DOCSLIB.ORG

Modern Logic 1850-1950, East and West Editors Francine F

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Modern Logic 1850-1950, East and West Editors Francine F Studies in Universal Logic Francine F. Abeles Mark E. Fuller Editors Modern Logic 1850 –1950, East and West Studies in Universal Logic Series Editor Jean-Yves Béziau (Federal University of Rio de Janeiro and Brazilian Research Council, Rio de Janeiro, Brazil) Editorial Board Members Hajnal Andréka (Hungarian Academy of Sciences, Budapest, Hungary) Mark Burgin (University of California, Los Angeles, USA) Razvan˘ Diaconescu (Romanian Academy, Bucharest, Romania) Josep Maria Font (University of Barcelona, Barcelona, Spain) Andreas Herzig (Centre National de la Recherche Scientifique, Toulouse, France) Arnold Koslow (City University of New York, New York, USA) Jui-Lin Lee (National Formosa University, Huwei Township, Taiwan) Larissa Maksimova (Russian Academy of Sciences, Novosibirsk, Russia) Grzegorz Malinowski (University of Łód´z, Łód´z, Poland) Darko Sarenac (Colorado State University, Fort Collins, USA) Peter Schröder-Heister (University Tübingen, Tübingen, Germany) Vladimir Vasyukov (Russian Academy of Sciences, Moscow, Russia) This series is devoted to the universal approach to logic and the development of a general theory of logics. It covers topics such as global set-ups for fundamental theorems of logic and frameworks for the study of logics, in particular logical matrices, Kripke structures, combination of logics, categorical logic, abstract proof theory, consequence operators, and algebraic logic. It includes also books with historical and philosophical discussions about the nature and scope of logic. Three types of books will appear in the series: graduate textbooks, research monographs, and volumes with contributed papers. More information about this series at http://www.springer.com/series/7391 Francine F. Abeles • Mark E. Fuller Editors Modern Logic 1850-1950, East and West Editors Francine F. Abeles Mark E. Fuller Departments of Mathematics and Computer University of Wisconsin Science Janesville, WI Kean University USA Union, NJ USA ISSN 2297-0282 ISSN 2297-0290 (electronic) Studies in Universal Logic ISBN 978-3-319-24754-0 ISBN 978-3-319-24756-4 (eBook) DOI 10.1007/978-3-319-24756-4 Library of Congress Control Number: 2016939218 Mathematics Subject Classification (2010): 01A55, 01A60, 03A05, 03F03, 03G25 © Springer International Publishing Switzerland 2016 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. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper This book is published under the trade name Birkhäuser The registered company is Springer International Publishing AG Switzerland (www.birkhauser-science.com) Contents Introduction ............................................................................ 1 Francine F. Abeles and Mark E. Fuller Preface and Prospectus to a planned “History vs. Philosophy of Logic” Text........................................................................... 5 Irving H. Anellis The Historical Sources of Tree Graphs and the Tree Method in the Work of Peirce and Gentzen ................................................... 35 Irving H. Anellis and Francine F. Abeles Logic and Argumentation in Belgium: The Role of Leo Apostel ................. 99 Jean Paul Van Bendegem Tarski’s Recantation: Reading the Postscript to “Wahrheitsbegriff” ............ 119 Philippe de Rouilhan Paradox of Analyticity and Related Issues .......................................... 135 Jan Wolenski´ Naturalizing Natural Deduction ...................................................... 139 David DeVidi and Herbert Korté Category Theory and the Search for Universals: A Very Short Guide for Philosophers ........................................................................ 159 Alberto Peruzzi On the Way to Modern Logic: The Case of Polish Logic .......................... 183 Roman Murawski Russian Origins of Non-Classical Logics ............................................ 197 Valentin A. Bazhanov Constructive Mathematics in St. Petersburg, Russia: A (Somewhat Subjective) View from Within ........................................................ 