections from situated cognition, the ones they have mostly reviewed here, leave the principle untouched. Simon Blackburn’s chapter, ‘Success semantics’, touches on the same topic. He explains success semantics as the implementation of the intuition that we are so successful in action because we are somehow anchored to the world. Success semantics develops the idea that success in action can serve as a guide for a theory of intentionality. Dorothy Edgington, in her chapter ‘Ramsey’s legacies on conditionals and truth’, discusses the compatibility between Ramsey’s theory of conditionals and his view on truth. A minimalist notion of truth, as Ramsey’s, would seem to be widely applicable because of its lack of content. Nevertheless, Ramsey defends that conditional sentences do not express propositions and thus that they are neither true nor false. Edgington’s way of making these two apparently discordant claims congruent is by reminding us that although the notion of truth is minimal, the notion of truth-bearer is not so. A conditional judgement does not produce a truth bearer. What might be assessed for truth or falsity is the consequent given the antecedent. 202 Book Reviews Peter Sullivan devotes his chapter, entitled ‘What is squiggle? Ramsey on Wittgenstein theory of judgement’, to the theory that Ramsey defended. He does so by focusing on Ramsey’s ‘Critical notice’ of Wittgenstein’s Tractatus. This piece places Ramsey not only as the first of the Wittgenstein commentators, but also, Sullivan maintains, as the best of them. Ramsey develops his own view on judgement and belief as a way of filling a gap in Wittgenstein’s position. Michael Potter writes on ‘Ramsey’s transcendental argument’, discussing Ramsey’s argument for the axiom of infinity as it appears in Ramsey’s Nachlass. Potter’s point is that Ramsey had a promising argument for the Russellian Axiom of Infinity. The argument is transcendental and is based on the idea that our normal way of representing the physical world already allows us to think of it as infinite. A defence of Ramsey’s view on universals is the subject of Macbride’s chapter, ‘Ramsey on universals’. Ramsey’s view on universals is a further topic on which he has been utterly misunderstood and underestimated. Macbride explains that Ramsey did not maintain the thesis usually attributed to him, that there is no essential difference between universals and particulars. His point was rather a very reasonable one, which was that language does not offer a reliable guide into the structure of reality. Pierre Cruise offers, in ‘Empiricism and Ramsey’s account of theories’, an interpretation and assessment of what is now known as the Ramsey sentence of a Downloaded By: [Universidad Granada] At: 11:20 22 May 2007 theory.
Load more

Recommended publications
  • 1 Radical Besinnung in Formale Und Transzendentale Logik (1929)
    1 Radical Besinnung in Formale und transzendentale Logik (1929)1 This is a pre-print of an article published in Husserl Studies. The final authenticated version is available online at: https://doi.org/DOI: 10.1007/s10743- 018-9228-5 ABSTRACT. This paper explicates Husserl’s usage of what he calls ‘radical Besinnung’ in Formale und transzendentale Logik (1929, henceforth FTL). Husserl introduces radical Besinnung as his method in the introduction to FTL. Radical Besinnung aims at criticizing the practice of formal sciences by means of transcendental phenomenological clarification of its aims and presuppositions. By showing how Husserl applies this method to the history of formal sciences down to mathematicians’ work in his time, the paper explains in detail the relationship between historical critical Besinnung and transcendental phenomenology. Ultimately the paper suggests that radical Besinnung should be viewed as a general methodological framework within which transcendental phenomenological descriptions are used to criticize historically given goal- directed practices. KEYWORDS: Husserl, Formal and Transcendental Logic, Besinnung, mathematics, apophantic logic, phenomenological method, criticism. Introduction This paper explicates Husserl’s usage of what he calls ‘radical Besinnung’ in Formale und transzendentale Logik (1929, henceforth FTL). Husserl started to emphasize the importance of Besinnung already in the early in the 1920s,2 but, for the sake of a clear argument, I limit myself 1 This paper has been greatly improved thanks to the detailed criticisms and useful and generous suggestions of George Heffernan. I am particularly thankful for him for drawing my attention to FTL §§102-105, where Husserl discusses transcendental Selbst-Besinnung. 2 The term is mentioned already in Logical Investigations (e.g., Hua1/1, 24-25; 304).
