One Hundred Years of Russell´s Paradox (eBook)

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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)).

Godehard Link ist Professor für Logik und Wissenschaftstheorie an der Ludwig-Maximilians-Universität München, verantwortlicher Dozent für den Bereich Logik im Reformstudiengang MPhil und affiliiertes Mitglied des Centrums für Informations- und Sprachverarbeitung (CIS).

Frontmatter 1
Table of Contents 7
Introduction. Bertrand Russell—The Invention of Mathematical Philosophy 11
Set Theory after Russell: The Journey Back to Eden 39
A Way Out 59
Completeness and Iteration in Modern Set Theory 95
Was sind und was sollen (neue) Axiome? 103
Iterating S Operations in Admissible Set Theory without Foundation: A Further Aspect of Metapredicative Mahlo 129
Typical Ambiguity: Trying to Have Your Cake and Eat It Too 145
Is ZF Finitistically Reducible? 163
Inconsistency in the Real World 191
Predicativity, Circularity, and Anti-Foundation 201
Russell’s Paradox and Diagonalization in a Constructive Context 231
Constructive Solutions of Continuous Equations 237
Russell’s Paradox in Consistent Fragments of Frege’s Grundgesetze der Arithmetik 257
On a Russellian Paradox about Propositions and Truth 269
The Consistency of the Naive Theory of Properties 295
The Significance of the Largest and Smallest Numbers for the Oldest Paradoxes 321
The Prehistory of Russell’s Paradox 359
Logicism’s ‘Insolubilia’ and Their Solution by Russell’s Substitutional Theory 383
Substitution and Types: Russell’s Intermediate Theory 411
Propositional Ontology and Logical Atomism 427
Classes of Classes and Classes of Functions in Principia Mathematica 445
A “Constructive” Proper Extension of Ramified Type Theory (The Logic of Principia Mathematica, Second Edition, Appendix B) 459
Russell on Method 491
Paradoxes in Göttingen 511
David Hilbert and Paul du Bois-Reymond: Limits and Ideals 527
Russell’s Paradox and Hilbert’s (much Forgotten) View of Set Theory 543
Objectivity: The Justification for Extrapolation 559
Russell’s Absolutism vs. (?) Structuralism 571
Mathematicians and Mathematical Objects 587
Russell’s Paradox and Our Conception of Properties, or: Why Semantics Is no Proper Guide to the Nature of Properties 601
The Many Lives of Ebenezer Wilkes Smith 621
What Makes Expressions Meaningful? A Reflection on Contexts and Actions 635
Backmatter 655

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"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