205 Vladik Kreinovich v vi Contents On Normalizing Disjunctive Intermediate Logics .................................. 237 Jonathan P. Seldin A Natural Axiom System for Boolean Algebras with Applications ............... 249 R.E. Hodel Contributors Francine F. Abeles is Professor Emerita at Kean University in Union, NJ, USA. For the ten years beforehand, she was Distinguished Professor of Mathematics and Computer Science and head of the graduate programs (master’s level) in mathematics, computing, statistics, and mathematics education. She has co-edited a proceedings of the Canadian Society for The History and Philosophy of Mathematics, and edited three volumes in the pamphlets of Lewis Carroll series for the University Press of Virginia. Dr. Abeles wrote a chapter on Charles L. Dodgson’s work in voting theory in Lewis Carroll Observed,a chapter on his mathematical work in yours very sincerely C. L. Dodgson (alias “Lewis Carroll”), a chapter on the popularizers of mathematics Martin Gardner, Richard Proctor, and Charles Dodgson in A Bouquet for The Gardner, and a chapter on Dodgson’s work in logic in volume 6 of Logica Universalis, “Toward a Visual Proof System: Lewis Carroll’s Method of Trees”. She is the author of nearly one hundred papers in journals on topics in geometry, number theory, voting theory, linear algebra, logic, and their history, most recently: “Nineteenth Century British Logic on Hypotheticals, Conditionals, and Implication” (History and Philosophy of Logic 35 (1), 2014, 24-37) and “Chiò’s and Dodgson’s Determinantal Identities” (Linear Algebra and Its Applications 454, 2014, 130-137). Dr. Abeles was a member of the editorial board and Reviews Editor of the international journal, Modern Logic and its successor, The Review of Modern Logic. Currently she is a member of the Publications Committee of The Lewis Carroll Society of North America and managing trustee of the Morton N. Cohen Publications Trust. A recipient of a grant from the American Philosophical Society and numerous faculty research grants from the State of New Jersey, she received an award from Kean University for distinguished research and a leadership award from Stevens Institute of Technology. Valentin A. Bazhanov is Chairperson in Philosophy at Ulyanovsk State University, a leading researcher at Tomsk State University, and member of the Russian Basic Research Foundation and the Russian Foundation for Humanities expertise committees. His major works include a biography of the logician, N.A.Vasiliev (1880–1940), Nauka, 1988, as well as the following: The Completeness of Quantum Theory, Kazan Univ. Press, 1983; Science as Self-Reflexive System, Kazan. Univ. Press, 1991; The Interrupted Flight. The History of University Philosophy and Logic in Russia (XIX - mid XX centuries),Moscow Univ. Press, 1995; Essays on the Social History of Logic in Russia, Mid Volga Research Center, 2002; British Philosophical and Social Sciences Ideas Reception in Russia vii viii Contributors (XIX - early XX centuries), Ulyanovsk Univ. Press, 2005; History of Logic in Russia and the USSR, Canon+, 2007; and Nicolai A. Vasiliev and his Imaginary Logic. The Revival of One Forgotten Idea, Canon+, 2009. In addition, Dr. Bazhanov has authored 480 published papers. Volumes which he has edited include: Mathematisation of Natural Sciences, Kazan Univ. Press, 1984; Vistas of Sciences, Kazan Univ. Press, 1989; The Scientists and Universities of Russia in the Transitional Period, Ulyanovsk, 1998; and Logic and Epistemology in Russian Philosophy of First Half of XX century, Rosspen, 2012. He also compiled A.V. Vasiliev’s book N.I. Lobachevsky (1792-1856), Nauka, 1992. Dr. Bazhanov is an Associate Editor of The Review of Modern Logic (formerly Modern Logic) since its founding in 1989, and an Associate Editor of Epistemology and Philosophy of Science; Reflexive Processes and Governing; News of Russia’s Universities.Volga Region (Humanities); Kant Studies; and Herald of Nizhny Novgorod University. He is the recipient of several research grants (British Academy, RBRF, RFH, Soros Foundation), including most recently a Lakatos Research Grant (2008). Philippe de Rouilhan is Directeur de Recherche émérite at the Centre National de la Recherche Scientifique (CNRS), and a member of the Institut d’histoire et de philosophie des sciences et des techniques (IHPST, of which he was the head for a long time). His works belong to logic lato sensu, or, more specifically, to formal ontology, formal semantics, philosophy of logic, philosophy
