One Hundred Years of Russell´s Paradox: Mathematics, Logic, Philosophy

Published by De Gruyter 2004

One Hundred Years of Russell´s Paradox

Mathematics, Logic, Philosophy

Edited by: Godehard Link
With contributions by: 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 and W. Hugh Woodin

Volume 6 in the series De Gruyter Series in Logic and Its Applications

https://doi.org/10.1515/9783110199680

Overview
Contents

About this book

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 therefore, to the well-established body of mathematical philosophy initiated to a large extent by Russell's work.

Author / Editor information

Godehard Link is Professor for Logic and Philosophy of Science at the University of Munich (Ludwig-Maximilians-Universität München), Responsible Lecturer on Logic at the reform curriculum MPhil and affiliate member of the Centre for Information and Language Processing (Centrum für Informations- und Sprachverarbeitung (CIS)).

Reviews

"This is an important collection. The new research presented in this one book is roughly equivalent to a year's worth of articles in an important journal. The overall quality is impressive."
Kevin C. Klement in: The Review of Modern Logic 1-2/2007/2008

"This is a well-done celebration of an important incident in the history of mathematics."
P.Schmitt in: Monatshefte für Mathematik 1/2006

Topics

Frontmatter Requires Authentication Unlicensed Licensed Download PDF	i
Table of Contents Requires Authentication Unlicensed Licensed Download PDF	vii
Introduction. Bertrand Russell—The Invention of Mathematical Philosophy Godehard Link Requires Authentication Unlicensed Licensed Download PDF	1
Set Theory after Russell: The Journey Back to Eden W. Hugh Woodin Requires Authentication Unlicensed Licensed Download PDF	29
A Way Out Harvey M. Friedman Requires Authentication Unlicensed Licensed Download PDF	49
Completeness and Iteration in Modern Set Theory Sy D. Friedman Requires Authentication Unlicensed Licensed Download PDF	85
Was sind und was sollen (neue) Axiome? Kai Hauser Requires Authentication Unlicensed Licensed Download PDF	93
Iterating Σ Operations in Admissible Set Theory without Foundation: A Further Aspect of Metapredicative Mahlo Gerhard Jäger and Dieter Probst Requires Authentication Unlicensed Licensed Download PDF	119
Typical Ambiguity: Trying to Have Your Cake and Eat It Too Solomon Feferman Requires Authentication Unlicensed Licensed Download PDF	135
Is ZF Finitistically Reducible? Karl-Georg Niebergall Requires Authentication Unlicensed Licensed Download PDF	153
Inconsistency in the Real World Tobias Hürter Requires Authentication Unlicensed Licensed Download PDF	181
Predicativity, Circularity, and Anti-Foundation Michael Rathjen Requires Authentication Unlicensed Licensed Download PDF	191
Russell’s Paradox and Diagonalization in a Constructive Context John L. Bell Requires Authentication Unlicensed Licensed Download PDF	221
Constructive Solutions of Continuous Equations Peter Schuster and Helmut Schwichtenberg Requires Authentication Unlicensed Licensed Download PDF	227
Russell’s Paradox in Consistent Fragments of Frege’s Grundgesetze der Arithmetik Kai F. Wehmeier Requires Authentication Unlicensed Licensed Download PDF	247
On a Russellian Paradox about Propositions and Truth Andrea Cantini Requires Authentication Unlicensed Licensed Download PDF	259
The Consistency of the Naive Theory of Properties Hartry Field Requires Authentication Unlicensed Licensed Download PDF	285
The Significance of the Largest and Smallest Numbers for the Oldest Paradoxes Ulrich Blau Requires Authentication Unlicensed Licensed Download PDF	311
The Prehistory of Russell’s Paradox Nicholas Griffin Requires Authentication Unlicensed Licensed Download PDF	349
Logicism’s ‘Insolubilia’ and Their Solution by Russell’s Substitutional Theory Gregory Landini Requires Authentication Unlicensed Licensed Download PDF	373
Substitution and Types: Russell’s Intermediate Theory Philippe Rouilhan Requires Authentication Unlicensed Licensed Download PDF	401
Propositional Ontology and Logical Atomism Francisco Rodríguez-Consuegra Requires Authentication Unlicensed Licensed Download PDF	417
Classes of Classes and Classes of Functions in Principia Mathematica Bernard Linsky Requires Authentication Unlicensed Licensed Download PDF	435
A “Constructive” Proper Extension of Ramified Type Theory (The Logic of Principia Mathematica, Second Edition, Appendix B) Allen P. Hazen Requires Authentication Unlicensed Licensed Download PDF	449
Russell on Method Andrew D. Irvine Requires Authentication Unlicensed Licensed Download PDF	481
Paradoxes in Göttingen Volker Peckhaus Requires Authentication Unlicensed Licensed Download PDF	501
David Hilbert and Paul du Bois-Reymond: Limits and Ideals David Charles McCarty Requires Authentication Unlicensed Licensed Download PDF	517
Russell’s Paradox and Hilbert’s (much Forgotten) View of Set Theory Jan Mycielski Requires Authentication Unlicensed Licensed Download PDF	533
Objectivity: The Justification for Extrapolation Shaughan Lavine Requires Authentication Unlicensed Licensed Download PDF	549
Russell’s Absolutism vs. (?) Structuralism Geoffrey Hellman Requires Authentication Unlicensed Licensed Download PDF	561
Mathematicians and Mathematical Objects Robert S. D. Thomas Requires Authentication Unlicensed Licensed Download PDF	577
Russell’s Paradox and Our Conception of Properties, or: Why Semantics Is no Proper Guide to the Nature of Properties Holger Sturm Requires Authentication Unlicensed Licensed Download PDF	591
The Many Lives of Ebenezer Wilkes Smith Vann McGee Requires Authentication Unlicensed Licensed Download PDF	611
What Makes Expressions Meaningful? A Reflection on Contexts and Actions Albert Visser Requires Authentication Unlicensed Licensed Download PDF	625
Backmatter Requires Authentication Unlicensed Licensed Download PDF	645

(Deutsch)

Language: English
Publisher: De Gruyter
Audience: Researchers in the Fields of Set Theory, Mathematical Logic, Russell Studies, Philosophy of Mathematics; Academic Libraries
Pages
- Front matter: 9
- Main content: 662
Keywords: Mathematische Logik; Analytische Philosophie; Sprachphilosophie

eBook

Published: August 22, 2008
ISBN: 9783110199680

Hardcover

Published: July 26, 2004
ISBN: 9783110174380