One Hundred Years of Russell's Paradox: Mathematics, Logic, Philosophy (De Gruyter Series in Logic and Its Applications #6)

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Overview

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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Editorial Reviews

From the Publisher
"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
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Product Details

Meet the Author

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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Table of Contents

Introduction : Bertrand Russell - the invention of mathematical philosophy 1
Set theory after Russell : the journey back to Eden 29
A way out 49
Completeness and iteration in modern set theory 85
Was sind und was sollen (neue) Axiome? 93
Iterating [Sigma] operations in admissible set theory without foundation : a further aspect of metapredicative Mahlo 119
Typical ambiguity : trying to have your cake and eat it too 135
Is ZF finitistically reducible? 153
Inconsistency in the real world 181
Predicativity, circularity, and anti-foundation 191
Russell's paradox and diagonalization in a constructive context 221
Constructive solutions of continuous equations 227
Russell's paradox in consistent fragments of Frege's 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 Russell's paradox 349
Logicism's 'insolubilia' and their solution by Russell's substitutional theory 373
Substitution and types : Russell's intermediate theory 401
Propositional ontology and logical atomism 417
Classes of classes and classes of functions in Principia Mathematica 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 Gottingen 501
David Hilbert and Paul du Bois-Reymond : limits and ideals 517
Russell's paradox and Hilbert's (much forgotten) view of set theory 533
Objectivity : the justification for extrapolation 549
Russell's absolutism vs. (?) structuralism 561
Mathematicians and mathematical objects 577
Russell's paradox and our conception of properties, or : why semantics is no proper guide to the nature of properties 591
The many lives of Ebenezer Wilkes Smith 611
What makes expressions meaningful? : a reflection on contexts and actions 625
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