Load more

Recommended publications
  • Deduction Systems Based on Resolution, We Limit the Following Considerations to Transition Systems Based on Analytic Calculi
    Author’s Address Norbert Eisinger European Computer–Industry Research Centre, ECRC Arabellastr. 17 D-8000 M¨unchen 81 F. R. Germany [email protected] and Hans J¨urgen Ohlbach Max–Planck–Institut f¨ur Informatik Im Stadtwald D-6600 Saarbr¨ucken 11 F. R. Germany [email protected] Publication Notes This report appears as chapter 4 in Dov Gabbay (ed.): ‘Handbook of Logic in Artificial Intelligence and Logic Programming, Volume I: Logical Foundations’. It will be published by Oxford University Press, 1992. Fragments of the material already appeared in chapter two of Bl¨asis & B¨urckert: Deduction Systems in Artificial Intelligence, Ellis Horwood Series in Artificial Intelligence, 1989. A draft version has been published as SEKI Report SR-90-12. The report is also published as an internal technical report of ECRC, Munich. Acknowledgements The writing of the chapters for the handbook has been a highly coordinated effort of all the people involved. We want to express our gratitude for their many helpful contributions, which unfortunately are impossible to list exhaustively. Special thanks for reading earlier drafts and giving us detailed feedback, go to our second reader, Bob Kowalski, and to Wolfgang Bibel, Elmar Eder, Melvin Fitting, Donald W. Loveland, David Plaisted, and J¨org Siekmann. Work on this chapter started when both of us were members of the Markgraf Karl group at the Universit¨at Kaiserslautern, Germany. With our former colleagues there we had countless fruitful discus- sions, which, again, cannot be credited in detail. During that time this research was supported by the “Sonderforschungsbereich 314, K¨unstliche Intelligenz” of the Deutsche Forschungsgemeinschaft (DFG).
    [Show full text]
  • MATHEMATICS and the DIVINE: a HISTORICAL STUDY Edited by T
    MATHEMATICS AND THE DIVINE: AHISTORICAL STUDY Cover illustration by Erich Lessing MATHEMATICS AND THE DIVINE: AHISTORICAL STUDY Edited by T. KOETSIER Vrije Universiteit, Amsterdam, The Netherlands L. BERGMANS Université de Paris IV – Sorbonne, Paris, France 2005 Amsterdam • Boston • Heidelberg • London • New York • Oxford • Paris • San Diego • San Francisco • Singapore • Sydney • Tokyo ELSEVIER B.V. ELSEVIER Inc. ELSEVIER Ltd ELSEVIER Ltd Sara Burgerhartstraat 25 525 B Street, Suite 1900 The Boulevard, Langford Lane 84 Theobalds Road P.O. Box 211, 1000 AE San Diego, CA 92101-4495 Kidlington, Oxford OX5 1GB London WC1X 8RR Amsterdam The Netherlands USA UK UK © 2005 Elsevier B.V. All rights reserved. This work is protected under copyright by Elsevier B.V., and the following terms and conditions apply to its use: Photocopying Single photocopies of single chapters may be made for personal use as allowed by national copyright laws. Permission of the Publisher and payment of a fee is required for all other photocopying, including multiple or systematic copying, copying for advertising or promotional purposes, resale, and all forms of document delivery. Special rates are available for educational institutions that wish to make photocopies for non-profit educational classroom use. Permissions may be sought directly from Elsevier’s Rights Department in Oxford, UK: phone (+44) 1865 843830, fax (+44) 1865 853333, e-mail: [email protected]. Requests may also be completed on-line via the Elsevier homepage (http://www.elsevier.com/locate/permissions). In the USA, users may clear permissions and make payments through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA; phone: (+1) (978) 7508400, fax: (+1) (978) 7504744, and in the UK through the Copyright Licensing Agency Rapid Clearance Service (CLARCS), 90 Tottenham Court Road, London W1P 0LP, UK; phone: (+44) 20 7631 5555; fax: (+44) 20 7631 5500.