    [Show full text]
  • 'N Goue Draad Wat Deur Die Geskiedenis Van Die Wiskunde Loop
    'n Goue Draad wat deur die Geskiedenis van die Wiskunde loop Prof D F M Strauss Dept Filosofie Fakulteit Geesteswetenskappe Universiteit van die Vrystaat Posbus 339, Bloemtontein 9300 [email protected] Opsomming Die aanvanklike sukses wat opgesluit gelê het in the Pythagoreïse oortuiging dat rasionale verhoudinge alles getalsmatig toeganklik maak het spoedig gegewens teëgekom wat nie met behulp van rasionale getalsverhoudinge hanteer kom word nie. Die onvermoë om hierdie probleem getalsmatig tot 'n oplossing tebring sou daartoe lei dat die Griekse wiskunde die weg van 'n geometrisering bewandel het. Daar is nie probeer om hierdie impasse met behulp van die idee van oneindige totaliteite te bowe te kom nie. Nie alleen het dit die aard van getal ondergeskik gemaak aan die ruimte nie, want dit het ook die middeleeuse spekulatiewe “metafisika van die syn” tot gevolg gehad. Eers via Descartes sou die moderne tyd 'n toenemende terugkeer na 'n aritmetiese perspektief vergestalt. Die ontdekking van die differensiaal- en integraalrekene deur Newton en Leibniz het egter opnuut probleme geskep, met name in die verantwoording van die aard van limiete. Die geykte benadering om limiete met behulp van konvergerende rye rasionale getalle te bepaal het 'n onverantwoorde sirkelredenasie bevat, want om as limiet te kan optree moes elke sodanige limiet rééds 'n getal gewees het. Skynbaar het Weierstrass daarin geslaag om 'n suksesvolle alternatiewe waardering van 'n veranderlike in sy statiese teorie te gee. Limiet- waardes kan willekeurig gekies word uit 'n domein van onderskeie getalle wat as 'n oneindige totaliteit opeens voorhande is. Toe hierdie benadering egter in die versamelingsteorie van Cantor tot Russel se kontradiksie lei, het twee teëgestelde reaksies die toneel oorheers.
    [Show full text]
  • Lorenzen's Proof of Consistency for Elementary Number Theory [With An
    Lorenzen’s proof of consistency for elementary number theory Thierry Coquand Computer science and engineering department, University of Gothenburg, Sweden, [email protected]. Stefan Neuwirth Laboratoire de mathématiques de Besançon, Université Bourgogne Franche-Comté, France, [email protected]. Abstract We present a manuscript of Paul Lorenzen that provides a proof of con- sistency for elementary number theory as an application of the construc- tion of the free countably complete pseudocomplemented semilattice over a preordered set. This manuscript rests in the Oskar-Becker-Nachlass at the Philosophisches Archiv of Universität Konstanz, file OB 5-3b-5. It has probably been written between March and May 1944. We also com- pare this proof to Gentzen’s and Novikov’s, and provide a translation of the manuscript. arXiv:2006.08996v1 [math.HO] 16 Jun 2020 Keywords: Paul Lorenzen, consistency of elementary number the- ory, free countably complete pseudocomplemented semilattice, inductive definition, ω-rule. We present a manuscript of Paul Lorenzen that arguably dates back to 1944 and provide an edition and a translation, with the kind permission of Lorenzen’s daughter, Jutta Reinhardt. It provides a constructive proof of consistency for elementary number theory by showing that it is a part of a trivially consistent cut-free calculus. The proof resorts only to the inductive definition of formulas and theorems. More precisely, Lorenzen proves the admissibility of cut by double induction, on the complexity of the cut formula and of the derivations, without using any ordinal assignment, contrary to the presentation of cut elimination in most standard texts on proof theory.
