JULIET FLOYD Addresses: Department of Philosophy, Boston
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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. -
Turing, Gödel and the Bright Abyss
Turing, Gödel and the “Bright Abyss” Juliet Floyd ! 2/5/2015 9:25 AM Comment [1]: 1. Check phone number okay to use this ong?; Also need 2. ABSTRACT of 1 Introduction 150-200 words and 3. a CONTRIBUTOR bi- ography of up to 100 words! Xxx, J. They have completely forgotten what is a mathematical creation: a vision that decants little by little over months and years, bringing to light the obvious [evident] thing that no one had seen, taking form in an obvious assertion of which no one had dreamed ... and that the first one to come along can then prove in five minutes, using techniques ready to hand [toutes cuites] • A. Grothendiek, Recoltes et Sémailles, 1986 Mathematics: there is that which is taken on faith and that which is proved; there is that which is buried deep inside the heart of the mathematician1 and that which is wholly public; there is intuition and fact and the “bright abyss” in be- tween; there is the raw, one might say, and the cooked. I hold up my hand and I count five fingers. I take it on faith that the mapping from fingers onto numbers is recursive in the sense of the mathematician’s defi- nition of the informal concept, “human calculability following a fixed routine.” I cannot prove the mapping is recursive—there is nothing to prove! Of course, mathematicians can prove many theorems about recursiveness, moving forward, so to speak, once the definition of the concept “recursive” has been isolated. Moving backwards is more difficult and this is as it should be: for how can one possibly hope to prove that a mathematical -
6 X 10.5 Long Title.P65
Cambridge University Press 978-0-521-83843-6 - Seeing Wittgenstein Anew Edited by William Day and Victor J. Krebs Frontmatter More information Seeing Wittgenstein Anew Seeing Wittgenstein Anew is the first collection to examine Ludwig Wittgenstein’s remarks on the concept of aspect-seeing. These essays show that aspect-seeing was not simply one more topic of in- vestigation in Wittgenstein’s later writings, but, rather, that it was a pervasive and guiding concept in his efforts to turn philosophy’s attention to the actual conditions of our common life in language. Arranged in sections that highlight the pertinence of the aspect- seeing remarks to aesthetic and moral perception, self-knowledge, mind and consciousness, linguistic agreement, philosophical therapy, and “seeing connections,” the sixteen essays, which were specially commissioned for this volume, demonstrate the unity of not only Philosophical Investigations but also Wittgenstein’s later thought as a whole. They open up novel paths across familiar fields of thought: the objectivity of interpretation, the fixity of the past, the acquisition of language, and the nature of human conscious- ness. Significantly, they exemplify how continuing consideration of the interrelated phenomena and concepts surrounding aspect- seeing might produce a fruitful way of doing philosophy. William Day is Associate Professor of Philosophy at Le Moyne College. A recipient of fellowships from the National Endowment for the Humanities, he has written articles on aesthetics and moral per- fectionist thought, with particular focus on the work of Wittgenstein, Cavell, Emerson, and Confucian thinkers. Victor J. Krebs is Associate Professor of Philosophy at the Pontificia Universidad Católica del Perú. -
Westphal Says That His Exhibition of Two Sources of a Commitment in Kant to Mental Content Externalism Ought to Be Understood
Can Mental Content Externalism Prove Realism?1 (Axel Mueller, Northwestern University) Recently, Kenneth Westphal has presented a highly interesting and innovative reading of Kant's critical philosophy.2 This reading continues a tradition of Kant- scholarship of which, e.g., Paul Guyer's work is representative, and in which the anti- idealistic potential of Kant's critical philosophy is pitted against its idealistic self- understanding. Much of the work in this tradition leaves matters at observing the tensions this introduces in Kant's work. But Westphal's proposed interpretation goes farther. Its attractiveness derives for the most part from the promise that it permits an internal critique of Kant's transcendental idealism (TI), that is, a critique that is based on the very resources of Kantian transcendental philosophy.3 In contrast to these resources, which currently seem to go through a sort of revival in an enormous array of fields, TI is notorious for dismaying even sympathetic interpreters. How attractive and needed such an internal critique of TI would be becomes all the more patent when we place such a promise in the context of some of the contemporary discussions about TI after Allison's famous defense of it. Before directly engaging with Westphal's interpretation, I would therefore like to quickly sketch on what background it acquires its force (I). After characterizing the main features of Westphal's view (II), and supporting it in more detail by an account of Kant's theory of cognitive significance (III), I then want to review the extent of its success to present Kant as issuing an anti-skeptical argument (IV.1), or semantic views that are incompatible with TI (IV.2), or a 'proof of not merely empirical realism' (IV.3). -