    [Show full text]
  • MGF 1106 Learning Objectives
    Learning Objectives L01 Set Concepts and Subsets (2.1, 2.2) 1. Indicate sets by the description method, roster method, and by using set builder notation. 2. Determine if a set is well defined. 3. Determine if a set is finite or infinite. 4. Determine if sets are equal, equivalent, or neither. 5. Find the cardinal number of a set. 6. Determine if a set is equal to the empty set. 7. Use the proper notation for the empty set. 8. Give an example of a universal set and list all of its subsets and all of its proper subsets. 9. Properly use notation for element, subset, and proper subset. 10. Determine if a number represents a cardinal number or an ordinal number. 11. Be able to determine the number of subsets and proper subsets that can be formed from a universal set without listing them. L02 Venn Diagrams and Set Operations (2.3, 2.4) 1. Determine if sets are disjoint. 2. Find the complement of a set 3. Find the intersection of two sets. 4. Find the union of two sets. 5. Find the difference of two sets. 6. Apply several set operations involved in a statement. 7. Determine sets from a Venn diagram. 8. Use the formula that yields the cardinal number of a union. 9. Construct a Venn diagram given two sets. 10. Construct a Venn diagram given three sets. L03 Equality of Sets; Applications of Sets (2.4, 2.5) 1. Determine if set statements are equal by using Venn diagrams or DeMorgan's laws.
    [Show full text]
  • Framing Cyclic Revolutionary Emergence of Opposing Symbols of Identity Eppur Si Muove: Biomimetic Embedding of N-Tuple Helices in Spherical Polyhedra - /
    Alternative view of segmented documents via Kairos 23 October 2017 | Draft Framing Cyclic Revolutionary Emergence of Opposing Symbols of Identity Eppur si muove: Biomimetic embedding of N-tuple helices in spherical polyhedra - / - Introduction Symbolic stars vs Strategic pillars; Polyhedra vs Helices; Logic vs Comprehension? Dynamic bonding patterns in n-tuple helices engendering n-fold rotating symbols Embedding the triple helix in a spherical octahedron Embedding the quadruple helix in a spherical cube Embedding the quintuple helix in a spherical dodecahedron and a Pentagramma Mirificum Embedding six-fold, eight-fold and ten-fold helices in appropriately encircled polyhedra Embedding twelve-fold, eleven-fold, nine-fold and seven-fold helices in appropriately encircled polyhedra Neglected recognition of logical patterns -- especially of opposition Dynamic relationship between polyhedra engendered by circles -- variously implying forms of unity Symbol rotation as dynamic essential to engaging with value-inversion References Introduction The contrast to the geocentric model of the solar system was framed by the Italian mathematician, physicist and philosopher Galileo Galilei (1564-1642). His much-cited phrase, " And yet it moves" (E pur si muove or Eppur si muove) was allegedly pronounced in 1633 when he was forced to recant his claims that the Earth moves around the immovable Sun rather than the converse -- known as the Galileo affair. Such a shift in perspective might usefully inspire the recognition that the stasis attributed so widely to logos and other much-valued cultural and heraldic symbols obscures the manner in which they imply a fundamental cognitive dynamic. Cultural symbols fundamental to the identity of a group might then be understood as variously moving and transforming in ways which currently elude comprehension.
    [Show full text]
  • Intuitionistic Euler-Venn Diagrams⋆
    Intuitionistic Euler-Venn Diagrams? Sven Linker[0000−0003−2913−7943] University of Liverpool, UK [email protected] Abstract. We present an intuitionistic interpretation of Euler-Venn di- agrams with respect to Heyting algebras. In contrast to classical Euler- Venn diagrams, we treat shaded and missing zones differently, to have diagrammatic representations of conjunction, disjunction and intuition- istic implication. Furthermore, we need to add new syntactic elements to express these concepts. We present a cut-free sequent calculus for this language, and prove it to be sound and complete. Furthermore, we show that the rules of cut, weakening and contraction are admissible. Keywords: intuitionistic logic · Euler-Venn diagrams · proof theory 1 Introduction Most visualisations for logical systems, like Peirce's Existential Graphs [6] and the Venn systems of Shin [16], are dedicated to some form of classical reasoning. However, for example, within Computer Science, constructive reasoning in the form of intuitionistic logic is very important as well, due to the Curry-Howard correspondence of constructive proofs and programs, or, similarly, of formulas and types. That is, each formula corresponds to a unique type, and a proof of the formula corresponds to the execution of a function of this type. Hence, a visu- alisation of intutionistic logic would be beneficial not only from the perspective of formal logic, but also for visualising program types and their relations. Typical semantics of intuitionistic logic are given in the form of Heyting algebras, a slight generalisation of Boolean algebras, and an important subclass of Heyting algebras is induced by topologies: the set of open sets of a topology forms a Heyting algebra.