    [Show full text]
  • Husserlian and Fichtean Leanings: Weyl on Logicism, Intuitionism, and Formalism
    Philosophia Scientiæ Travaux d'histoire et de philosophie des sciences 13-2 | 2009 Varia Husserlian and Fichtean Leanings: Weyl on Logicism, Intuitionism, and Formalism Norman Sieroka Electronic version URL: http://journals.openedition.org/philosophiascientiae/295 DOI: 10.4000/philosophiascientiae.295 ISSN: 1775-4283 Publisher Éditions Kimé Printed version Date of publication: 1 October 2009 Number of pages: 85-96 ISBN: 978-2-84174-504-3 ISSN: 1281-2463 Electronic reference Norman Sieroka, « Husserlian and Fichtean Leanings: Weyl on Logicism, Intuitionism, and Formalism », Philosophia Scientiæ [Online], 13-2 | 2009, Online since 01 October 2012, connection on 02 November 2020. URL : http://journals.openedition.org/philosophiascientiae/295 ; DOI : https:// doi.org/10.4000/philosophiascientiae.295 Tous droits réservés Husserlian and Fichtean Leanings: Weyl on Logicism, Intuitionism, and Formalism Norman Sieroka ETH Zürich Résumé : Vers 1918 Hermann Weyl abandonnait le logicisme et donc la ten- tative de réduire les mathématiques à la logique et la théorie des ensembles. Au niveau philosophique, ses points de référence furent ensuite Husserl et Fichte. Dans les années 1920 il distingua leurs positions, entre une direc- tion intuitionniste-phénoménologique d’un côté, et formaliste-constructiviste de l’autre. Peu après Weyl, Oskar Becker adopta une distinction similaire. Mais à la différence du phénoménologue Becker, Weyl considérait l’approche active du constructivisme de Fichte comme supérieure à la vision d’essences passive de Husserl. Dans cet essai, je montre ce développement dans la pensée de Weyl. Bien que certains points dans sa réception de Husserl et Fichte ne soient pas soutenables, je vais argumenter en faveur de la distinction fonda- mentale mentionnée ci-dessus.
    [Show full text]
  • Logic's Lost Genius
    HISTORY OF MATHEMATICS • VOLUME 33 Logic’s Lost Genius The Life of Gerhard Gentzen Eckart Menzler-Trott American Mathematical Society • London Mathematical Society Logic’s Lost Genius The Life of Gerhard Gentzen https://doi.org/10.1090/hmath/033 HISTORY OF MATHEMATICS VOLUME 33 Logic’s Lost Genius The Life of Gerhard Gentzen Eckart Menzler-Trott Translated by Craig Smorynski ´ and Edward Griffor Editorial Board American Mathematical Society London Mathematical Society Joseph W. Dauben Alex D. D. Craik Peter Duren Jeremy J. Gray Karen Parshall, Chair Robin Wilson, Chair MichaelI.Rosen This work was originally published in German by Birkh¨auser Verlag under the title Gentzens Problem c 2001. The present translation was created under license for the American Mathematical Society and is published by permission. Photo of Gentzen in hat courtesy of the Archives of the Mathematisches Forschungsinstitut Oberwolfach. Reprinted with permission. 2010 Mathematics Subject Classification. Primary 01A60. For additional information and updates on this book, visit www.ams.org/bookpages/hmath-33 Library of Congress Cataloging-in-Publication Data Menzler-Trott, Eckart. [Gentzens Problem. English] Logic’s lost genius : the life of Gerhard Gentzen / Eckart Menzler-Trott ; translated by Craig Smory´nski and Edward Griffor. p. cm. (History of mathematics ; v. 33) ISBN 978-0-8218-3550-0 (alk. paper) 1. Gentzen, Gerhard. 2. Mathematicians—Germany—Biography. 3. Logic, Symbolic and mathematical. I. Title. QA29 .G467M46 2007 510.92—dc22 2007060550 AMS softcover ISBN: 978-1-4704-2812-9 Copying and reprinting. Individual readers of this publication, and nonprofit libraries acting for them, are permitted to make fair use of the material, such as to copy select pages for use in teaching or research.
