One Hundred Years of Russell´s Paradox ：Mathematics, Logic, Philosophy ( De Gruyter Series in Logic and Its Applications )

Publication subTitle ：Mathematics, Logic, Philosophy

Publication series ：De Gruyter Series in Logic and Its Applications

Author： John L. Bell   Ulrich Blau   Andrea Cantini   Solomon Feferman   Hartry Field   Harvey M. Friedman   Sy-David Friedman   Nicholas Griffin   Kai Hauser   Allen P. Hazen   Geoffrey Hellman   Tobias Hürter   Andrew D. Irvine   Gerhard Jäger   Gregory Landini   Shaughan Lavine   Bernard Linsky   David Charles McCarty   Vann McGee   Jan Mycielsky   Karl-Georg Niebergall   Volker Peckhaus   Dieter Probst   Michael Rathjen   Francisco Rodriguez-Consuegra   Philippe de Rouilhan   Peter Schuster   Helmut Schwichtenberg   Holger Sturm   Robert S. D. Thomas   Albert Visser   Kai F. Wehmeier   W. Hugh Woodin   Godehard Link  

Publisher： De Gruyter‎

Publication year： 2004

E-ISBN: 9783110199680

P-ISBN(Paperback): 9783110174380

Subject： B812.5 and sophism, fallacy

Language： ENG

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Description

The papers collected in this volume represent the main body of research arising from the International Munich Centenary Conference in 2001, which commemorated the discovery of the famous Russell Paradox a hundred years ago. The 31 contributions and the introductory essay by the editor were (with two exceptions) all originally written for the volume.

The volume serves a twofold purpose, historical and systematic. One focus is on Bertrand Russell's logic and logical philosophy, taking into account the rich sources of the Russell Archives, many of which have become available only recently. The second equally important aim is to present original research in the broad range of foundational studies that draws on both current conceptions and recent technical advances in the above-mentioned fields. The volume contributes thereby to the well-established body of mathematical philosophy initiated to a large extent by Russell's work.

Chapter

Preface

pp.：  1 – 5

Introduction. Bertrand Russell – The Invention of Mathematical Philosophy

pp.：  5 – 11

Set Theory after Russell: The Journey Back to Eden

pp.：  11 – 39

A Way Out

pp.：  39 – 59

Completeness and Iteration in Modern Set Theory

pp.：  59 – 95

Was sind und was sollen (neue) Axiome?

pp.：  95 – 103

Iterating Σ Operations in Admissible Set Theory without Foundation: A Further Aspect of Metapredicative Mahlo

pp.：  103 – 129

Typical Ambiguity: Trying to Have Your Cake and Eat It Too

pp.：  129 – 145

Is ZF Finitistically Reducible?

pp.：  145 – 163

Inconsistency in the Real World

pp.：  163 – 191

Predicativity, Circularity, and Anti-Foundation

pp.：  191 – 201

Russell’s Paradox and Diagonalization in a Constructive Context

pp.：  201 – 231

Constructive Solutions of Continuous Equations

pp.：  231 – 237

Russell'’s Paradox in Consistent Fragments of Frege’s Grundgesetze der Arithmetik

pp.：  237 – 257

On a Russellian Paradox about Propositions and Truth

pp.：  257 – 269

The Consistency of the Naive Theory of Properties

pp.：  269 – 295

The Significance of the Largest and Smallest Numbers for the Oldest Paradoxes

pp.：  295 – 321

The Prehistory of Russell’s Paradox

pp.：  321 – 359

Logicism’s ‘Insolubilia’ and Their Solution by Russell’s Substitutional Theory

pp.：  359 – 383

Substitution and Types: Russell’s Intermediate Theory

pp.：  383 – 411

Propositional Ontology and Logical Atomism

pp.：  411 – 427

Classes of Classes and Classes of Functions in Principia Mathematica

pp.：  427 – 445

A “Constructive” Proper Extension of Ramified Type Theory (The Logic of Principia Mathematica, Second Edition, Appendix B)

pp.：  445 – 459

Russell on Method

pp.：  459 – 491

Paradoxes in Göttingen

pp.：  491 – 511

David Hilbert and Paul du Bois-Reymond: Limits and Ideals

pp.：  511 – 527

Russell’s Paradox and Hilbert’s (much Forgotten) View of Set Theory

pp.：  527 – 543

Objectivity: The Justification for Extrapolation

pp.：  543 – 559

Russell’s Absolutism vs. (?) Structuralism

pp.：  559 – 571

Mathematicians and Mathematical Objects

pp.：  571 – 587

Russell’s Paradox and Our Conception of Properties, or: Why Semantics Is no Proper Guide to the Nature of Properties

pp.：  587 – 601

The Many Lives of Ebenezer Wilkes Smith

pp.：  601 – 621

What Makes Expressions Meaningful? A Reflection on Contexts and Actions

pp.：  621 – 635

List of Contributors

pp.：  635 – 655

Name Index

pp.：  655 – 659

Subject Index

pp.：  659 – 663

LastPages

pp.：  663 – 673

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