    [Show full text]
  • 1 Psychological Operationisms at Harvard: Skinner, Boring, And
    [Forthcoming in Journal of the History of the Behavioral Sciences] Psychological operationisms at Harvard: Skinner, Boring, and Stevens Sander Verhaegh Tilburg University Abstract: Contemporary discussions about operational definition often hark back to Stanley Smith Stevens’ classic papers on psychological operationism (1935ab). Still, he was far from the only psychologist to call for conceptual hygiene. Some of Stevens’ direct colleagues at I would like to thank Julie Vargas, anonymous referees for the Journal of the History of the Behavioral Sciences, and the staff at the Harvard University Archives for their help with this project. Drafts of this paper were presented at the 2019 conference of the History of Science Society (Utrecht University) and the 2019 conference of the Canadian Society for the History and Philosophy of Science (University of British Columbia). I would like to thank the audiences at both events for their valuable suggestions. This research is funded by The Netherlands Organisation for Scientific Research (grant 275–20–064). My archival research was funded by a Kristeller-Popkin Travel Fellowship from the Journal of the History of Philosophy, by a Rodney G. Dennis Fellowship in the Study of Manuscripts from Houghton Library, and a travel grant from the Evert Willem Beth Foundation. Correspondence concerning this paper should be addressed to Tilburg University, Department of Philosophy, Warandelaan 2, 5037AB, Tilburg, The Netherlands or to [email protected]. 1 Harvard⎯ most notably B. F. Skinner and E. G. Boring⎯ were also actively applying Bridgman’s conceptual strictures to the study of mind and behavior. In this paper, I shed new light on the history of operationism by reconstructing the Harvard debates about operational definition in the years before Stevens published his seminal articles.
    [Show full text]
  • Introduction Sally Shuttleworth and Geoffrey Cantor
    1 Introduction Sally Shuttleworth and Geoffrey Cantor “Reviews are a substitute for all other kinds of reading—a new and royal road to knowledge,” trumpeted Josiah Conder in 1811.1 Conder, who sub- sequently became proprietor and editor of the Eclectic Review, recognized that periodicals were proliferating, rapidly increasing in popularity, and becoming a major sector in the market for print. Although this process had barely begun at the time Conder was writing, the number of peri- odical publications accelerated considerably over the ensuing decades. According to John North, who is currently cataloguing the wonderfully rich variety of British newspapers and periodicals, some 125,000 titles were published in the nineteenth century.2 Many were short-lived, but others, including the Edinburgh Review (1802–1929) and Punch (1841 on), possess long and honorable histories. Not only did titles proliferate, but, as publishers, editors, and proprietors realized, the often-buoyant market for periodicals could be highly profitable and open to entrepreneurial exploitation. A new title might tap—or create—a previously unexploited niche in the market. Although the expensive quarterly reviews, such as the Edinburgh Review and the Quarterly, have attracted much scholarly attention, their circulation figures were small (they generally sold only a few thousand copies), and their readership was predominantly upper middle class. By contrast, the tupenny weekly Mirror of Literature is claimed to have achieved an unprecedented circulation of 150,000 when it was launched in 1822. A few later titles that were likewise cheap and aimed at a mass readership also achieved circulation figures of this magnitude.