2.2 Glock Et Al
Journal for the History of Book Symposium: Analytical Philosophy Hans-Johann Glock, What is Analytic Philosophy? Volume 2, Number 2 Introduction Hans-Johann Glock..................... 1 Editor in Chief Mark Textor, King’s College London Commentaries Guest Editor Leila Haaparanta......................... 2 Mirja Hartimo, University of Helsinki Christopher Pincock....................6 Editorial Board Panu Raatikainen........................11 Juliet Floyd, Boston University Graham Stevens.......................... 28 Greg Frost-Arnold, Hobart and William Smith Colleges Ryan Hickerson, University of Western Oregon Replies Henry Jackman, York University Hans-Johann Glock..................... 36 Sandra Lapointe, McMaster University Chris Pincock, Ohio State University Richard Zach, University of Calgary Production Editor Ryan Hickerson Editorial Assistant Daniel Harris, CUNY Graduate Center Design Douglas Patterson and Daniel Harris ©2013 The Authors What is Analytic Philosophy? shall not be able to respond to all of the noteworthy criticisms and questions of my commentators. I have divided my responses ac- Hans-Johann Glock cording to commentator rather than topic, while also indicating some connections between their ideas where appropriate. Let me start by thanking the Journal for the History of Analytical Phi- losophy for offering me this opportunity to discuss my book What is Analytical Philosophy? (Cambridge, 2008). I am also very grateful Hans-Johann Glock for the valuable feedback from the contributors. And I thank both University of Zurich the journal and the contributors for their patience in waiting for [email protected] my replies. I was pleased to discover that all of my commentators express a certain sympathy with the central contention of my book, namely that analytic philosophy is an intellectual movement of the twentieth-century (with roots in the nineteenth and offshoots in the twenty-first), held together by family-resemblances on the one hand, ties of historical influence on the other. -
Interpreting Gödel: Critical Essays Edited by Juliette Kennedy Frontmatter More Information
Cambridge University Press 978-1-107-00266-1 - Interpreting Gödel: Critical Essays Edited by Juliette Kennedy Frontmatter More information INTERPRETING GÖDEL: CRITICAL ESSAYS The logician Kurt Gödel (1906–1978) published a paper in 1931 formulating what have come to be known as his “incompleteness theorems,” which prove, among other things, that within any formal system with resources sufficient to code arithmetic, questions exist which are neither provable nor disprovable on the basis of the axioms which define the system. These are among the most celebrated results in logic today. In this volume, leading philosophers and mathemat- icians assess important aspects of Gödel’s work on the foundations and philosophy of mathematics. Their essays explore almost every aspect of Godel’s intellectual legacy including his concepts of intu- ition and analyticity, the Completeness Theorem, the set-theoretic multiverse, and the state of mathematical logic today. This ground- breaking volume will be invaluable to students, historians, logicians, and philosophers of mathematics who wish to understand the current thinking on these issues. juliette kennedy is an Associate Professor in the Department of Mathematics and Statistics at the University of Helsinki. © in this web service Cambridge University Press www.cambridge.org Cambridge University Press 978-1-107-00266-1 - Interpreting Gödel: Critical Essays Edited by Juliette Kennedy Frontmatter More information © in this web service Cambridge University Press www.cambridge.org Cambridge University Press 978-1-107-00266-1 - Interpreting Gödel: Critical Essays Edited by Juliette Kennedy Frontmatter More information INTERPRETING GÖDEL Critical Essays edited by JULIETTE KENNEDY University of Helsinki © in this web service Cambridge University Press www.cambridge.org Cambridge University Press 978-1-107-00266-1 - Interpreting Gödel: Critical Essays Edited by Juliette Kennedy Frontmatter More information University Printing House, Cambridge cb2 8bs, United Kingdom Cambridge University Press is part of the University of Cambridge. -
Juliet Floyd