    [Show full text]
  • Logical Investigations, Vols I & II Edmund Husserl Logical Investigations
    International Library of Philosophy Edited by Jose Bermudez, Tim Crane and Peter Sullivan Advisory Board: Jonathan Barnes, Fred Dretske, Frances Kamm, Brian Leiter, Huw Price and Sydney Shoemaker Recent titles in the ILP: The Facts of Causation D. H. Mellor The Conceptual Roots of Mathematics j. R. Lucas Stream of Consciousness Barry Dainton Knowledge and Reference in Empirical Science Jody Azzouni Reason without Freedom David Owens The Price of Doubt N. M. L Nathan Matters of Mind Scott Sturgeon Logic, Form and Grammar Peter Long The Metaphysicians of Meaning Gideon Makin Logical Investigations, Vols I & II Edmund Husserl Logical Investigations Edmund Husserl Translated by J. N. Findlay from the Second German edition of Logische Untersuchungen with a new Preface by Michael Dummett and edited with a new Introduction by Dermot Moran Volume I Prolegomena to pure logic (Volume I of the German editions) Expression and meaning (Investigation I, Volume II of the German editions) The ideal unity of the species and modern theories of abstraction (Investigation II, Volume II of the German editions) London and New York First published in German as Logische Untersuchungen by M. Niemeyer, Halle 1900/1901 Second German edition, Vol. I and Vol. II, Part I, first published 1913 First published in English 1970 by Routledge & Kegan Paul Ltd Reprinted 1976, 1977, 1982 This paperback edition first published 200 I by Routledge I I New Fetter Lane, London EC4P 4EE Simultaneously published in the USA and Canada by Routledge 29 West 35th Street, New York, NY 10001 Routledge is on imprint of the Taylor & Francis Group Translation © 1970 J.
    [Show full text]
  • Stefanie Ursula Eminger Phd Thesis
    CARL FRIEDRICH GEISER AND FERDINAND RUDIO: THE MEN BEHIND THE FIRST INTERNATIONAL CONGRESS OF MATHEMATICIANS Stefanie Ursula Eminger A Thesis Submitted for the Degree of PhD at the University of St Andrews 2015 Full metadata for this item is available in Research@StAndrews:FullText at: http://research-repository.st-andrews.ac.uk/ Please use this identifier to cite or link to this item: http://hdl.handle.net/10023/6536 This item is protected by original copyright Carl Friedrich Geiser and Ferdinand Rudio: The Men Behind the First International Congress of Mathematicians Stefanie Ursula Eminger This thesis is submitted in partial fulfilment for the degree of PhD at the University of St Andrews 2014 Table of Contents Abstract 7 Acknowledgements 9 1. Introduction 11 2. Carl Friedrich Geiser (1843 – 1934) 15 2.1 Life 15 2.2 Connection with Steiner 33 2.3 Impact at the Polytechnic and on Education 39 3. Ferdinand Karl Rudio (1856 – 1929) 49 3.1 Life 49 3.2 Contribution to Euler’s Opera Omnia 53 4. The First International Congress of Mathematicians, Zurich 1897 57 4.1 Background and Organisation 57 4.1.1 Historical Developments 57 4.1.2 Organising the Congress 62 4.1.3 The Congress Itself 67 4.1.4 Geiser’s Contribution 76 4.1.5 Rudio’s Contribution 77 4.2 The Swiss Organising Committee 79 4.2.1 Ernst Julius Amberg (1871 – 1952) 79 4.2.2 Christian Beyel (1854 – 1941) 82 4.2.3 Hermann Bleuler (1837 – 1912) 83 4.2.4 Heinrich Burkhardt (1861 – 1914) 86 4.2.5 Fritz Bützberger (1862 – 1922) 89 4.2.5.1 Bützberger’s Work on Steiner 92 4.2.6 Gustave Dumas
    [Show full text]
  • Phenomenological Foundations of Mathematics
    META: Research in Hermeneutics, Phenomenology, and Practical Philosophy – XI (2) / 2019 META: RESEARCH IN HERMENEUTICS, PHENOMENOLOGY, AND PRACTICAL PHILOSOPHY VOL. XI, NO. 2 / DECEMBER 2019: 322, ISSN 2067-3655, www.metajournal.org Editorial After Husserl: Phenomenological Foundations of Mathematics First and foremost, I would like to express my gratitude to all contributors for all of the hard work they put into writing their pieces of original work to show the lasting vibrancy and vitality of Edmund Husserl‟s ideas and to encourage further investigations. From the outset it was my intention to open up a way of research on different interpretative perspectives on Edmund Husserl and his interlocutors (Gottlob Frege, Oskar Becker, David Hilbert, Hermann Weyl, J. Klein, L.E.J. Brouwer, Kurt Gödel, Bourbaki, Marc Richir), which does not end up either in the naive celebration of Husserl‟s investigations of das Mathematisierendes Dasein