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

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Godehard Link
Walter de Gruyter, 2004 - Mathematics - 662 pages
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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.

 

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Contents

Introduction Bertrand RussellThe Invention of Mathematical Philosophy
1
The Journey Back to Eden
29
AWay Out
49
Completeness and Iteration in Modern Set Theory
85
Iterating
119
Trying to Have Your Cake and Eat It Too
135
Is ZF Finitistically Reducible?
153
Inconsistency in the RealWorld
181
Russells Intermediate Theory
401
Propositional Ontology and Logical Atomism
417
Classes of Classes and Classes of Functions in
435
A Constructive Proper Extension of Ramified Type Theory The Logic of Principia Mathematica Second Edition Appendix B
449
Russell on Method
481
Paradoxes in Göttingen
501
Limits and Ideals
517
Russells Paradox and Hilberts much Forgotten View of Set Theory
533

Predicativity Circularity and AntiFoundation
191
Russells Paradox and Diagonalization in a Constructive Context
221
Constructive Solutions of Continuous Equations
227
Russells Paradox in Consistent Fragments of Freges Grundgesetze der Arithmetik
247
On a Russellian Paradox about Propositions and Truth
259
The Consistency of the Naive Theory of Properties
285
The Significance of the Largest and Smallest Numbers for the Oldest Paradoxes
311
The Prehistory of Russells Paradox
349
Logicisms Insolubilia and Their Solution by Russells Substitutional Theory
373
The Justification for Extrapolation
549
Russells Absolutism vs ? Structuralism
561
Mathematicians and Mathematical Objects
577
Why Semantics Is no Proper Guide to the Nature of Properties
591
The Many Lives of EbenezerWilkes Smith
611
What Makes Expressions Meaningful? A Reflection on Contexts and Actions
625
List of Contributors
645
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About the author (2004)

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)).

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