    [Show full text]
  • Introducing 3D Venn and Euler Diagrams
    Introducing 3D Venn and Euler Diagrams Peter Rodgers1, Jean Flower2, and Gem Stapleton3 1 University of Kent, UK [email protected] 2 Autodesk, UK 3 Visual Modelling Group, University of Brighton, UK [email protected] Abstract. In 2D, Venn and Euler diagrams consist of labelled simple closed curves and have been widely studied. The advent of 3D display and interaction mechanisms means that extending these diagrams to 3D is now feasible. However, 3D versions of these diagrams have not yet been examined. Here, we begin the investigation into 3D Euler diagrams by defining them to comprise of labelled, orientable closed surfaces. As in 2D, these 3D Euler diagrams visually represent the set-theoretic notions of intersection, containment and disjointness. We extend the concept of wellformedness to the 3D case and compare it to wellformedness in the 2D case. In particular, we demonstrate that some data can be visualized with wellformed 3D diagrams that cannot be visualized with wellformed 2D diagrams. We also note that whilst there is only one topologically distinct embedding of wellformed Venn-3 in 2D, there are four such em- beddings in 3D when the surfaces are topologically equivalent to spheres. Furthermore, we hypothesize that all data sets can be visualized with 3D Euler diagrams whereas this is not the case for 2D Euler diagrams, unless non-simple curves and/or duplicated labels are permitted. As this paper is the first to consider 3D Venn and Euler diagrams, we include a set of open problems and conjectures to stimulate further research.
    [Show full text]
  • Prime Numbers and Implication Free Reducts of Mvn-Chains.Pdf
    SYSMICS2019 Syntax Meets Semantics Amsterdam, The Netherlands 21-25 January 2019 Institute for Logic, Language and Computation University of Amsterdam SYSMICS 2019 The international conference “Syntax meet Semantics 2019” (SYSMICS 2019) will take place from 21 to 25 January 2019 at the University of Amsterdam, The Nether- lands. This is the closing conference of the European Marie Sk lodowska-Curie Rise project Syntax meets Semantics – Methods, Interactions, and Connections in Sub- structural logics, which unites more than twenty universities from Europe, USA, Brazil, Argentina, South Africa, Australia, Japan, and Singapore. Substructural logics are formal reasoning systems that refine classical logic by weakening structural rules in a Gentzen-style sequent calculus. Traditionally, non- classical logics have been investigated using proof-theoretic and algebraic methods. In recent years, combined approaches have started to emerge, thus establishing new links with various branches of non-classical logic. The program of the SYSMICS conference focuses on interactions between syntactic and semantic methods in substructural and other non-classical logics. The scope of the conference includes but is not limited to algebraic, proof-theoretic and relational approaches towards the study of non-classical logics. This booklet consists of the abstracts of SYSMICS 2019 invited lectures and contributed talks. In addition, it also features the abstract of the SYSMICS 2019 Public Lecture, on the interaction of logic and artificial intelligence. We thank all authors, members of the Programme and Organising Committees and reviewers of SYSMICS 2019 for their contribution. Apart from the generous financial support by the SYSMICS project, we would like to acknowledge the sponsorship by the Evert Willem Beth Foundation and the Association for Symbolic Logic.
    [Show full text]
  • Mutation COS 326 Speaker: Andrew Appel Princeton University
    Mutation COS 326 Speaker: Andrew Appel Princeton University slides copyright 2020 David Walker and Andrew Appel permission granted to reuse these slides for non-commercial educational purposes C structures are mutable, ML structures are immutable C program OCaml program let fst(x:int,y:int) = x struct foo {int x; int y} *p; let p: int*int = ... in int a,b,u; let a = fst p in a = p->x; let u = f p in u = f(p); let b = fst p in b = p->x; xxx (* does a==b? Yes! *) /* does a==b? maybe */ 2 Reasoning about Mutable State is Hard mutable set immutable set insert i s1; let s1 = insert i s0 in f x; f x; member i s1 member i s1 Is member i s1 == true? … – When s1 is mutable, one must look at f to determine if it modifies s1. – Worse, one must often solve the aliasing problem. – Worse, in a concurrent setting, one must look at every other function that any other thread may be executing to see if it modifies s1. 3 Thus far… We have considered the (almost) purely functional subset of OCaml. – We’ve had a few side effects: printing & raising exceptions. Two reasons for this emphasis: – Reasoning about functional code is easier. • Both formal reasoning – equationally, using the substitution model – and informal reasoning • Data structures are persistent. – They don’t change – we build new ones and let the garbage collector reclaim the unused old ones. • Hence, any invariant you prove true stays true. – e.g., 3 is a member of set S.
