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

Godehard Link9783110174380, 3-11-017438-3

These 31 papers come from the June 2001 international conference held to commemorate the centenary of the discover of the famous “Russell’s Paradox,” and include contributions from Russell scholars, mathematical logicians, set theorists, and scholars in the philosophy of mathematics. Papers include an introduction by Godehard Link that credits Russell with the invention of the new mathematical philosophy, W. Hugh Woodin on set theory after Russell, Harvey Friedman on a way out of Russell’s paradox, Sy Friedman on completeness and iteration in modern set theory, and John S. Bell on “Russell’s Paradox and Diagonalization in a Constructive Context. Other papers include examinations of aspects of the Principia Mathematica, Russell on method, and critiques of works related to Russell’s fields of study.

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Table of contents :
Preface……Page 5
Table of Contents……Page 7
Introduction. Bertrand Russell—The Invention of Mathematical Philosophy……Page 11
Set Theory after Russell: The Journey Back to Eden……Page 39
AWay Out……Page 59
Completeness and Iteration in Modern Set Theory……Page 95
Operations in Admissible Set Theory without Foundation: A Further Aspect of Metapredicative Mahlo……Page 129
Typical Ambiguity: Trying to Have Your Cake and Eat It Too……Page 145
Is ZF Finitistically Reducible?……Page 163
Inconsistency in the RealWorld……Page 191
Predicativity, Circularity, and Anti-Foundation……Page 201
Russell’s Paradox and Diagonalization in a Constructive Context……Page 231
Constructive Solutions of Continuous Equations……Page 237
Russell’s Paradox in Consistent Fragments of Frege’s Grundgesetze der Arithmetik……Page 257
On a Russellian Paradox about Propositions and Truth……Page 269
The Consistency of the Naive Theory of Properties……Page 295
The Significance of the Largest and Smallest Numbers for the Oldest Paradoxes……Page 321
The Prehistory of Russell’s Paradox……Page 359
Logicism’s ‘Insolubilia’ and Their Solution by Russell’s Substitutional Theory……Page 383
Substitution and Types: Russell’s Intermediate Theory……Page 411
Propositional Ontology and Logical Atomism……Page 427
Classes of Classes and Classes of Functions in……Page 445
A “Constructive” Proper Extension of Ramified Type Theory (The Logic of Principia Mathematica, Second Edition, Appendix B)……Page 459
Russell on Method……Page 491
Paradoxes in Göttingen……Page 511
David Hilbert and Paul du Bois-Reymond: Limits and Ideals……Page 527
Russell’s Paradox and Hilbert’s (much Forgotten) View of Set Theory……Page 543
Objectivity: The Justification for Extrapolation……Page 559
Russell’s Absolutism vs. (?) Structuralism……Page 571
Mathematicians and Mathematical Objects……Page 587
Russell’s Paradox and Our Conception of Properties, or: Why Semantics Is no Proper Guide to the Nature of Properties……Page 601
The Many Lives of EbenezerWilkes Smith……Page 621
What Makes Expressions Meaningful? A Reflection on Contexts and Actions……Page 635
List of Contributors……Page 655