September 21, 2017 Juliet Floyd Department of Philosophy Work: + 01 (617) 353-3745 Boston University, 745 Commonwealth Avenue Fax: +01 (617) 353-6805 Boston, MA 02215 E-mail: jfl[email protected] Academic Positions: 2006- Professor of Philosophy, Boston University 2003- Affiliated faculty in the following Boston University programs: - Linguistics - Center for the Philosophy and History of Science - Institute for the Philosophy of Religion - Graduate Division of Religious Studies - European Studies Program - Institute of Editorial Studies 1996-2006 Associate Professor of Philosophy, Boston University 1995 Visiting Assistant Professor of Philosophy, Boston University 1993-94 Deputy Executive Officer, Graduate Program in Philosophy, C.U.N.Y. 1992-95 Graduate Faculty Member in Philosophy, C.U.N.Y. 1990-95 Assistant Professor of Philosophy, City College of New York, C.U.N.Y. Visiting Positions: 2012 Visiting Professor, Philosophy, Universit´eMichel de Montaigne Bordeaux 2009 Visiting Professor, Philosophy, Universit´ede Paris I Panth´eon-Sorbonne 2007 Visiting Professor, Facult¨atf¨urPhilosophie, Universit¨atWien 1996 Visiting Professor, Boston University Research: History and Development of Analytic and Twentieth Century Philosophy Philosophy of Logic and Mathematics, Philosophy of Language Philosophy of Completeness and Incompleteness Formal and Traditional Epistemology, Theories of Truth Modern Philosophy (Kant), Aesthetics, Wittgenstein, Pragmatism History and Philosophy of Science, especially Logic and Mathematics Philosophy of Emerging Computational -
Simplicity: Ideals of Practice in Mathematics and the Arts
Mathematics, Culture, and the Arts Simplicity Ideals of Practice in Mathematics and the Arts Roman Kossak · Philip Ording Editors Mathematics, Culture, and the Arts Series editors Jed Z. Buchwald Jeremy Gray Marjorie Senechal The series Mathematics in Culture and the Arts will publish books on all aspects of the relationships between mathematics and the mathematical sciences and their roles in culture, art, architecture, literature, and music. This new book series will be a major resource for researchers, educators, scientifically minded artists, and students alike. More information about this series at http://www.springer.com/series/13129 Roman Kossak • Philip Ording Editors Simplicity: Ideals of Practice in Mathematics and the Arts 123 Editors Roman Kossak Philip Ording Department of Mathematics Department of Mathematics The Graduate Center Sarah Lawrence College City University of New York Bronxville, NY, USA New York, NY, USA ISSN 2520-8578 ISSN 2520-8586 (electronic) Mathematics, Culture, and the Arts ISBN 978-3-319-53383-4 ISBN 978-3-319-53385-8 (eBook) DOI 10.1007/978-3-319-53385-8 Library of Congress Control Number: 2017935487 © Springer International Publishing AG 2017 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. -
Wittgenstein and His Literary Executors Volume 4, Number 3 Christian Erbacher Editor in Chief Kevin C
Journal FOR THE History OF Analytical Philosophy Wittgenstein AND His LiterARY ExECUTORS VOLUME 4, Number 3 Christian Erbacher Editor IN Chief KeVIN C. Klement, University OF Massachusetts Rush Rhees, Georg Henrik von Wright and Elizabeth Anscombe are well known as the literary executors who made Ludwig Editorial BoarD Wittgenstein’s later philosophy available to all interested read- Gary Ebbs, INDIANA University Bloomington ers. Their editions of Wittgenstein’s writings have become an GrEG Frost-Arnold, Hobart AND William Smith Colleges integral part of the modern philosophical canon. However, sur- Henry Jackman, YORK University prisingly little is known about the circumstances and reasons SandrA Lapointe, McMaster University that made Wittgenstein choose them to edit and publish his Lydia Patton, VirGINIA TECH papers. This essay sheds light on these questions by present- MarCUS Rossberg, University OF Connecticut ing the story of their personal relationships—relationships that, Mark TExtor, King’S College London on the one hand, gave Rhees, von Wright and Anscombe dis- AudrEY Yap, University OF Victoria tinct insights into Wittgenstein’s philosophizing; and, on the RicharD Zach, University OF Calgary other hand, let Wittgenstein assume that these three former stu- dents, and later colleagues and friends, were the most capable ReVIEW Editors of preparing his work for publication. Using hitherto unpub- Juliet Floyd, Boston University lished archival material as well as information from published Chris Pincock, Ohio State University recollections, the essay sketches the development of the per- sonal and philosophical bonds from which the literary heirs’ Assistant ReVIEW Editor distinct ways of handling Wittgenstein’s unpublished writings Sean Morris, MetrOPOLITAN State University OF Denver grew in later years. -
Philosophy of Set Theory