or in its brute rejection. Professor Ilie Pârvu, my doctoral supervisor and an exemplary philosopher, was an inspiration: his erudition and analytical creativity spurred me on. This special issue would have been a very different project without his philosophical support. Also, I benefitted greatly from conversations on Oskar Becker‟s opus magnum from 1927, Mathematical Existence (Mathematische Existenz), and David Hilbert‟s „transcenden- talism‟ exposed in his metamathematics, with Constantin C. Brîncuş, with whom I worked in the project “The Phenomenological Analysis of Axiomatic Mathematics.” Brigitte Parakenings, the archivist at the Philosophical Archive of the University of Konstanz, helped me enormously with archival materials from The Oskar Becker collection. I am very grateful to George Bondor for his constructive suggestions and excellent editorial support.
    [Show full text]
  • 304 REVIEW ARTICLES Heidegger's Way to Hermeneutic
    304 REVIEW ARTICLES Heidegger's Way to Hermeneutic Phenomenology Martin Heidegger. Zur Bestimmung der Philosophie. 1: Die Idee der Philosophie und das Weltanschauungsproblem. 2: Phänomenologie und transzendentale Wertphilosophie. Mit einer Nachschrift der Vorlesung Über das Wesen der Universität und des academischen Studiums." Gesamtausgabe vol. 56/57, edited by Bernd Heimbüchel. Frankfurt am Main: V. Klostermann, 1987. viii & 218 pp. 1. According to Heidegger's account, Husserl's phenomenology (already by 1909) exercised a fascinating influence on and awakened a "restlessness" in his own mind.' The discovery of "phenomenological seeing," however, does not lead him to a separation from, but rather to a new interpretation of, Aristotle and to a deeper grasp of "Greek thinking, if not indeed of philo- sophy as such."' Heinrich Rickert-Husserl's predecessor at Freiburg until 1919 and the teacher of Heidegger-a neo-Kantian philosopher, shaped quite substantially Heidegger's early development especially through his seminars dealing with the writings of Emil Lask (who mediates between neo-Kantian philosophy and Husserl, but remains open to the Greeks). Taking the first steps on his path to the question of Being, the young Heidegger becomes critical of both Rickert and Husserl, indeed of the philosophical trends of the times, without forgetting his indebtness to his "masters." Thus Husserl was perceptive in saying that "he (Heidegger) was obviously already into his own thing when he studied my writings."3 Phe- nomenology, for Heidegger, is not
    [Show full text]
  • 03 Bedurftig Murawski Studiasemiot 32 Z2 2018.Indd
    STUDIA SEMIOTYCZNE, t. XXXII, nr 2 (2018), s. 33–50 ISSN 0137-6608, e-ISSN 2544-073X DOI: 10.26333/sts.xxxii2.03 Rozprawa THOMAS BEDÜRFTIG*, ROMAN MURAWSKI** PHENOMENOLOGICAL IDEAS IN THE PHILOSOPHY OF MATHEMATICS. FROM HUSSERL TO GÖDEL S UMMARY: The paper is devoted to phenomenological ideas in conceptions of modern philosophy of mathematics. Views of Husserl, Weyl, Becker and Gödel will be discussed and analysed. The aim of the paper is to show the influence of phenomenological ideas on the philosophical conceptions concerning mathematics. We shall start by indicating the attachment of Edmund Husserl to mathematics and by presenting the main points of his philosophy of mathematics. Next, works of two philosophers who attempted to apply Husserl’s phenomenological ideas to the philosophy of mathematics, namely Hermann Weyl and Oskar Becker, will be briefly discussed. Lastly, the connections between Husserl’s ideas and the philosophy of mathematics of Kurt Gödel will be studied.1 Key words: mathematics, philosophy, phenomenology, intuition. HUSSERL’S PHILOSOPHY OF MATHEMATICS Husserl came in a certain sense from mathematics. He began his studies of mathematics at the universities of Leipzig and Berlin with Carl Weierstraß and Leopold Kronecker. In 1881 he moved * Leibniz Universität Hannover, Institut für Didaktik der Mathematik und Physik. E-mail: [email protected]. ** Adam Mickiewicz University, Faculty of Mathematics and Comp. Sci. E-mail: [email protected]. ORCID: 0000-0002-2392-4869. 1 We would like to thank both anonymous referees for helpful comments and suggestions. 34 THOMAS BEDÜRFTIG, ROMAN MURAWSKI to Vienna where he studied with Leo Königsberger and, in 1883 obtained his doctor’s degree on the base of the dissertation Beiträge zur Variationsrechnung.
