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(s): Godehard Link
Series: De Gruyter Series in Logic and Its Applications
Publisher: Walter de Gruyter
Year: 2004
Language: English
Pages: 673
Front cover......Page 1
Table of Contents......Page 8
Introduction. Bertrand Russell—The Invention of Mathematical Philosophy......Page 12
Set Theory after Russell: The Journey Back to Eden......Page 40
AWay Out......Page 60
Completeness and Iteration in Modern Set Theory......Page 96
Operations in Admissible Set Theory without Foundation: A Further Aspect of Metapredicative Mahlo......Page 130
Typical Ambiguity: Trying to Have Your Cake and Eat It Too......Page 146
Is ZF Finitistically Reducible?......Page 164
Inconsistency in the RealWorld......Page 192
Predicativity, Circularity, and Anti-Foundation......Page 202
Russell’s Paradox and Diagonalization in a Constructive Context......Page 232
Constructive Solutions of Continuous Equations......Page 238
Russell’s Paradox in Consistent Fragments of Frege’s Grundgesetze der Arithmetik......Page 258
On a Russellian Paradox about Propositions and Truth......Page 270
The Consistency of the Naive Theory of Properties......Page 296
The Significance of the Largest and Smallest Numbers for the Oldest Paradoxes......Page 322
The Prehistory of Russell’s Paradox......Page 360
Logicism’s ‘Insolubilia’ and Their Solution by Russell’s Substitutional Theory......Page 384
Substitution and Types: Russell’s Intermediate Theory......Page 412
Propositional Ontology and Logical Atomism......Page 428
Classes of Classes and Classes of Functions in......Page 446
A “Constructive” Proper Extension of Ramified Type Theory (The Logic of Principia Mathematica, Second Edition, Appendix B)......Page 460
Russell on Method......Page 492
Preface......Page 6
Paradoxes in Göttingen......Page 512
David Hilbert and Paul du Bois-Reymond: Limits and Ideals......Page 528
Russell’s Paradox and Hilbert’s (much Forgotten) View of Set Theory......Page 544
Objectivity: The Justification for Extrapolation......Page 560
Russell’s Absolutism vs. (?) Structuralism......Page 572
Mathematicians and Mathematical Objects......Page 588
Russell’s Paradox and Our Conception of Properties, or: Why Semantics Is no Proper Guide to the Nature of Properties......Page 602
The Many Lives of EbenezerWilkes Smith......Page 622
What Makes Expressions Meaningful? A Reflection on Contexts and Actions......Page 636
List of Contributors......Page 656