    [Show full text]
  • Anton Pannekoek: Ways of Viewing Science and Society
    STUDIES IN THE HISTORY OF KNOWLEDGE Tai, Van der Steen & Van Dongen (eds) Dongen & Van Steen der Van Tai, Edited by Chaokang Tai, Bart van der Steen, and Jeroen van Dongen Anton Pannekoek: Ways of Viewing Science and Society Ways of Viewing ScienceWays and Society Anton Pannekoek: Anton Pannekoek: Ways of Viewing Science and Society Studies in the History of Knowledge This book series publishes leading volumes that study the history of knowledge in its cultural context. It aspires to offer accounts that cut across disciplinary and geographical boundaries, while being sensitive to how institutional circumstances and different scales of time shape the making of knowledge. Series Editors Klaas van Berkel, University of Groningen Jeroen van Dongen, University of Amsterdam Anton Pannekoek: Ways of Viewing Science and Society Edited by Chaokang Tai, Bart van der Steen, and Jeroen van Dongen Amsterdam University Press Cover illustration: (Background) Fisheye lens photo of the Zeiss Planetarium Projector of Artis Amsterdam Royal Zoo in action. (Foreground) Fisheye lens photo of a portrait of Anton Pannekoek displayed in the common room of the Anton Pannekoek Institute for Astronomy. Source: Jeronimo Voss Cover design: Coördesign, Leiden Lay-out: Crius Group, Hulshout isbn 978 94 6298 434 9 e-isbn 978 90 4853 500 2 (pdf) doi 10.5117/9789462984349 nur 686 Creative Commons License CC BY NC ND (http://creativecommons.org/licenses/by-nc-nd/3.0) The authors / Amsterdam University Press B.V., Amsterdam 2019 Some rights reserved. Without limiting the rights under copyright reserved above, any part of this book may be reproduced, stored in or introduced into a retrieval system, or transmitted, in any form or by any means (electronic, mechanical, photocopying, recording or otherwise).
    [Show full text]
  • Alternative Claims to the Discovery of Modern Logic: Coincidences and Diversification
    Fran¸cois,K., L¨owe, B., Muller,¨ T., Van Kerkhove, B., editors, Foundations of the Formal Sciences VII Bringing together Philosophy and Sociology of Science Alternative claims to the discovery of modern logic: Coincidences and diversification Paul Ziche∗ Departement Wijsbegeerte, Universiteit Utrecht, Janskerkhof 13a, 3512 BL Utrecht, The Netherlands E-mail: [email protected] 1 Multiple and alternative discoveries No discipline could lay stronger claim to clarity and unequivocality than logic. Curiously, though, the historical genesis of modern logic presents a picture riven with rival claims over the discipline’s founding contributions. As will be shown, protagonists from highly different backgrounds assert that the genesis of modern logic—indeed, its very discovery—rests on their contribution. Not only are these claims, to some extent, mutually exclusive, they also cut across standards of scientificity and rationality. By standard narratives of the history of modern logic, some claimants to paternity seem downright obscure and anti-rational. Yet, all these claims are made within a narrow time-frame, and they all refer back to the same developments in mathematics. This makes it impossible to easily dismiss the rival claims. This paper argues that the co-existence of alternative claims concerning the discovery of modern logic, in fact, places the historian in an advanta- geous situation. It might appear as if the alternative claims make the the genesis of modern logic into a story of a multiple discovery, the coincidence of simultaneous discoveries of the same phenomenon. This is, however, not what the historical picture shows. The competing claims, very explicitly placed by the protagonists themselves, rather have to be viewed as stages within an open-ended process that would contribute not to an integrated picture of logic, but generate diversified conceptions of rationality.
    [Show full text]