    [Show full text]
  • Oskar Becker Or the Reconciliation of Mathematics and Existential Philosophy
    Hans Sluga / Oskar Becker or the Reconciliation of Mathematics…. META: RESEARCH IN HERMENEUTICS, PHENOMENOLOGY, AND PRACTICAL PHILOSOPHY VOL. XI, NO. 2 / DECEMBER 2019: 569-588, ISSN 2067-3655, www.metajournal.org Oskar Becker or the Reconciliation of Mathematics and Existential Philosophy Hans Sluga Department of Philosophy, UC Berkeley Abstract Oskar Becker’s work in the philosophy of mathematics makes an important contribution to the philosophical understanding of the constructivist program. Becker (1889-1964), a student of Edmund Husserl and an associate of Martin Heidegger, initially sought to ground a constructivist view of mathematics in Husserl’s transcendental phenomenology; subsequently he adopted a Heideggerian and existential view of mathematics that, he argued, would allow one to rescue large parts of classical mathematics from an intuitionist and constructive perspective. In his later writings he finally turned to a radically historicist interpretation of the constructivist program. Keywords: Edmund Husserl; Hermann Weyl; L.E.J. Brouwer; Martin Heidegger; Mathematical intuitionism; Constructivism; Historicism I begin with a piece of autobiography. When I first heard of symbolic logic I was a schoolboy, about fifteen years old. By chance, I had discovered a little book on the topic in some local bookstore and had found its treatment of the propositional and the predicate calculus an endlessly intriguing subject matter. It was a time when I dreamt at night of sex and truth-tables. I don’t know any more in what order. Then,
    [Show full text]
  • The Condition of Possibility of Transcendental Philosophy Steven Galt Crowell: Husserl, Heidegger, and the Space of Meaning
    Marquette University e-Publications@Marquette Philosophy Faculty Research and Publications Philosophy, Department of 2-1-2006 The onditC ion of Possibility of Transcendental Philosophy Sebastian Luft Marquette University, [email protected] Accepted version. Husserl Studies, Vol. 22, No. 1 (February 2006): 53-75. DOI. © 2006 Springer. Used with permission. Shareable Link. Provided by the Springer Nature SharedIt content-sharing initiative. Review Essay: The Condition of Possibility of Transcendental Philosophy Steven Galt Crowell: Husserl, Heidegger, and the Space of Meaning. Paths Toward Transcendental Phenomenology, Evanston: Northwestern University Press, 2001 (Northwestern Studies in Phenomenology and Existential Philosophy) 323 pp., US-$ 32 (paper). By Sebastian Luft Introduction In this intriguing book, Steven G. Crowell takes on the challenge of situating phenomenology in contemporary philosophy. To this end, he engages with several traditions outside of, and interpretative strands within, phenomenology. The real topic of the book is seemingly Heidegger; yet it is a Heidegger who can only be understood in the rich tradition that made his originality possible, namely, Husserl and, in critical rejection, the dominant school in Germany at the time, Neo-Kantianism. In this sense, it is a book Husserl aficionados should consider as well. Crowell presents the reader with a collection of thirteen substantial articles, twelve of which have been published previously, ranging over more than a decade in which the author has worked
    [Show full text]