Philosophy of Set Theory LPS 247 Fall 2016 - Winter 2017 The mathematical theory of sets is both a foundation (in some sense) for classical mathematics and a branch of mathematics in its own right. Both its foundational role and its particular mathematical features -- the centrality of axiomatization and the prevalence of independence phenomena -- raise philosophical questions that have been debated since the birth of the subject at the end of the 19th century: what is a ‘foundation’ supposed to do?, what makes one system of axioms ‘better’ than another?, how can problems independent of the axioms, like Cantor’s famous Continuum Hypothesis, be addressed? Our goal in this course is to survey these matters, from their beginnings to contemporary debates. Some familiarity with the mathematical fundamentals of the theory (say at the level of Herbert Enderton’s Elements of Set Theory) and with the central results of intermediate logic (completeness, compactness, Löwenheim-Skolem, non- standard models, Gödel’s incompleteness theorems) will be presupposed. The rest will be sketched in readings and/or in class. The default requirement for those taking the course for a grade (other than S/U, which involves only reading and attending) is three short papers (750-1250 words) due at the beginning of class in the 4th week, 7th week, and 10th week. These papers should isolate one localized philosophical, conceptual or methodological point within one of the readings and offer some analysis and/or critique. The thesis and its defense needn’t be earth-shattering in any way; this is really just an exercise in finding a topic of the right size and crafting a thesis and defense to match. -
Women in Early Analytic Philosophy: Volume Volume 5, Number 2 Introduction Editor in Chief Maria Van Der Schaar and Eric Schliesser Kevin C
JOURNAL FOR THE HISTORY OF ANALYTICAL PHILOSOPHY WOMEN IN EARLY ANALYTIC PHILOSOPHY: VOLUME VOLUME 5, NUMBER 2 INTRODUCTION EDITOR IN CHIEF MARIA VAN DER SCHAAR AND ERIC SCHLIESSER KEVIN C. KLEMENt, UnIVERSITY OF MASSACHUSETTS EDITORIAL BOARD ANNALISA COLIVA, UnIVERSITY OF MODENA AND UC IRVINE GaRY EBBS, INDIANA UnIVERSITY BLOOMINGTON GrEG FROSt-ARNOLD, HOBART AND WILLIAM SMITH COLLEGES HENRY JACKMAN, YORK UnIVERSITY SANDRA LaPOINte, MCMASTER UnIVERSITY CONSUELO PRETI, THE COLLEGE OF NEW JERSEY MARCUS ROSSBERG, UnIVERSITY OF CONNECTICUT ANTHONY SKELTON, WESTERN UnIVERSITY MARK TEXTOR, KING’S COLLEGE LonDON AUDREY YAP, UnIVERSITY OF VICTORIA RICHARD ZACH, UnIVERSITY OF CALGARY REVIEW EDITORS JULIET FLOYD, BOSTON UnIVERSITY CHRIS PINCOCK, OHIO STATE UnIVERSITY ASSISTANT REVIEW EDITOR SEAN MORRIS, METROPOLITAN STATE UnIVERSITY OF DenVER DESIGN DaNIEL HARRIS, HUNTER COLLEGE JHAPONLINE.ORG SPECIAL ISSUE: WOMEN IN EARLY ANALYTIC PHILOSOPHY © 2017 MARIA VAN DER SCHAAR AND ERIC SCHLIESSER EDITED BY MARIA VAN DER SCHAAR AND ERIC SCHLIESSER WOMEN IN EARLY ANALYTIC PHILOSOPHY: movement in the more strict sense of analytic philosophy, and VOLUME INTRODUCTION they were educated at the centres of analytic philosophy of their time. If we focus on the period before World War II, centres of MARIA VAN DER SCHAAR AND ERIC SCHLIESSER analytic philosophy in the strict sense are to be found in Lvov, Warsaw, Vienna, Cambridge, and Harvard. Of these, perhaps, the inclusion of Harvard is controversial, but the paper by Giulia Felappi helps us to understand why it is legitimate to include The three women that form the focus of this special issue, Susan Harvard. Stebbing (1895–1943), Susanne Langer (1895–1985), and Maria We speak of the Lvov-Warsaw School, the Vienna Circle, and Kokoszyńska (1905–1981), belong to the first group of women the Cambridge School of Analysis, and of British analytic philos- who became recognized philosophers by obtaining a perma- ophy in general. -
From Kant to Davidson Philosophy and the Idea of the Transcendental
From Kant to Davidson Philosophy and the idea of the transcendental Edited by Jeff Malpas First published 2003 by Routledge 11 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 an imprint of the Taylor & Francis Group This edition published in the Taylor & Francis e-Library, 2003. © 2003 Selection and editorial material, Jeff Malpas; individual chapters, the contributors All rights reserved. No part of this book may be reprinted or reproduced or utilised in any form or by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying and recording, or in any information storage or retrieval system, without permission in writing from the publishers. British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library Library of Congress Cataloging in Publication Data From Kant to Davidson : philosophy and the idea of the transcendental / edited by Jeff Malpas. Includes bibliographical references and index. 1. Transcendentalism. 2. Philosophy–History. 3. Kant, Immanual, 1724–1804. I. Malpas J. E. B823 .F76 2002 141'.3dc21 2002068157 ISBN 0-203-21957-0 Master e-book ISBN ISBN 0-203-27465-2 (Adobe eReader Format) ISBN 0–415–27904–6 (Print Edition) Contents Notes on contributors vii Acknowledgements ix Introduction: The idea of the transcendental 1 JEFF MALPAS 1 Kant’s critical debut: The idea of the transcendental in Kant’s early thought 7 CAMILLA SERCK-HANSSEN